286. Grading for Growth

Traditional grading systems provide incentives for students to focus on maximizing their grades, rather than their learning. In this episode, David Clark and Robert Talbert join us to discuss alternative grading systems that encourage students to recognize that learning from mistakes is a normal part of the learning process.

Robert is a Professor of Mathematics at Grand Valley State University and the author of Flipped Learning: A Guide for Higher Education Faculty. David is an Associate Professor of Mathematics, also at Grand Valley State University. Robert and David are co-authors of Grading for Growth: A Guide to Alternative Grading Practices that Promote Authentic Learning and Student Engagement in Higher Education, which will be published this summer by Stylus Publishing.

Show Notes

  • Talbert, R. (2017). Flipped learning: A guide for higher education faculty. Stylus Publishing, LLC.
  • Talbert, Robert and David Clark (2023, forthcoming). Grading for Growth: A Guide to Alternative Grading Practices that Promote Authentic Learning and Student Engagement in Higher Education, Stylus Publishing.
  • Nilson, L. B. (2015). Specifications grading: Restoring rigor, motivating students, and saving faculty time. Stylus Publishing, LLC.
  • Grading for Growth blog
  • Robert Talbert’s other blog

Transcript

John: Traditional grading systems provide incentives for students to focus on maximizing their grades, rather than their learning. In this episode, we discuss alternative grading systems that encourage students to recognize that learning from mistakes is a normal part of the learning process.

[MUSIC]

John: Thanks for joining us for Tea for Teaching, an informal discussion of innovative and effective practices in teaching and learning.

Rebecca: This podcast series is hosted by John Kane, an economist…

John: …and Rebecca Mushtare, a graphic designer…

Rebecca: …and features guests doing important research and advocacy work to make higher education more inclusive and supportive of all learners.

[MUSIC]

Rebecca: Our guests today are Robert Talbert and David Clark. Robert is a Professor of Mathematics at Grand Valley State University and the author of Flipped Learning: A Guide for Higher Education Faculty. David is an Associate Professor of Mathematics, also at Grand Valley State University. Robert and David are co-authors of Grading for Growth: A Guide to Alternative Grading Practices that Promote Authentic Learning and Student Engagement in Higher Education, which will be published later this year by Stylus Publishing. Welcome, Robert. And David.

David: Good to be here.

Robert: Thanks for having us.

John: Today’s teas are:… are either of you drinking tea?

David: I am.

Robert: I am drinking tea. I’m more of a coffee guy normally, but I figured for the occasion I would bust the tea out.

John: What type of tea are you drinking?

David: I have, because its afternoon, a really lovely almost white jasmine right here.

Rebecca: Nice.

David: …really delicate and anybody who cares about tea is going to be horrified that I sweetened it with honey,

Rebecca: But it is in a really nice polka dotted mug. It is a lovely mug. Thanks.

Robert: And I have cheap stuff from the grocery store, because that’s my brand. This is a Bengal Spice by Celestial Seasoning, and my wife and I are addicted to this tea. We drink probably four or five cups a day of it, though to be honest when it’s cold out, but it usually is [LAUGHTER] here in Michigan.

Rebecca: And I have Jasmine dragon pearls today.

David: Oh, nice choice. Both Jasmine.

John: And I have spring cherry green tea. It’s a very cold wintry day here as we approach spring in upstate New York. We’re recording this a bit before it’ll be released, so by the time you hear this, we should be having the beginning of spring both here and Michigan, I’m hoping.

David: We hope, yeah..

Rebecca: Your tea choice is definitely a big wish for spring. [LAUGHTER] So we’ve invited you here today to discuss Grading for Growth. Can you talk a little bit about how this book came to be?

David: I don’t remember, Robert, if we were in person, or on a Zoom call or something, but I remember you saying at some point, I got a phrase for you: academic book about alternative grading. And I said, “You know, I need a project for my sabbatical.” And then I think it just happened from there [LAUGHTER], and so…

Robert: Yeah, we were in person, David. David and I, we’re not on the same hallway, we’re kind of on opposite arms of a T-shaped hallway. And so we run into each other, sometimes literally, at the intersection of these two hallways, and that happened one day. It was pre-pandemic, I guess. And it was just like, “Hey, Dave, I have this idea, Somebody should write a book about alternative grading. Because David and I have been using various forms of alternative grading in our classes for a while. And he was like, “Yeah,” and that was it. [LAUGHTER] But I think we were also tapping into some stuff that we have been hearing and around our Math Department and elsewhere, our colleagues outside of Grand Valley that started growing even three years ago, just a growing interest or dissatisfaction with the way grading is working. And we’ve been trying some stuff and thought, don’t you know, the best way to make change is to just get your ideas out there. And so this seems like the right place, right time for us.

John: So what types of alternative grading systems do you discuss in this book?

David: A pretty wide variety. And actually, something I’ll say, I think, both Robert and I tend to try to avoid labels too much for these, like there’s useful names to describe different approaches. But we do things like standards-based grading, specifications grading, ungrading, standards-based assessment. standards-based testing, but we look at a really wide variety of alternative grading approaches. And we’ve actually tried to come up with a framework that sort of describes what their common elements are, so that we don’t have to worry as much about names as what the useful features of them are. We found that people can really get locked into an idea of what, for example, upgrading means, and it’s not always a super useful thing to argue about with them.

Robert: Yeah, I would echo that too. Being mathematicians, Dave and I are both really into abstraction and so we look at these specific things that we see, but we’re more interested in the big, general overarching unification principles like what are all these models that are all good, and all applicable, in different places, to different levels of success, and what do they all have in common? And we do discuss ungrading, we do discuss specifications grading, standards-based grading, and a whole lot of approaches that are kind of in the in-between interstitial space, mostly through other people’s stories. I think the heart of this book and David’s real amazing contribution, what you really spend your sabbatical doing, Dave, was interviewing dozens and dozens and dozens of actual real life frontline professors, nobody is in one camp exclusively, everybody’s using some kind of combination, some kind of mix of all these different ideas. And so I think, to me, what the real contribution that our book makes is showing how different things can look, you can start from these basic building blocks, but real people with all kinds of different classes and life situations and professional situations are making this work by listening to their students and adapting appropriately.

David: I can’t emphasize enough how much variety there is in the people we’ve interviewed and the disciplines that they’re in, the types of classes they’re teaching, like it was an amazing thing to talk with all these people and see, okay, they’re able to use different types of alternative grading but absolutely across the board: in labs, in huge classes and tiny classes, and upper-level classes, and absolute freshman-level intro classes. And so it’s been just fantastic to hear how everyone’s doing this and try to put it together into something that could work for anyone, that everyone will find something useful.

Robert: Yeah, no two of them are alike either. And what’s even more amazing to me is that we had to cut a lot of those case studies. And we almost have enough material for a second book just for the case studies. We’re going to keep it on the blog, I think, unless Stylus wants us to do it. But, I mean, there was a lot out there that we don’t talk about in the book. So there’s more where that stuff comes from.

Rebecca: You mentioned that these alternative methods have some common themes or common threads. And maybe it would be helpful to talk about those common threads in relationship to the problems with traditional grading that lead people to these other alternative methods. Can you talk a little bit about that?

Robert: Well, I think one of the places that you begin to see some of the shortcomings of traditional grading is just looking at the history of where traditional grading came from. And it’s sort of a weird and checkered, and very short, history. Many of your listeners might be surprised to know that the current system of points based A-B-C-D-E-F, 4.0 GPA type of grading system is only about 100 years old. It’s a relatively recent innovation in higher education. Higher education, formally, is about 1000 years old. 1088 was the first university and the first readily identifiable grading system that we know of now is like 1890s. So it showed up very, very late to the party. And immediately it was co-opted by Industrial Revolution era approaches to teaching and learning which treated students more or less as subjects. The word “grading” really comes from agriculture, when it comes to like grading Grade A beef and grading grain and flour and that kind of thing. And pretty soon it became entrenched. And we have a situation now where when you look at where grading has led us, it’s highly questionable whether grades really do what we want them to do. And it seems almost certain that they do some things that we don’t want them to do. They lead to issues with ranking and sorting students, pitting students against each other. It’s not clear to me that the statistical validity of points-based grading is even well established. I mean, we put points on things, but they’re not really numerical data in any sense. Computing an average of points across a system of exams does not necessarily tell you how much a student knows. And that, to me, in my view, is the fundamental issue that I have with traditional grading, why I moved away from it. I just didn’t feel like the data was telling me anything.

David: I’d like to jump in on that one, in particular. A thought experiment that I think is really helpful for anybody to do is, let’s say you give a big exam, and a student takes it and they get 60%. So, most systems, that’s basically failing. What does that 60% tell you? What did they know? What don’t they know? Why did they do that poorly? Did they actually do poorly? Do they know 60% of the things that you’ve covered on that exam really well, and the other 40% not at all? Do they have a mediocre level of understanding of everything? Maybe they understand absolutely everything great, and they had a terrible day, and they had to get the kids to Grandma’s house or their work had to keep them late. Maybe they’re sick. All those things are wrapped up together, in that 60% and you just don’t know what it means. And then to add to that, if that student learns, and they really show great effort, and they can tell you later on, “Hey, I’ve got all this stuff, and let me show you how, maybe on like a cumulative final, that 60% is still averaged in and it’s going to permanently weigh them down and their final grade won’t represent what they actually came to know.

Robert: Right. And so grading really cuts against the very process that humans engage in when they learn anything. When I’m learning how to play a song on my bass guitar, and I play it once and I do terribly at it, if I eventually learn how to play it, people should not be looking back at the first time I tried it, [LAUGHTER] they should be looking at the last time I tried or the maybe the best time I tried it. That’s not how recording artists record. It’s not how athletes are ranked, and so forth. And it’s all because of this sort of Industrial Revolution era routes where we have everything measured and sorted out and put together and it inhibits growth. It sort of poisons our relationship with students, it leads to all these extrinsic goals that students now have. Rather than focusing on learning and growth, students get the idea that it’s wrong to fail at things the first time, whereas it’s actually normal to fail at things the first time and then grow from it. And I guess that’s where the name of our book came from, I forget where that phrase “Grading for Growth” popped up. It was way before we were asked for a title for our book. But it’s like that’s what we really want. We want to have a system, even if we must call it grading, we want it to be a system evaluating student work that focuses on and encourages growth as you are learning because that’s one of the great things about being human is that we do grow and we do learn from our mistakes. So where is it in our assessment systems? That’s kind of the fundamental question we’re asking.

David: So it might be helpful if we talk a little bit about this four pillars framework that we have in terms of where we go with that. We kind of spent a while trashing traditional grading here, and I could do that all day. So what did you do instead? What are the things you want to do instead of these things you don’t? And so from my point of view, the most important thing I want to know out of a grade is what does the student actually know? What do they learn? And so, as I said, we have this four pillars model, we talked about four pillars that any good rating system should have and one of those is really a clearly defined description of what it is you’re assessing. So we call it clearly defined standards. I don’t want to catch on to the name standards too much there, but a description of what it is you’re assessing and what it is that matters in that assessment. So how do you know that the student has achieved it? And what is it that the student has achieved? So in that way, that takes care of this issue of what does that 60% mean? 60% of what? And if you’re grading based on a specific thing that you’re testing a student about, then you can say, okay, maybe they’re achieved that or they have not achieved that specific goal. And then we try to incorporate in our other pillars, this idea of feedback loops. So humans work on feedback, they work on trying things multiple times, they work on trying and failing, and having to come back again, and that it should be the ultimate level of what they know, that really matters. So focusing on feedback, rather than focusing on numerical rates. So focusing heavily on feedback, on what’s happened, and how that relates to the standards or the specifications, or whatever the description is that they were trying to reach, and then making that feedback actionable so the student has a chance to actually act on that, and either through a new attempt show that they’ve got that idea, or through revising previous work, show that they come to understand it in a way that counts fully, so that they’re not penalized for needing multiple attempts, just like Robert was talking about with his bass, we’re not going to look at well, the first time you tried, it didn’t work out, too bad. We want to know, ultimately, where were they, so we shouldn’t penalize multiple attempts at understanding something. And finally, it feels like a technical thing, but it’s actually a really big move, moving away from points or percentages and instead, if you’re gonna put a grade on work at all, to make that grade something that’s sort of a descriptor of the feedback, something that basically says, you’ve met this standard or you’ve met these requirements or you haven’t and gives the students an idea of where to go next: you need to revise this, you should try this again, you’ve made it, something like that.

John: I know you’ve experimented with a variety of alternative grading systems. Could you talk a little bit about how you view some alternative grading systems in your own classes?

Robert: Sure, I’ll jump in on that. So around 2017, I described this in the book in my origin story where I came from with this. I had just taught a calculus class and I had just a terrible experience with grades. One student in particular, a fantastic student, she was the epitome of what we’re discussing here. She was on a 10 day delay from the rest of the class and after those 10 days were up, she’d be at the top of the class, but the exam is today, and so her exam scores just went down, down, down, down, down. It was just an awful way for a student to experience my subject. And so I started casting about and I read this book that had just come out by Linda Nilson, who is a legend in the area of professional development, and my former boss at Vanderbilt University. And it’s called specifications grading, and I said “What is specifications grading?” So I read this book, and I was converted on the spot. And I’ve been using specifications grading in almost all of my classes, except for one instance of ungrading last year, ever since. And so, I’m in various forms, and always tweaking, always experimenting, and trying to change things up. But, specifications grading is exactly along the lines of these four pillars that David is mentioning. There are clear content standards that we call specifications. The idea is not to give like points, but marks, to use a sort of a non-American term for those, marks that indicate progress, like you’ve met the standard, that’s what you get instead of a 10. Or you’re progressing, that’s what you get instead of a five, and giving lots of helpful feedback and especially letting students retry things without penalizing them for retry. To me, that’s like the thing that drives the loops. That’s been my main sort of area ever since for the last several years,

David: I’ve used a pretty wide variety of different alternatives. It’s come to the point for me where I think about all these different types of alternative grading systems that have names like standards-based grading, or specifications, or ungrading as elements to put in and they may be appropriate in some classes and not in others, depending on a whole bunch of factors. For example, I’ve taught intro level classes where I use a lot of standards-based grading where that means I’ve sort of divided up the topics into fairly fine-grained standards describing what a specific skill is, and what it would look like for a student to achieve it. And then the grade is essentially based on have they shown me that they thoroughly understand that, they can do the thing described in each of these standards and grades are based on meeting or not meeting those standards. And that can look like pretty traditional assessments, quizzes or exams or homework or such things. But instead of getting an overall grade, they get a mark, like Robert was talking about, for each standard. Yup, you’ve achieved this. Nope, you haven’t yet. Maybe they need to do it a few times. But that’s one element. It’s really useful for sort of discrete skills, intro level things. I’ve used specifications in a similar way that Robert is talking about. One of the strengths of specifications is that you sort of look at a student’s work holistically and say, “Have they overall shown me they can put these ideas together, understand the concepts, use all the different things that I think matter within this assignment,” and that works really well on written work… We’re mathematicians where students write proofs, it’s a detailed explanations of why something’s true, or in a project or in a portfolio or something longer than that. It’s really useful, maybe in upper-level classes or in places where I want students to show synthesis. And I’ve gotten pretty deeply into ungrading, or at least as I use the word ungrading, meaning removing grades entirely, even marks, in the way we’ve been talking about as another element that can be useful either in an entire class or just as individual things to do within some assignment. So I’ve covered a lot of this, I continue to push on what’s most appropriate in different classroom situations and different student situations.

John: I’ve tried some of the same things too. But one concern from a lot of faculty who have tried mastery grading systems or mastery quizzing and those types of things, is that it can put a lot more work on the instructor to do the grading on multiple attempts. In Linda Nilsen book, she suggests giving students a certain number of attempts, but limiting those. How do you keep the work manageable so that you’re not spending all of your time grading additional attempts, as students are working towards mastery.

David: Yeah, the thing you mentioned from Linda Nilson’s book, attempts without penalty doesn’t mean attempts without limits, and that is really important. And yeah, limits like that are one way to do it. There can be limits on number of attempts, or on frequency of re-attempting something or revising something once per week, once total, something like that. Those sorts of limits can just be really useful. And I know, I always encourage new instructors or people just starting to use these systems to start out limited, and then add flexibility because that way, they will be able to do it if they need to, and not do it if they don’t want to.

Robert: Yeah, you know, another thing too is, not just in the reassessments, but in your overall design of your course, including the grading system, you got to keep things as simple as humanly possible. This is something David and I just hammer home constantly, like every other paragraph ends with keep it simple, because people who want to mess around with grading systems are people who like tinkering with systems, and I am one of those people, and I know that when you start tinkering, it’s very hard to stop. And you end up with this massive Rube Goldberg like device that is your class and to you, it looks beautiful, but when you face it towards students… I mean, the first time I did specs breeding, I had 68 learning objectives that students had to meet throughout the semester and it was a nightmare. At the first of the semester, I thought, I’m a genius. I mean, look at this beautiful grading system I’ve devised. It’s going to revolutionize everything. And the only thing it did was give me a grading jail for four months. Just keep it as simple as humanly possible, and you’ve got to cut the work off at the source, I think. David and I wrote a book about grading, but we don’t like grading. I mean, nobody really likes the process of it. But it can be made at least a fulfilling undertaking if you are orienting it towards growth. But you still don’t want to be doing it 8-10 hours a day. So keep things as simple as humanly possible and put some limits on that. It’s okay to create a little bit of scarcity when it comes to the reattempt side of things. The feedback needs to be helpful that you give to students, but it doesn’t have to be incredibly lengthy. It might just be a couple of sentences, it might just be: “You did this really well, and this needs work.” …to kind of keep it right to the point, and then that helps the students who are on the other end of this too also experiencing a workflow possibly overload. And I worry more about them than I worry about myself. And so this makes it more likely they’re going to read your feedback if it’s shorter, more concise, and it makes it shorter to give.

David: Yeah, I want to emphasize that it can be a lot of work for students as well. Something that I suggest a lot is, if you want to use a system that emphasizes these pillars, especially reattempts without penalty, you’ve got to then think about those re-attempts as part of the regular workload of your class. Really what it means is you’ve got to think about the process of learning, that whole process, is part of the time that students are going to have to invest into it, and that you need to value that in your timeline for the class. So I like to think of maybe if you expect a student to work, however many hours per week on your class, account for whatever time each assessment takes, add another half for how much they might need to do revising or reassessing or reworking on things. And that can lead to really difficult decisions. You’ve got to cut stuff out if that’s going to happen. I don’t know, basically, anybody who looks at a classroom teaching and says, you know, there’s not enough in here. And so you got to make those difficult decisions, but it is worth it. Because what comes out of it is a student knowing things that are still in there way better than they would have otherwise.

Rebecca: I think one other barrier that faculty sometimes face is learning management systems, and how they guide you towards particular kinds of grading systems and evaluation systems. I wonder if you can share some tips that you have from your own experience of dealing with a learning management system to help you and your process rather than getting in the way of implementing some of these techniques.

Robert: We’re a Blackboard campus, and we’re making a transition right now and I’m honestly not sure how the new system handles those. But in at least the next to most recent version of Blackboard there was a thing called a schema, which is basically a way of going into your gradebook and defining a way to map number inputs to text outputs. And so I can set an assignment up to be graded on zero or one point. And then I can only enter in zero or one. But I could tell Blackboard if I enter in a one put “meets expectations” in the gradebook, and if I’ve put a zero put “does not meet expectations” or a happy face emoji and a frowny face emoji or whatever I feel like doing. And I have zero experience with any other learning management systems over the last 15 years, so I can’t really speak to that. But I know that many memory management systems allow you to customize the way that your numerical inputs present themselves in the students’ gradebook. And if you can find out how to do that, that’s the way to go, as far as I’m concerned.

David: And even if you can’t, the thing Robert mentioned, that essentially everything is a zero or a one, these systems all want to use points. So just refusing to play that game by making everything a zero or one. Even if students are seeing the zero or the one, it’s a lot easier to interpret the zero or one as success or not, than it is if you have points showing up somewhere else, and you’re trying to convince students No, no, no, when I put in a five, that meant something that doesn’t mean five points, that’s not going to fly. So limiting it to just a zero or one, a complete or incomplete, something like that works pretty well. That’s also true for spreadsheets. So if you just want to keep your info in a spreadsheet, they still want to work with numbers for the most part, but you can think of everything as a zero or a one. And then you start to change your mind from averaging or totaling things to counting. So I’m counting how many standards a student has completed, I’m counting how many assignments they’ve met the specifications on. And that’s really the same as saying, how many ones do I see here? One last thing is, everybody seems to have a different LMS. Even those of us who use the same one don’t quite use the same version of it [LAUGHTER]. So the best thing to do is to find someone who knows it really well and talk with them and say, “How do I make this type of thing display?” …and they probably know a way,

Rebecca: I’m gonna have this conversation with John about our LMS.

John: We’re using Brightspace from Desire to Learn, and it does have those capabilities.

Robert: And one thing I would say is that these days, as the ideas about alternative grading get more and more airplay, I think the tech companies are starting to listen to these things. I mean, you’re actually starting to build these things in as a competitive device like “Ah, you should adopt our LMS, because we can let you do ungrading and you don’t have to deal with all the hassle of hacking your own LMS. So I feel like ed tech companies should be paying attention to all this great interest that’s swelling up, it’s like this is a way to earn customers, honestly.

David: Something I’lll say most LMS’s do seem to do pretty well is to allow you to get feedback in a variety of ways. And so if you can de-emphasize that grade portion, just 0-1 or hide it or something, especially like I accept all assignments through Blackboard nowadays, giving feedback’s pretty easy on that. So that, in my mind, is a benefit.

Robert: Yeah, Blackboard does a really well, actually, that if you submit a PDF into Blackboard as an assignment, it’s easy to leave comments on it, and it keeps all the versions of it. So you can go back and easily see the students trajectory from the very first draft that they do all the way to the present day. And I think that’s really powerful, actually.

Rebecca: I’ve used rubrics to set up essentially specifications as well, like it’s met or not met.

David: Absolutely, yeah. If you know what you’re doing setting up rubrics, I don’t, that’s the problem for me. But if you know what you’re doing, that’s fantastic and it can also save you time.

John: Since the pandemic, there’s been an explosion of interest in ungrading. Does this approach work as well in all contexts, and for all students?

Robert: People are starting to use ungrading to mean anything other than traditional grading. And I think that’s leading to a lot of confusion, honestly. I was working with some teachers recently who were saying that, “Oh, I’m using ungrading but don’t have time, I’m being overwhelmed by all these quests for reattempts.” And it turns out, they weren’t using ungrading at all, they were totally grading thing. When we say ungrading, we mean like a specific approach to evaluating student work where nothing gets a mark, literally ungrading. You get a letter grade at the end of the semester, because most places require that, but it’s all based on a term that’s come up recently, that I really prefer, is collaborative grading. You’re working together with the students throughout the semester to talk about the quality of work, but nothing is getting a mark on it. I have a comment for you and you can either choose to iterate on that comment with a feedback loop or leave it alone. At the end of the semester, you’re going to sit down together and collaboratively determine what your course grade is based on the body of work that you’ve accumulated in some sort of portfolio situation with some clear standards for what an A would look like, a B would look like, and so forth. So that’s what we mean by ungrading. The explosion of interest in “ungrading” may or may not be all about ungrading the way we’re referring to it. So I just want to be clear about the terms before we answer this question.

David: And just add even another thing, it’s both that sort of umbrella term and what Robert just said and the general philosophy and a buzzword that people attempt to apply to random things they use. It’s unclear what someone means when they say ungrading.

John: When we’ve been talking about it, we’ve been talking about it exactly as you described as an extreme form of alternative grading where there are no grades other than one that is decided in consultation with the student at the end of the semester. And sometimes at midterm if that’s required in the institution. From what we’ve seen, this is used quite a bit in humanities fields, but it tends not to be used very much in the STEM fields. What are some of the barriers or some of the concerns that might be raised for ungrading in terms of in what contexts it may not work as well.

Robert: I have tried to fully ungrade a course once, and I might use it again. But the issue that I was coming up with with my students, is what I say is that ungradiing works precisely as well as students’ ability to self assess. If you have students who are struggling with the ability to self assess, or they’ve never tried it, or they’re new students, or younger students who maybe are still emerging with that idea… the whole thing about ungraded is that it’s predicated on students looking at their own work and self evaluating. And if that’s an issue, then I’m not totally sure that ungrading, as we’re defining it, best serves that population. I know I struggled with it. And this can be more me than anything else. Maybe I just don’t know how to draw students out and I need to work on that. It’s an area of growth for me, certainly. But if you have a population of students, for whatever reason, whose ability to self regulate or self evaluate is questionable, or kind of low, we’re not going to say bad students, because we’re all growing… it’s the whole point of our book… if you deploy ungrading with that population, you might be sort of targeting the weakest point in your class. And so maybe, in that case, some marks wouldn’t be such a bad thing, like use a specifications grading approach where the marks are just like: you’re progressing or you’ve met the standard. Just some kind of simple mile marker that shows students where they are. When I used this, once, it was an upper-level class, it did have a lot of writing in it, a math class. I would leave comments on their paper and I would just get questions like, so does it meet the standard or not. And I didn’t like to sort of be telling students this, but I felt like this is the way I helped them. I said like, “hasn’t met our standard yet, here is what you need to do.” So I thought, if I’m going to do that, why don’t I just put a mark on it? It seems like I’m just beating around the bush and trying to be cool by not giving marks and it’s like I’m thinking more about myself than I am about the students at that point.

David: I think that a general thing that everybody needs to think about when using any kind of alternative grading is, this is something new for students… almost guaranteed. And like any other new thing, it needs time to learn, you need to encounter it a few ways, you need to try to make sense of and probably fail initially, and then come back and you’ve got to work to understand it. Ungrading is sort of an extreme form of that. There’s more that needs to be understood about how it works, there’s more skills that need to be built. And I think, as instructors, we need to think about that and think about teaching how our evaluation systems are working and how the grading is going to work. And think about what skills we need students to build up in order to successfully engage with those. And ungrading asks a large amount of that. And I say this, as I very much enjoy using ungrading also in some upper-level math classes and I think it’s worked pretty successfully for me. But this sounds funny to say about something called ungrading, it requires scaffolding, it requires helping students build up that ability to self evaluate, advocate for themselves, to be able to understand what it is that matters in that particular system. But what I just said is also equally true for standards-based grading or for specifications grading, but with different skills that they’re building up. It’s also true for traditional grading, although it feels more familiar to students, but it still requires some scaffolding for them to understand what exactly is going on in the evaluation in this class.

Rebecca: Can you talk a little bit about some of your own experiences with ungrading and how you have done some of that scaffolding, what some of those early stages of scaffolding might look like, to understand the system.

David: So initially, I was having I think it was three check in meetings per semester, where I would meet with every single student in my class, like a 10- or 15-minute discussion, and we would talk about where they’re at. And that inevitably brings out students’ questions, and they don’t understand this part of they don’t know what that is about. And so that was one thing that I did, right? Those were the collaborative aspects of ungrading, and it was overwhelming, it was too much to meet with every single student that often. I still love being able to meet with students. And I use that as one of the tools in the toolbox. But nowadays, to sort of help build that up, I have a system where… this is actually done through homeworks for me… it’s like periodic homeworks and there’s some mathematical content. And there’s also some little additional thing where I ask a question, and early on, it might be something like, “Okay, what is a specific goal related to… and then I might have some of the math related content in the class or as a specific goal you’d like to work on related to this.” And that’s a fairly small thing. I ask students to say something along the lines of “I really want to work on improving my understanding of this one thing” and I can either respond to that as “Okay, great. Here’s the way I can suggest that you work on that,” or I can respond to it as… well, I don’t say it this way, but… “I can see that you’re having trouble elucidating the goal and so let’s talk about that” instead. And then another week or two down the line, there’s another maybe slightly higher-level task having to do with assessing themselves or thinking about their progress in the class. And so they’re scaffolded and I can, at each stage, see if a student is succeeding, in sort of the way that I’m looking for them to be thinking about their progress. And if not, then I can pull in a, “Hey, let’s actually meet and talk about this. And then I’m gonna give you a task to practice with that.” It’s really individualized, which can be a tough thing. But for me, it’s really fun to actually see students grow in that particular way, in addition to growing in the mathematical content.

Rebecca: So faculty that want to move to less traditional methods, what are some small steps a faculty could take to get started?

Robert: Well, I really appreciate that question. Because we don’t ever want to give the impression that you have to go all in on one particular grading system in order to like, be cool, or be a good professor or whatever, because everybody’s in a different position. Some people may not be in a position to ungrade, and we are never going to come out and say, “If you really care about students, you will do ungrading or you’ll do standards-based grading or whatever.” It’s like people care about students all over the place and just can’t or have mitigating circumstances. So I would say we laid out these four pillars: clear content standards, helpful feedback, marks that indicate progress, and reattempts without penalty. If a professor takes one of those pillars, and kind of drills into it on just a handful of assignments, that’s definitely progress in the right direction. So for example, you could take your next test you’re gonna give, experiment with letting students reattempt it, or reattempt different versions of it. So go one test, one class, allow reattempts without penalty, or give feedback that really gets to the point, not gives points, but gets to the point of what’s being done well and what isn’t being done well. Just pick one of these four pillars and just go with it. There are some small scale methods you might think about, let’s say, instead of grading your final exam, how about ungrading your final exam. Just say you need to lay out some standards for what constitutes successful work on your final exam and maybe that’s like 70% on the content. And then you got to write some reflective essays, and say, if you don’t meet expectations on the final exam, that’s a minus on your course grade, or something like that. So you can roll in aspects of alternative grading systems, whatever seems to resonate with you on small-scale individual assignments. And that’s really good progress. It’s really good data for you as the instructor too. You run these experiments, you ask students how it went, and then you just make notes and you iterate on that. It’s exactly the same thing that we asked students to do in these grading systems. You try something, you get feedback on it from a trusted third party, you iterate on it and try again.

David: I want to add one thing, because this is something that I always see happen when people first start using some kinds of alternative grading. Just for yourself, write a really quick list of what you think the major topics are in your class, aim for 10 to 20 things that are the important things to get out of the class, and then go pick some of your exams or quizzes, or whatever, and match them up. “Oh, on this one I was addressing these things and on this one, I was addressing those things.” And that can help you actually think about, “Oh, you know, I’m not really addressing this thing in my assessments at all, that I said was really important.” Or “Holy Moly, I have hit this one thing over and over and over all the assessments at the cost of not covering a bunch of others.” The first time you do this, even if you’re not showing students what the standards are, it can be amazing. “Wow, I’m not assessing what I say matters.” And that can adjust just how your assessments are focused.

John: Sounds like you’re advocating a backwards-design process where you start out with clearly defined objectives, and then you make sure that there’s alignment. And also, I think it might be important to make sure that students see the connection between those things, and that it’s a transparent process, which I know is something you’ve advocated in terms of your work on assessment.

David: Absolutely. And sharing your reasoning with students I think is very valuable, bringing something in from above and saying we shall now do it this way, because I said so, doesn’t work and you’re gonna get a lot of pushback, but talking with students about why you’re doing things and how it’s good for them, that makes a huge difference.

Robert: And don’t call it an experiment, okay. [LAUGHTER]

David: Yeah.

Robert: I’ve read some syllabi lately. It says, I’m going to be experimenting with this experimental new experimental grading system. And of course, you know what that is going to sound like to students… that I’m the subject of an experiment. What am I doing here? And so you’ve instantly killed your buy-in.

David: I’ll actually say, I don’t even give names to what I’m doing. So I am ungrading a class this semester, I have never used the word ungrading or any other name for it. I find that giving a name to things like that can help people sort of reduce it down to like a one dimensional idea, rather than engaging with what it actually is. I’m just “Oh, this is what we’re doing, and here’s why we’re doing it this way.”

Robert: Yeah, I have to share this story. When I started doing specs grading I did actually put we are using a thing called specifications grading on my syllabus. So, I got a call from our research office on our campus, they had gotten a call from the parent of one of my students complaining to them that I was experimenting on their child without informed consent, that I needed to give an informed consent form to my students before this happened. And I thought, well, that’s a weird flex from a parent and they call up the Office of Research Compliance [LAUGHTER] and complain about the Professor, but as you can just see even just the barest mention… Just tell students what you’re doing, and why you’re doing it. If I have to name it, nobody cares what the name is, it may not even have a name. And all this we mentioned before, that most of the people we interviewed for the book are not using any sort of canonical form of anything. It’s just like a little bit of this, a little bit of that, like cooking in your kitchen, you don’t use just one spice, you combine them, that’s where you get your unique flavor of what you’re doing.

John: Would it be fair to say that, given the title of your book and focusing on grading for growth, that one of the things you’re addressing is how to shift students from focusing on trying to maximize their grades to maximizing their learning?

Robert: Yeah, absolutely, yeah. I think a lot of frustration that I know I feel and I hear from other faculty is students tend to spend an order of magnitude more time talking about what they have to get on exam X to get grade Y than they talk about the actual content in the course. And we teach math, and I think some of the students who struggle the most with our math are doing like these amazing statistical calculations to try to figure out what the average has to work out to be. It’s like, “where was this in my actual math lesson?” I remember riding the bus home one day, from our downtown campus back to where we live, and I overheard this conversation and I said “Oh, this is this has got to come to an end.” [LAUGHTER] And absolutely, we want students to focus on their growth and I think students want to focus on their growth, too. I mean, students really, in the end, don’t want to think about all this stuff. They want to think about, “How am I growing as a human being? Is when I’m doing really meaningful? Where am I as a learner? Do I have any value in this vast educational system that I’m entering into?” And so if we can even just orient one small thing, like our grading system, towards convincing students that they have value, and are human beings in a stage of development, I think that’s worth it.

David: And that means we need to believe it, too. So I like to tell people who are thinking of using an alternative grading system, think about why you’re doing it, and what your students are going to get out of it. But definitely approach it as like, “Okay, I care about my students, and I want them to succeed.” And we’ll sometimes talk about incentives… grading systems set incentives in a class, and that can feel sort of like you’re trying to mess around with people and then incentivize you to do things a certain way. Traditional grading systems set incentives that are really kind of perverse towards learning. And if we can change those incentives, or just remove some of the ones that aren’t as good, that’s really a lot of what we’re aiming for here. And yeah, just respecting how people naturally want to learn anyway, that just allows them to do what they are as human beings going to do anyhow, or what they would naturally do.

Rebecca: So everyone wants to know, when can we have your book in our hands?

Robert: Well, it looks like on the Stylus website, it says July. So that’s what we’re going with for now. [LAUGHTER] I guess it’s sort of out of our hands at this point. We have one more round of copy edits to do. But it says July, you can preorder it now through the Stylus website and should be in your hands this summer.

John: My preorder has already been sent in. [LAUGHTER] So I’m waiting for a copy.

David: Awesome.

Robert: Awesome. Thank you.

Rebecca: And you mentioned earlier something about a blog. Do you want to tell us a little bit about that?

David: Yeah, if you’re interested in some of our ideas, go check out our blog, it’s gratingforgrowth.com …all spelled out. So, Robert and I started this sort of as a way to workshop some of our ideas for the book. So you can see proto-ideas. And we’ve also posted some examples of some of the case studies of some of these interviews that I have done with people using a lot of different alternative grading systems there. Every week, we post something new, or we have guest posters. There’s a really huge variety of ideas that show up on there.

Robert: And if any listener wants to contribute a guest post, we are accepting applications at this time… not really applications, just reach out. And we’re looking to hear. Now that the book is kind of close to coming out, we’ve had this discussion, you and I, David about where does the blog go from here once the book is out, and I feel like a great use of our time is to elevate the voices of other people. I mean, there are so many people out there doing great work, who are not education rockstars, they’re not on the lecture circuit or whatever. They’re just rank and file heads down people doing great work in the classroom. I love those people getting their ideas out there and seeing what they’re doing. So to me, that’s been a really rewarding experience.

David: So gradingforgrowth.com.

Robert: Right. It’s actually a substack. You can subscribe to it. It is free. It’s never going to cost anything and it comes every Monday. Except for taking planned breaks for holidays, we haven’t missed a Monday in two years.

David: Well, now you’ve cursed us, Robert. [LAUGHTER]

Robert: No, I put the pressure on me because then I got to step up. I think I’m next, actually. No, you’re next.

David: Oh, crap. [LAUGHTER]

Robert: Sorry, Dave.

John: We will put a link to that in our show notes.

Robert: Great.

John: Are there any other topics that you’d like to emphasize?

Robert: Well, I think I would just re emphasize simplicity. I mean, simplicity is the ultimate sophistication. I think Leonardo da Vinci said that. And so, when you’re designing a class simplify as much as humanly possible, and no more. But I think your students are going to be well served by less, honestly. I think we tried to do way too much in our classes, and we will be well served by this too. I mean, I have another blog that deals with productivity and time management in academia. And that’s the key thing. I mean, a lot of faculty struggle with overwork and burnout or just doing too much and there’s a lot of stuff you can say no to and I think keep things very, very simple and that can be a whole lot. podcast about how to simplify your life in higher education, especially applyied to course design and grading systems. You don’t want to make choices in July when you’re planning your fall courses that you end up regretting by October.

David: I will say that something that did come up earlier, briefly, but there’s not one right way to do it. You should not feel like you must go all out ungrading, you shouldn’t feel like you have to do specifications grading exactly the right way. Find something that works for you, look for models, pick and choose the things. If you look at something and say, “How could that possibly work?” then don’t do that. And yeah, we’re not judging you. Find something that works well and it’s going to be good beer students.

Robert: Yeah, and especially the last thing you just said, David is so important. All this stuff is predicated on actually communicating with your students. Don’t just sort of wait for the course evaluations. You have to really get in and talk, actually talk with your students on a regular basis and get feedback and see how things are going. And that’s one of the great strengths of all these four pillars sort of oriented approaches is that it really does get students talking with each other and with their faculty members. And I think that’s, maybe in the end, the best thing about all this.

Rebecca: Well, we always wrap up by asking what’s next?

Robert: Well, for me, I know I’ve been spending the last two years not only as a faculty member, but working in our president’s office under what’s called a presidential fellowship. And I’ve been coordinating large-scale institutional cross-institutional teaching and learning initiatives, mostly focused on active learning spaces. And so that’s been a particular focus of mine for a few years. That is wrapping up now. But we’re looking at maybe some interesting and exciting extensions of that idea where we’re going to try to surface and looking for what our faculty are already doing in terms of instructional innovation. There’s a lot of stuff out there, like we said earlier, but even in our own institution, a lot of faculty are doing really innovative and creative things and effective things but are kind of working under the radar. So the President and I, and those around us, are kind of thinking how can we look and find these faculty, get them together, elevate what they’re doing, and sort of make Instructional Innovation a normative practice at our university. So that’s that’s kind of what’s next for me is figuring out how to make that work on a practical level.

John: Sounds like a wonderful plan. I know, we’ve been talking about some ways of doing the same thing at SUNY-Oswego. And it’s a challenge.

Rebecca: It’s no small task. [LAUGHTER]

Robert: It is, it is.

David: Something that I am getting more and more interested in is what helps instructors be successful in any kind of educational innovation, not just alternative grading and changes in their pedagogy, anything like that. But especially when it comes to grading, there’s so many variations. And in so many different situations where instructors are working, what are the things that help them best succeed? And what are the things they do that help their students buy in and succeed most? And so looking at those sort of things from a more fine grain perspective, I think it’s going to be somewhere that I’m going next.

Rebecca: That sounds exciting.

John: It does. And I hope you’re both come back and talk about the success of these initiatives in future podcasts.

Robert: We’d very much like to.

David: Absolutely.

Rebecca: Well, thank you so much for joining us and sharing your stories. And I know that many people are looking forward to your book.

Robert: Thanks a lot for having us.

David: Yeah, it was great to be here. Thank you

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John: If you’ve enjoyed this podcast, please subscribe and leave a review on iTunes or your favorite podcast service. To continue the conversation, join us on our Tea for Teaching Facebook page.

Rebecca: You can find show notes, transcripts and other materials on teaforteaching.com. Music by Michael Gary Brewer.

John: Editing assistance provided by Anna Croyle, Annalyn Smith, and Joshua Vega.

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188. Student-Ready Courses

College faculty sometimes complain that many of the first-year students who enter their courses are not “college ready.” In this episode, Natalie Hurley joins us to examine strategies that can be used to ease this transition and help ensure that our courses are “student ready.” Natalie is a New York State Master Teacher and a 2018 NNSTOY STEM Fellow who teaches high school mathematics in the Indian River Central School District in Watertown, NY.

Shownotes

Transcript

John: College faculty sometimes complain that many of the first-year students who enter their courses are not “college ready.” In this episode, we examine strategies that can be used to ease this transition and help ensure that our courses are “student ready.”

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John: Thanks for joining us for Tea for Teaching, an informal discussion of innovative and effective practices in teaching and learning.

Rebecca: This podcast series is hosted by John Kane, an economist…

John: …and Rebecca Mushtare, a graphic designer.

Rebecca: Together, we run the Center for Excellence in Learning and Teaching at the State University of New York at Oswego.

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John: Our guest today is Natalie Hurley. Natalie is a New York State Master Teacher and a 2018 NNSTOY STEM Fellow who teaches high school mathematics in the Indian River Central School District in Watertown, NY. Natalie was also one of our students here at SUNY Oswego. Welcome, Natalie,

Natalie: T hank you so much for having me. It’s a pleasure to be here.

Rebecca: Today’s teas are… Natalie, are you drinking any tea?

Natalie: I am, I’m drinking a peach tea because it’s warming up outside and I want to feel that warmth.

Rebecca: That sounds right up John’s alley,

John: …and I am drinking a ginger peach green tea.

Rebecca: I knew there’d be peach. It’s almost like you guys coordinated. I have Irish breakfast today.

John: No Scottish?

Rebecca: I am almost out of the Irish breakfast. And then we will move on to a different container.

John: Move down the Empire [LAUGHTER] and head back to your English breakfast and afternoon.

Rebecca: Yeah. [LAUGHTER]

John: Okay, we’ve invited you here to talk about the transition between high school and college. Could you first tell us a little bit about the courses that you teach?

Natalie: I teach high school math. And I have a pretty nice spectrum. I teach algebra I, calculus, and precalculus. I’m in my fifth year of teaching precalculus and calculus, and I have taught algebra I, eight years.

John: Excellent. What were your majors in college?

Natalie: So, I was a math major from the get go. And then I had this fantastic professor who helped me find my love of economics. His name is Professor John Kane, and he’s here with us too. [LAUGHTER] And then, once I started to find my love of economics, I picked up a minor in it. Unfortunately, it was too late in the game to pick up a double major, but the minor was great too.

John: And we did talk a little bit about you going on to grad school in economics. And I was a little disappointed that you didn’t, but then I thought you could do a lot of good in the school system. So, one of the things we want to talk to you about is the differences between your experiences in college and the way you teach your classes now. Could you talk a little bit about some of the differences between what you observed as an undergraduate student and the way in which you teach now in secondary school?

Natalie: Yes. So there are definitely a lot of differences. Although I tried to definitely keep that idea of college and career readiness, being wholesome in my classroom. I remember in college it was a lot of lecture style, a combination between very, very large classes of hundreds. And my math classes were usually pretty small, less than 20, generally. In my classroom, in a non pandemic year, I have somewhere between 15 and 20 students usually. Of course, now we’re doing cohorts. So I have a class as small as two and another class as large as 13… is my largest class… on Thursdays and Fridays. So I just remember, in college, a lot of lecture style: the teacher talks, you write notes, you can ask questions, but it’s very much like you raise your hand, if a teacher calls on you, you can ask a question. In my classroom, it’s more a conversation about math, whereas I’m leading them to discover the math, hopefully on their own, with a little bit of questioning from me to lead them there. There’s a lot of… in a non-pandemic year, think-pair-shares, or working in groups, or talking it out with their partner, or somebody that they sit near… things like that, that’s a little bit harder to do these days, especially when I only have a class of two in there sitting six feet away from each other or more.

Rebecca: Everything’s a think-pair-share. [LAUGHTER]

Natalie: Right. So yeah, and as I grow, and I become more seasoned, it becomes more student centered and less about me than it had been before. So I want to put the students in the center, whereas when I was there, it was very much the teachers up there telling you how to do it. And then this is how you do the calculus. And then this is how you do calc 2, this is how you do calc 3, and they just show you and you find your study groups, and then you work with each other after class as opposed to in class. So that seems to be some of the differences. I remember in college is a lot of rote memorization: know these words, be able to regurgitate this proof, things like that, where just now, in my classroom, and really the focus of high school math, and really all math through the Common Core standards, is that deep understanding, getting to the core and understanding vertically, what number sense and number theory is throughout all the grade levels.

Rebecca: It sounds like you’ve incorporated a lot of evidence-based practices into your own practice, which we encourage all of our faculty, even at the college level, to do as well. We hear a lot of faculty complaining about students not being “college ready.” And maybe that’s because there’s still a lot of lecture and memorization, and we want to keep changing that. What are some ways that we can become more “student ready” and bring students in?

Natalie: I think it’s very important that colleges understand what it’s like in the high school, how teachers are teaching, what they’re teaching. I’m in my ninth year, and the next year, we’ll start to move into the next gen math standards. And then that’s going to be the third set of standards. And I think it’s really important for college professors at all levels to be able to understand what did these standards look like for these kids? And how do I need to change what I’m teaching to adapt to that? I recently had a very informal discussion with the master teacher program and SUNY professors at SUNY Delhi about their math and science curriculum. And there was just a lot of surprises on both ends about what’s being taught, what isn’t being taught any more… emphasis on the calculator… standards now are being written so that there’s a lot of calculator use and students are losing a lot of their number sense, because you don’t need to know how to add and subtract, multiply and divide fractions when you get into high school, because you have a calculator that’s going to do it all, which turns into a lot of button pushing. But that’s definitely going to have a trickle down effect into… or trickle up effect, I guess… in college, when these students get there and they’re so used to being fully dependent on calculator and technology use… which is great if you’re a college that also promotes that. But some colleges may also still say, “Hey, we want to limit technology.”

John: Since you were in college, I think much of our teaching has changed. I know in my own department, most of us were doing a lot of lecturing when you were a student. And there’s been a pretty steady transition away from that. And that’s been true in many departments, including our math department.

Natalie: That’s great to hear.

John: But we still see a lot of lecture. And one of the things we’re hoping is that perhaps the experience of the transition to remote instruction has encouraged more people to try some new approaches to teaching and learning.

Natalie: We have definitely seen that in the high school, a lot of teachers who were behind the ball, as far as utilizing technology in their classrooms, it’s been forced to become great at it… literally overnight. So I guess if there’s a silver lining to all of this, that is definitely key right there. I think something that’s extremely important in high school is making connections to real world, making everything very real life, how am I ever going to use this in real life and making sure that that is evident in the student learning. And I don’t teach in a college, I haven’t been in a college in 10-15 years. But I think that if you wanted to be more student ready is also connecting all of your curricula to career readiness. Students want to know why am I taking this class if I’m going to be a librarian, or if I’m going to be a social worker. So just being able to bring those connections to them, could also help colleges be more student ready.

Rebecca: Just that relevance alone is more motivating to get students excited about topics. So finding ways to connect to students, no matter the level, high school or college, is a really great way to bring them in and bring them along.

John: One of the challenges I know in economics we face, is with students saying, “I’m just not very good at math,” or “I have trouble with graphs.” And I suspect maybe you might have seen a little bit of that, too. How do you address that issue of a fixed mindset concerning student’s ability to engage in mathematics?

Natalie: In my calculus and precalculus classes, and you’ll be even surprised to hear it that I do hear that there. But it’s extremely prevalent in algebra I, that idea of “My mom wasn’t good at math, so I’m not going to be good at math.” “I’ve always had math support, AIS,” or “I’ve been able to get through because I’ve always stayed after with the teacher.” I definitely still hear that, but the idea is to kind of break that mold by saying, “Hey, listen, this is a new year. This is a new teacher, this is a new curriculum, maybe this is going to be the one for you.” I find a lot of students struggle through geometry. So as soon as I bring up geometry, it’s like, “Oh, no, I don’t want to.” And I say, “Listen, let’s connect it to algebra, then. Do you feel more comfortable making the connections to algebra?” …or I don’t even know. I don’t know how to tell them that you can be better. Maybe you had a bad teacher, maybe you had a teacher who didn’t make things relevant for you, or just some bad experiences, but every year’s a new year. I’ve seen all sorts of success stories of students who truly find their niche late in high school math. So in my class, I’ve definitely adopted the idea of a growth mindset. And I’ve been studying on best practices to help do this. And part of that has been through standards-based grading. I’m kind of a beginner, a novice, of standards-based grading… more of a cafeteria, I’m choosing which aspects of it that I’d like to implement versus which ones don’t work for me, yet, as I learn and grow, which is definitely not the high school or college that I went to, to implement things like re-quizzes and retests. And it was hard for me to even start with this idea. Nobody else in my department was doing anything like this. And to be honest, as I was starting my career, I started my career right as common core was being implemented. So there was a ton of work in developing all the new curricula. I started in an eighth grade and moved all the way up and I’m like, “Wait, you want me to make two tests? four tests? two quizzes? three quizzes? four? And you want me to give them to these kids and grade them and change their grades and all of the clerical work. But now that I’m nine years in, I’m ready for it. And I find that the students have such a better… I guess they feel better about themselves when they go in to take a quiz when they know that there’s going to be redemption. One thing that I do is, if their test grade beats their quiz grade, I let the test grade replace the quiz grade in the gradebook. If you can show growth, by the time you get to the test… and that idea actually comes from college. If your grade on the final is better than your grade in the class, some professors will do something like that. Or if your grade is high enough, you don’t even need to take the final or I don’t know if anybody’s still doing things like that. But that kind of way, it takes the stress of testing and quizzing, and it takes it off of the grade and puts it more onto the learning. And, however, I do understand that that practice might not be making my students “college ready” if their college professors are not following that, which probably they are not. However, it’s something that I feel I need to do in order to focus on the learning that needs to happen.

Rebecca: I think one of the things that we’ve been working really hard to do at the college level is to incorporate some of those practices as well, to encourage learning, and that it’s about test taking and the testing effect as a way of remembering and learning and practicing rather than some moment in time that somehow reflects all learning that has ever occurred, which is not really relevant or accurate.

John: And you would be happy to know that many people in our math department are doing mastery quizzing and mastery learning approaches where they allow students multiple attempts to demonstrate mastery.

Rebecca: One of the things that I think is somewhat problematic for the transition of students from high school to college is that we don’t have these kinds of conversations very often. They’re not in place unless we go out of our way to talk to local high school teachers about what’s going on in local schools and vice versa, where high school teachers are asking us what’s going on at the college level. Can you talk a little bit about how your Delhi experience evolved in ways that you could encourage others to have those same kinds of conversations?

Natalie: I believe it was somebody from SUNY Delhi reached out to the Executive Director of the New York State Master Teacher program, if you haven’t heard about it, it’s a STEM initiative to retain teachers in math and science. And it’s a four-year fellowship that you have to apply and interview and be selected to join. But, it ends up creating a very strong network of teachers statewide that are actually affiliated with SUNY, every region has a SUNY campus that they are affiliated with, Up here in the North Country, mine is Plattsburgh. And since our program has moved more to an online format, we were able to all participate with SUNY Delhi through this conversation. And I think that just leads to more ideas for the future or to somebody who has an in with some SUNY people. I think we all do professional development. I do it as a high school teacher, and you guys do it as professors. But then, where can we find the middle ground that can maybe mesh some professional development and share some best practices between our two groups?

Rebecca: Sounds like an excellent idea.

John: That is a practice that I think we should do more of. One of the issues that we have is that in general, high schools provide a lot of support for students. And often some of that support comes from parents who help encourage students to be successful in school, and then all of a sudden, people go away to college. And sometimes that doesn’t work quite as well, and we lose a lot of people. Do you have any suggestions on what perhaps colleges could do better to help retain more students?

Natalie: That’s a great question. And I think as we grow through the years, you’re noticing a lot more of, shall I say, helicopter parents or parents who are very, very involved in their children’s lives, and so much to the fact that they actually can become bulldozer parents and literally take roadblocks out of their children’s way so that they never experienced any kind of struggle. And that, of course, is not anything that me as a high school teacher, or you guys as college faculty can do, other than just encouraging parents to step back. Students should be very autonomous. I think that, if anything, we’re going to see out of this pandemic. Another I guess silver lining is the students are becoming more autonomous. They have to when their parents are working and they’re only going to school two days a week and they’re responsible for their own learning the other three days a week. They’re also learning skills, like do I care for online learning? So when I get to college, should I steer towards classes that are online or steer away from classes that are online. So these are definitely going to be skills. So you guys might want to look out for when you’re screening students or as advisors, “Hey, how did you do when you were fully remote? Were you able to get all of your work done? Did your mom have to come home and sit down with you and work with you? Or were you able to get up in the morning, eat your breakfast, and then get right started on your schoolwork?” I make a joke to my seniors about this time of year that if they are still being woken up by their parents, they are not ready for college. You will be home by Christmas if your mother is still waking you up to get you in the shower and get to school on time. Students are going to have a lot of free time when they get to college. Their lives are managed for 40 hours a week, an hour bus ride in and back, somebody tells them when it’s time to eat lunch, then they go right to sports practice and come back. They’re so busy when they’re in high school. And then when they get to college, and they have class that are for 15 hours a week, that’s a lot of extra time for these kids to have to manage. And then when they start to find out, “Oh, nobody’s gonna call my mom, if I don’t go to school?” That’s the kind of mentality that these kids are going to. And I ask my students often, “What do you think is going to be one of your biggest struggles?” or “What do you think is going to be a biggest struggle of your peers? …and it is time management. The students are used to doing a lot of their work in school, either in the class or given class time to start assignments, to do assignments, or they have a study hall where somebody says, “Okay, get your books out, get to work.” And now they’re just going to go to class, they’re going to learn for an hour, hour and a half, and then go back to their dorm and have to start studying on their own. And even that, just the idea of needing to study, a lot of students can very easily get through high school without studying, without ever learning how to study. They just are good students, they know how to sit and behave, they learn well, they do their assignments, and that’s enough. I was a victim of that. I was always above average just by doing exactly what is expected of me. And then when you get to the bigger pond and you become the smaller fish, that can cause a lot of struggle for students, that idea of time that’s not managed, that they need to learn how to manage on their own.

Rebecca: I think you’re highlighting a lot of great themes here. And we certainly experience as college faculty, but your students are right: time management is the number one struggle of our college students. [LAUGHTER] They already know that it’s a problem. We know that it’s a problem. High school teachers know it’s a problem. But we don’t actively necessarily all collaborate on finding solutions to that problem. We just expect overnight students are somehow magically going to have autonomy and know what to do with it. [LAUGHTER]

John: And that’s especially true for first-gen students who haven’t had family members talk to them about those challenges and those issues, and who don’t have that sort of support. And suddenly, they have all this free time. And they don’t have any tests until weeks away or months away. And they just had these big assignments due so they don’t have anything they have to do right away. But one of the things that we know makes that worse is online instruction. Because there’s a lot of research. I did some about 17 or 18 years ago that found that freshmen and sophomores just did dramatically worse with online courses. And we had a guest on our podcast several months ago now, who found the same thing in a much larger study… that juniors and seniors and older individuals, if they’ve been successful in making it to that stage of college, they tend to be relatively successful at managing their time effectively. So online instruction is much more challenging for freshmen. And one of the things that I know many faculty are concerned about is the fact that all of our students coming in next year will have spent at least a year in some sort of remote or online instruction. And the quality of that varies quite a bit across school districts. And I think that is going to be a challenge we’re going to need to address. Do you have any thoughts on how we can help students be better at this?

Natalie: You are definitely correct, there are going to be a lot of gaps to fill, based on how students have received instruction, in how much instruction, we were given guidance that perhaps we’d only get through 80% of our material. And as you know, at the end of the 2020 school year, some of the learning immediately stopped in mid March with the “do no harm” idea of you can’t do harm to any of their grades, whatever their grade is when they left is what their grade needs to be. So we saw students who had very high averages that said, “You know what, it’s good enough. So I know you can’t give me anything less than a 98. So I’m not doing anything for the rest of the year.” And that was a very real situation that’s not going to be reflected in a transcript that you receive as a college advisor or as a college applicant when these kids are applying to school. I’m hopeful that students could self assess where they’re at, that if a college is going to have a lot of remote opportunities, and they are good at online learning, absolutely, go there, that’s for you. And if not, then that might not be for you.

John: I think we can also refer back to an earlier podcast we did with Viji Sathy and Kelly Hogan, who talked about the importance of structure in all of our classes, that providing students with clear directions, with giving them more expectations, and a couple of other podcasts that we had with Betsy Barre, she discusses the importance of sharing information about the time that’s required for various tasks. So giving students more detailed instructions and giving them more guidance on how much time they should be expected to work on things, perhaps, may help.

Natalie: I completely agree, I remember the rule of thumb was a three-credit level class would have about nine hours, the total amount of work, including class time for that class. And I try to drill this into my students heads as a pre-calc and calc teacher that you’re going to be doing a lot of work outside of this class, which is not what they’re used to. They’re used to, “I’m going to go home, I’m going to do 15 minutes worth of homework, and it’s going to be graded based on effort. So I get a free 100 in the gradebook if I did it, and nobody’s gonna care if I did it correctly, I could do the whole thing wrong, I could copy from my friend, and there we go, I get the credit.” And that’s just not college readiness, or career readiness, for hopefully most careers. But I would love to see some kind of, even in high schools and then have it trickle right up to college, some kind of bridging from each course… ninth grade, these are our expectations, 10th grade, you get a little bit more strict restrictions, and then all of that being an idea of we’re bridging the gap from 12th grade to college. And as well as college professors and faculty looking back and saying, “Okay, this is where they’re at when they’re coming to us. And so we can pick it up from here.”

Rebecca: Yeah, that ramping is so important. And just acknowledging where students are at, and meeting them where they’re at, and not having some false expectation of where we wish they were, which is very different. And I think what John was talking about, like providing some time allotments and things, but just even providing students with a sample of what their outside of class time should just generally be looking like, maybe you are spending three hours outside of class studying or six hours outside of class studying. But what are those six hours look like? What does studying look like for this class? What are the kinds of exercises that would be really helpful. And faculty have a vision of what that should be, we just often don’t communicate it.

John: And often when faculty do, though, they communicate what worked for them, which is what had worked for their professors before them, which is not always what would work for a typical student.

Rebecca: What do you mean? Highlighting, John?

John: …and repeated rereading, and focusing on learning styles, but there’s a lot of things out there that faculty may encourage students to do that is not really always consistent with evidence. And going back to your point earlier, Natalie, about providing the relevance of things, one of the problems I think that faculty have is we got into these things, because we’re just really interested in the questions of the discipline. And the things that interest us now are based on having studied the discipline for a long time. And it’s a little harder, often, to connect with the types of things that would interest a student who’s just coming out of high school or is in a sophomore or junior position in college, because they don’t have that same network of concepts to make the topics that we find interesting as interesting to them. That’s something I think we definitely need to work on.

Rebecca: I know one thing that I always struggle with in the design classes that I teach is I’m constantly trying to get students to think about audiences other than themselves. But then when you start to put things in perspective, you realize they don’t really know much beyond themselves. They know maybe what an audience younger than them might experience or have expectations of, but they have a really hard time envisioning what a professional world might be like, because you just don’t have any experience in it. So we often come to the table with so many assumptions that we think that they have, and they just don’t have the life experience to match it.

John: We’ve talked a little bit about how instruction was affected during the pandemic, how did your classes transition?

Natalie: I saw this, the pandemic, as a way to be able to spread my wings and try and implement some different teaching strategies that I had thought about, but I wasn’t totally sure if I wanted to dive right in in one given year. And one of those ideas was the idea of a flipped classroom. I had never felt confident to be able to create a flipped classroom that I felt students would be responsible for. That being, watching the videos at home and then us just working on problems together in class. And to be honest, that’s pretty much what has happened. I have students who will have to watch videos on the two days, three days that they’re not here, and they have to, and I’ve figured out now how to assess that they’ve watched the videos, and to make sure that they are responsible for that learning. It’s not totally flipped. But I do have to provide instruction to these students three days of the week that they’re not around. And I did that in a couple of different ways for each one of my preps, because I didn’t want to get so solid in just one way was “the way,” and I wanted to try some things out. So for calculus, I teach calculus fully synchronous. My students who are at home Google meet live with the students that I have in class in front of me. We’re able to talk about problems as a bigger class instead of just the five who are in front of me. And that’s worked out quite well for us. Granted, class is at 10 o’clock, so it’s not too super early for these students. So, precalculus, I do kind of more HyFlex. They have the opportunity to come to the live session if they want to, or I do make videos for them to watch on their own. One thing that we had to keep in mind this year was that some of these students are responsible for younger siblings while parents are at work. So we needed to be a little bit more flexible in how we set up our classes. And when I had the conversation with my calculus students, they said, “Nope, we could totally do synchronous.” And if they needed me to make a video, I can make them a video. And then algebraI, I do completely asynchronous, the videos are already set up. There’s no live session. When they come in the next day, or whatever day follows watching the videos, I check and make sure that they watch their videos, give them a little bit of credit, just for doing what they were supposed to do. And, to be honest, I have become very, very graceful compared to how I ever was in the first seven and a half, eight years of teaching. My department very rarely ever accepts late work. Math is a sequential subject, you need to do the work today so that you know what’s going on tomorrow in class. This year, I’m just happy it’s getting done and getting done with integrity. So I’ve become so extremely graceful with students who are getting work done after due dates, right before the quarter ends. It’s not great, but they are also learning a very important lesson in “it’s a lot easier if I just do a little bit every day instead of trying to cram it all in at the end of the semester, or at the end of the quarter.” So, hopefully, that idea can trickle up to college as well. It’s not very easy to dig yourself out of a hole, especially in college.

John: You mentioned with your recordings that you were verifying that they actually watched the videos. How do you do that?

Natalie: With my algebra I, the videos obviously match their note packet, they have guided notes that matches very nicely. So the next day I just come in, check, they’re going to show me a front and back with all of the notes filled in. For precalculus, I feel like I shouldn’t have to check their notes, that they should be responsible enough for that level to actually watch the videos, I did get a sense that they weren’t watching the videos, mostly because I was bringing things up when they came to class, and I had a lot of blank stares looking at me. So I started using a program called Edpuzzle. They have to sign into it with their Google account. Lots of teachers in my school use this. And I was able to see who was actually watching. And it was funny, I had a student come to me and he goes, “I’m going to make a guess that 1/3 of the kids are actually watching the videos.” And as soon as I started counting up the number of students who actually watched the videos, it was about 1/3. So that gave a very stern talking to about what my expectations were in that they’re not going to have the best understanding and knowledge if they’re just practicing the homework assignments, that it needs to be the full package, coming to class in whatever shape or form that looks like, be it coming to the live session or watching the videos. But all of it needs to be done in order to be successful in precalculus.

John: Do you embed questions in the videos?

Natalie: I am just getting my feet wet with it. I just started using it. So no, I haven’t gotten that far. But I did hear that you can and you can do a little checkup and it will not let you get through unless you do the question. So is that something you guys have used?

John: I haven’t used EdPuzzle. But I have been using PlayPosit this year. And I embed questions in it and it is required as part of the grade in my econometrics class and in my introductory microeconomics class, and I’m probably incorporating it in more classes as I go forward. But students actually have responded really positively. They discovered that when they watch the videos, it’s really helpful, because when there was no grading involved or no questions, the level of use of the videos was dramatically lower. So this provides just a small incentive, it’s a trivial part of their grade, but it’s enough to induce them to watch them, though. I’ve been really pleased with it. One advantage of Edpuzzle though, is that It’s free, as far as I understand, whilel, I do have to pay for PlayPosit.

Natalie: Yep, it’s free. And we’re a Google school. So they are able to sign right in. And it was easy for me to use, I could see all the students, I could see how much of it they watched. So that was pretty cool.

Rebecca: That’s great. As I’m hearing you talk about how your teaching has transitioned, it largely matches how faculty at the college level have also had to transition. So in some ways, we may have been brought together unexpectedly. [LAUGHTER] So there’s a lot more college faculty also using a flipped classroom model, and using more class time to solve problems and work on the more complicated things. Because often the video lectures or that kind of part of the material is foundational. Some of it might be memorization things, it might be terms and things like this, and then you put it into action in the class, and you can have guidance and coaching. So what’s really interesting is that the pandemic may have brought these two experiences together, and that bridge might be more present than it has ever been before.

Natalie: Exactly, I used to think that there was no way for my students to learn, if I wasn’t the one who was telling them and showing them. If I wasn’t up at the front of the board, doing it with them, doing it for them, then they weren’t going to learn… there was no way they can learn this on their own, and boy, was I ever wrong. Even though I could do 10 problems with them up at the board, whereas they could do three working together in a small group or in a pair, it’s so much more valuable to listen to them have those conversations, and to hear them explain these things, in their own words, or what’s very powerful too, is when I hear my words come out of their mouth, as they’re explaining it to another student. So that’s totally cool to hear that. And I think that’s the direction of education. The prep work is more important than what the teacher role is in the classroom. So the role of the teacher plays planning and prepping for a lesson is so much more powerful than what the teacher is doing in the classroom at that time as far as leading instruction.

Rebecca: That design of experience is so powerful, just generally. I think one of the things that I know I have always struggled with using a flipped classroom model, but I’m definitely getting better, the more and more I do it, is really scaling back on how much can actually be done in class, when students are working through problems and they’re not having quite as much coaching. You’re really letting them struggle and fail and try again. That takes time. It’s not like something that can happen automatically. So we might be used to going through more examples, but less examples, but more depth can be really powerful. And your right, students explaining to other students is an amazing thing to see. But it also helps them articulate or realize where they don’t understand, which is something that you don’t necessarily recognize when someone’s explaining something to you. Because when someone explains it to you, of course it seems obvious, until you have to do it yourself.

Natalie: Absolutely.

John: One of the things I was thinking about is I have to create a video on log transformations in econometrics tonight, and that reminded me of all that.

Natalie: Do you want one of mine? I can grab it right off Edpuzzle. [LAUGHTER]

Rebecca: Can you imagine that, though, like sharing back and forth between high school and college and sharing resources? We should do more of this.

Natalie: Oh, absolutely. Why are we always reinventing the wheel for ourselves, when there’s so much already out there?

John: When you first create a flipped classroom model, it’s a lot of work, creating those videos, maybe embedding some questions in them. And doing that is a tremendous amount of work upfront. But it’s taking this stuff that’s relatively easy for students to learn and shifting it outside of the classroom. So that when students are in class, they’re able to focus on the things they have the most trouble with. Because, as Rebecca said, you can provide a really good lecture on how to do something, but if students haven’t wrestled with it, they’re not going to learn it as well. I know for many years, I was doing an awful lot of lecturing, and I’ve cut back to very, very little now other than when I’m recording lectures, and I’m seeing students struggle with materials, but then when they are assessed on it, there’s much more balance in their performance. Because before there were always some students who would pick up on everything you did… people like you, Natalie, and people like those who are faculty. We were able to learn the stuff by listening to people tell us how to do it and figure it out on our own. But that doesn’t work well for a lot of students. And when they’re there explaining it to each other, they learn it much more deeply than they ever would by trying to do the more difficult parts on their own. Because in the traditional model, we’d give them the basics and show them how to do things. But the only time when they really got to apply that was either when they were working alone, doing homework, trying to struggle to solve some problems. or on a high-stakes exam. And those are times when perhaps they need the most support and the flipped classroom model can really address that really nicely.

Natalie: Yep, I absolutely agree.

John: We always end with the question: “What’s next?” …which is a question I think everyone in education is wondering.

Natalie: I think what’s next is filling in the gaps. There is going to be a lot of gaps for a lot of years. And we keep saying I can’t wait till next year, I can’t wait till it’s back to normal. But pandemic aside, I don’t think it’s going to be normal for a long time, we’re going to have a lot of students who need a lot of support for a lot of years, and it’s going to affect me. And then it’s going to affect college faculty, as the students get up there, addressing where the gaps are, how can we fill them? How can we give these students the support that they need, even under just budgets that were being given that were cut in this past year or could be getting cut? We’re going to need a lot of support from each other, from our colleagues, from our administrators from the community… and I think a lot of understanding… these students are going to need understanding, we’re going to need understanding.

Rebecca: I really like the underscoring of this empathy towards one another, both between faculty and teachers, as well as between students and teachers. I think that’s a really nice note to end on. Thanks so much for sharing your insights, Natalie. I think many faculty will want to take the time and effort to reach out to some high school teachers and make some connections and start to figure out ways to bridge those gaps.

Natalie: Thank you so much for having me, this has been such a valuable experience. And I’m always grateful when anybody wants to listen to my opinion and share conversation with me.

John: Well, it’s great talking to you again, I very much enjoyed working with you when you were a student here, and it’s nice to see just how successful you’ve been. And I suppose I should mention that this came about because one of my current students had listened to the podcast, had shared it with people on Facebook, and then she said, “And you know, you really should invite one of my former teachers,” and so we invited you.

Natalie: That is so awesome. I feel very honored that that student thought that I had something great to share. And it’s been so great to be back in SUNY Oswego, among other Lakers, and of course, a professor who was a great mentor and led me down a path of success.

John: Thank you.

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John: If you’ve enjoyed this podcast, please subscribe and leave a review on iTunes or your favorite podcast service. To continue the conversation, join us on our Tea for Teaching Facebook page.

Rebecca: You can find show notes, transcripts and other materials on teaforteaching.com. Music by Michael Gary Brewer.

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123. New Trends in Science Instruction

Science instruction in K-12 education has long been provided as if science consisted of a body of facts to be memorized. The Next Generation Science Standards, however, rely on an inquiry-based approach in which students learn about science by engaging in scientific exploration. In this episode, Dr. Kristina Mitchell joins us to discuss this approach and its implications for college instruction.

After six years as a director of online education at Texas Tech University, Kristina now works for a science curriculum publishing company and teaches part time at San Jose State University.

Show Notes

Transcript

John: Science instruction in K-12 education has long been provided as if science consisted of a body of facts to be memorized. The Next Generation Science Standards, however, rely on an inquiry-based approach in which students learn about science by engaging in scientific exploration. In this episode, we discuss this approach and its implications for college instruction.

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John: Thanks for joining us for Tea for Teaching, an informal discussion of innovative and effective practices in teaching and learning.

Rebecca: This podcast series is hosted by John Kane, an economist…

John: …and Rebecca Mushtare, a graphic designer.

Rebecca: Together, we run the Center for Excellence in Learning and Teaching at the State University of New York at Oswego.

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John: Our guest today is Dr. Kristina Mitchell. After six years as a director of online education at Texas Tech University, Kristina now works for a science curriculum publishing company and teaches part-time at San Jose State University. Welcome back, Kristina.

Kristina: Thank you. It’s good to be back.

Rebecca: Today our teas are…

Kristina: Diet Dr. Pepper.

John: The same as last time. [LAUGHTER] I have a green tea today.

Rebecca: And I have a nice pot of brewed English Breakfast tea.

John: We’ve invited you here today to talk about the Next Generation Science Standards. How did you get involved with the Next Generation Science Standards?

Kristina: During my work at Texas Tech University in online education, I was doing a lot of consulting for publishing companies on their online and curriculum offerings, which led to a full-time job offer from a curriculum company that works specifically in K-12 and some higher ed science curriculum, and I learned very quickly that one of the newest trends in science education at the K-12 level are these Next Generation Science Standards that were created by college-level science professors in order to change the way we teach science to K-12 students.

John: How did these standards come about?

Kristina: I have to admit that because I’m relatively new to the science curriculum world, I am not an expert on their creation. But I do know that there were several panels of scientists from various higher education institutions that got together to try and figure out from the perspectives of different disciplines, “What do we want our students who come to university to know about science once they get there?” When I was in middle school, I don’t know how much you remember your middle school science lessons, but I remember dissecting frogs and doing our Punnett squares about genetics, but what I remember most is that we would learn those principles of science like Newton’s laws throughout the week, and then Friday, we would do a lab to prove that they were true. And unfortunately, that’s not how any of us do science. Being a social scientist myself, that’s not how I did science at the college level, as a researcher. So, the panel of experts from various scientific disciplines sought to change the way students think about science to think about it more as a process of investigation, rather than something you sort of memorize and then confirm.

Rebecca: The Next Generation Science Standards have three dimensions. Can you talk about those a little bit?

Kristina: Sure. So, these sort of three dimensions, or the three pillars of the way students are learning in K-12 about science, the first is they’re learning disciplinary core ideas. So these disciplinary core ideas are the core features of disciplines like physics or chemistry and the things that they really have to know about that specific discipline in order to build on that knowledge. The second one is science and engineering practices, so these are the ways we study science. And the great thing about the ways that we study science is that it doesn’t change across disciplines. Whether you’re a physicist or a chemist or a sociologist, you’re going to use the same types of scientific practices to answer your research questions. And then the final dimension, the third dimension, are cross cutting concepts. So, these are things like observing patterns or observing cause and effect, concepts that also span across all disciplines, not necessarily limited only to science. So it’s concepts that students can use to understand the world around them, regardless of what questions they’re asking.

Rebecca: Can you give us an example of how these three dimensions play out in a particular grade level?

Kristina: Sure. So when we’re thinking about what students are doing in science classrooms these days that might be different from the way we learned science when we were in seventh grade, students are doing a lot more investigation centered science. So, you walked into your classroom, your college classroom, and somebody walks in and says to one of your students, “What are you guys doing?” And your student might say, “Oh, we’re reading this chapter on…” Rebecca, I think you’re an art person, right?

Rebecca: Yeah, design.

Kristina: “So we’re reading this chapter on Photoshop,” and you ask them, “Okay, well, why are you doing that?” And they’d say “Well, because Professor Mushtare told us to.” In trying to get them away from that instead, the way they’re trying to implement science in the classrooms now would be to get students, you know, if they came into your classroom to say, “Well what are you guys working on?” And they might say, “Well, we’re trying to make a flyer for this project.” And you’d say “Why?” And they’d say, “Well, because we’re trying to figure out how we can make people more excited in this project that we’re working on.” So, getting students to start from the point of “What are we trying to figure out and why do we have to do this activity in order to figure that out?” …rather than “What are we memorizing, what are we learning because the teacher told us to?”

John: So it’s more of a project-based learning or inquiry-based approach to the discipline.

Kristina: Absolutely. And we’ve seen that a lot emerging in higher ed. So, it’s really great to see it reflected in the K-12 space too.

John: But it’s important probably for faculty to be aware of this, because if students are starting to use this approach, as they move forward, they might expect to see more of that in higher ed, where they might see it as a step backwards if they have to move to something that involves more rote learning, for example.

Kristina: Exactly. We’re seeing a lot less “sage on the stage”-type activities, both in K-12 and in higher ed. So it’s really important, I think, that we all kind of know what both sides of education are doing so we can at least know where our students are coming from.

Rebecca: How do you see this new approach helping students be better prepared for college?

Kristina: Well I definitely think that the idea of empowering students to be in charge of their own knowledge is really important. Sometimes I find that a struggle that my students have is doing this sort of figuring things out on their own. If I don’t give explicit instructions with explicit rubrics, they sometimes feel very lost. And so empowering them to recognize themselves as people who can ask questions and figure out the answers to those questions, that goes far beyond just physics class. That goes into just being a responsible and productive member of society. So, I think hopefully we can see students taking a little bit more ownership in their learning because of these trends at K-12.

John: Does it also perhaps give students a little more motivation when they have a goal in mind, and they know why they’re doing things rather than just doing it because their instructors told them to?

Kristina: Yeah, I would definitely think so. I definitely remember my seventh grade year not being passionate about the science, other than “Wow, cool. It’s a dead frog.” So thinking about empowering students to ask these questions might get them more excited about what they’re learning about.

John: In one of our earlier podcasts, we talked to Josh Eyler, who emphasized the importance of curiosity and nurturing curiosity and this approach seems to be very nicely tied into that.

Kristina: Absolutely. And I think about my own political science classroom. One of the fun activities I’ve done and I swear the first time I went through it, it was one of those days where I thought, “Ah… I’m tired. I don’t have anything that I’m interested in lecturing about. We’re almost through this semester, what am I going to do today?” And so I decided, I’m just going to have the students write questions on index cards related to political science and hand them all in and I’ll answer all of the ones that I can. And that was one of the best days of class. I’ve recreated that many times in semesters. And so seeing that these Next Generation Science Standards where we’re trying to get students to think there are some things you learn about each discipline, but there are some practices and concepts that apply everywhere and you just learn how to ask the right questions and you use these concepts and practices to answer them. It’s something that I’m using in my political science class, even really, before I realized that I was specifically doing so.

Rebecca: Do you have any idea how students are responding to this curricula?

Kristina: So every individual curriculum and program is going to be a little bit different, but they are all going to tie into these main ideas. And one thing that we’ve seen in student performance and student preferences is that the students really like doing things in class, having activities and hands on specifically to science. Of course, that often means labs. But one thing that I often talk to teachers about and get a lot of really good feedback on is the idea that we kind of think of doing science looks like it’s in lab coats with safety goggles, but we all know as researchers ourselves that science looks like talking sometimes. And sometimes it looks like asking questions, and sometimes it looks like taking notes or revising models, and getting the teachers and students to realize that that’s all part of what doing science is. They get really excited at the idea of doing science themselves. Of course, they like to see things explode in class, but sometimes just getting them the opportunity to have discussions with each other. It’s amazing to me what the middle school students are capable of, and our elementary age students, what they’re capable of. I have kids myself and I didn’t know that they were learning such higher level concepts of science in class.

Rebecca: There’s big movements to move STEM to STEAM. Is the humanities represented in this new model?

Kristina: So, when we think about STEM, that’s kind of what everyone’s prioritizing these days: the science, the technology, engineering and mathematics… and the A to add it to STEAM would be the arts. So the idea that the arts are also important, but I think there are some key pieces missing here. When we focus exclusively on STEM and on creation and innovation, that’s really good. We need creation and innovation. But as I feel like sometimes we’re learning right now, without a good background knowledge of history, we might be creating and innovating things that either already exist, or have already been tried, or that don’t have a good basis in what we’ve experienced as a society. It’s like they said on Jurassic Park, you spend so much time wondering whether you can and you don’t stop to think about whether you should.

Rebecca: So you were just raising that question about ethics and things like this. So,how do you see this curriculum evolving so that the humanities are better represented or integrate more into our integrated learning in K through 12?

Kristina: Well, one thing that I think is really great about the NGSS is that it definitely starts to sort of de-silo the disciplines of science. So, when we think about physics and chemistry and earth science and life science, when I was in school, those were all completely separate years, both in middle school and in high school. And the NGSS standards definitely start to recognize that we can’t silo our disciplines like that because they have so much to speak to each other. Some questions you need many disciplines of science to answer. And so I’m hoping that slowly, more and more curriculum writers will apply that same standard to the humanities, to the social sciences, and to the arts, the idea that nothing can truly be siloed because social science speaks to even questions like “What scientific research do we do? What research questions do we ask?” That can’t be explained using natural sciences alone. Because yes, natural sciences might seem really unbiased, but we’re asking certain questions and we’re not asking others. So using social science and humanities to help answer those bigger questions. I’m hoping that we see less siloing across disciplines over time. And even at universities, we’re starting to see increases in things like cluster hires, where multiple people from different disciplines all come at a sort of similar question, kind of like what we’re doing here. We’re three people from very different disciplines. But we’re all interested in the question of, you know, what makes teaching good or bad.

Rebecca: One of the questions that’s risen a lot in higher ed, and I know as a popular conversation on our campus, is about fake news and debunking pseudoscience. Do you see that this curriculum helps with that,? …perpetuates that?

Kristina: I think that’s a really good question, and kind of a difficult one, because I think it’s really important to teach students how to interpret the world around them, and what science is and how it’s done, because that can help us determine the validity of the information that we get. But I also think, like we were just talking about, there is a move away from rote learning, from the idea that an expert in a field tells us what is true about that field and we learn it. The fact that we’re moving toward anyone can be an expert, anyone can do the research themselves, anyone can ask questions. Sometimes, I also worry that that pendulum might swing too far, because that’s sometimes where we get people who go online and find whatever Google can tell them about vaccines not being safe or about climate change not being real. And because they feel empowered to be their own expert, they’re treating themselves and their research as equivalent to people who have devoted their lives to getting advanced degrees and who know the answers to these questions. And so I worry that maybe we’ll see the pendulum swing a little too far in the other direction, but I’m not sure.

Rebecca: Based on knowing what you know about higher ed and what you know about this science curriculum, what do you think faculty should be thinking about in terms of what their students might know or might not know, or how they might know differently than they did before?

Kristina: I think that it’s important to teach students what expertise is to begin with, when we think about what it means to be an expert and know something. So, when we go back to those next generation science standards, and think about those three dimensions, the disciplinary core ideas, to me, those are the things that experts already know and that we can accept as the core ideas of each discipline. So, starting from that point and saying the question of vaccine safety has already been established, we know that the vaccines that are here are safe. That’s a disciplinary core idea. But now let’s use our science and engineering practices and our cross-cutting concepts to think about other types of preventative medicine that maybe don’t have the same consensus or new types of vaccines? How would we know that those are safe or how would we know that those are effective? So, I think it’s important not to forget about those disciplinary core ideas that are things that experts have already figured out questions that have already been settled, and then allowing people to start from that point and ask their own questions and do their own research using the scientific method.

John: Changing the topic just a little bit, we get a fair number of people who are interested in the STEM fields when they’re in middle school and even high school, but then they get to college, and all of a sudden, they have to start taking calculus classes, and Matrix Algebra, and Organic Chemistry. Is there any way that perhaps lessons learned from this approach could be used to make college classes more effective and not having so many people get lost along the way once they hit these courses that have been traditionally a bit of a barrier to progress in those areas?

Kristina: That’s a really great question, and we even see that in political science. I teach our research methods class in political science and it has just the tiniest bit of statistics in it. And students are like, “Why am I doing math in a political science class?” And then of course, in graduate school, we’re seeing increasing amounts of quantitative knowledge needed to finish graduate programs and then to compete on the job market. So, I definitely think that the rise of math as something important is a deterrent to some students who might otherwise be interested in entering STEM or social science fields, but I think that also comes down to the pendulum again. I think that it’s important to realize that quantitative methodology is a method of understanding scientific questions, and you don’t have to use quantitative methodology to answer every scientific question. Some of them can be answered using qualitative methods, and even discussing political theory or other types of theories in other sciences or in the humanities. I think it would be good if we could open up the doors a little bit to people who have really high level intelligence and interest and curiosity, but maybe don’t have an interest in math. I think both by making math more accessible and less required, we might be able to get some really interesting new perspectives in our college level courses. I don’t like the idea of using hard math classes as a way to weed students out. And I think that’s sometimes what they’re used for, because I took Matrix Algebra in grad school, and it was really hard. And I’ve never used it since that class… ever again. So it’s not as though it was a skill I needed to be a PhD in political science. It felt more like a class that was used to weed out students who weren’t as interested or weren’t as good at memorizing how to do Matrix Algebra.

John: The point I was trying to get to, I think, is that perhaps if more of these inquiry-based methods were used to motivate the material, it could help get past that. I actually had a similar experience with Matrix Algebra. And when I was learning, I was able to do the proofs and work through it, but I didn’t really understand it until I started using it in econometrics and other disciplines, when all of a sudden it just made so much sense and why all those theorems were there and useful. But we lost a lot of people along the way there. And perhaps that’s something we could build into all of our classes to help motivate students and not just hit them with a lot of theorems and not necessarily even just rote learning, but a lot of inquiry for which the motivation may not be obvious to people when they take it.

Kristina: Definitely. And I think that when I teach my Statistics and Research Methods class, it always is easier for the students, and they always do better, when I tie the math we’re doing to a real question. So even something as simple as “We’re trying to figure out whether the average American is conservative or liberal,” and this is our question that we’re trying to figure out. Now we need to do a difference of means test to figure it out. And so that would be, going back to what we were saying earlier, the idea of you walking into my class and asking my students what they’re doing. Well, they could answer “We’re memorizing how to do a difference of means test from chapter 12 because Dr. Mitchell told us to,” versus saying, “Well, we’re trying to figure out what the ideology is of Americans from different regions, so we have to use this mathematical test so we can answer that question.” So really about framing it in terms of “What are you doing and why are you doing it?” and making sure that we know that the students would answer in a way that gets them excited about the material.

Rebecca: I think context is everything. The real world problems that you’re talking about in the new science curriculum is not unlike the kinds of things that you’re talking about in your classes or even when you have to use math in design class. So, a lot of visual arts students think math is completely irrelevant to them, but when it’s put in context, when you need to do certain things, all of the sudden it makes more sense. I teach a creative code class and we do fairly complicated geometries there, actually. And if you can see the results, sometimes it makes a lot more sense to some of our students.

Kristina: Exactly. So the fact that they would know why they’re doing this and it’s to accomplish a specific goal, rather than just “We’re memorizing this because the professor told us we had to, it was going to be on the exam.”

Rebecca: Yeah. [LAUGHTER]

Kristina: Lord, help us for how many times we hear “Is this going to be on the exam?” That seems like the motivation for trying to learn something. And it would be great if we could move it away from that being the motivation, toward the motivation being “Well, we’re trying to learn this because it helps us figure out this question or this design problem.”

Rebecca: Or the motivation, like, “Hey, I really need to understand this mathematical principle, because I really want to know the answer to this question.”

Kristina: Exactly.

Rebecca: And that leads to where they actually start asking for the things that we’ve prescribed previously. [LAUGHTER]

Kristina: Yeah, and it becomes just a tool to figure things out. And if they want to figure the answer out, then they’re going to need all the tools.

John: Could you tell us what this would look like if we were to stop by a seventh grade class, and this was being put in practice?

Kristina: Absolutely. So if we think about what a seventh grader might be doing, so if we start from that point of the goal is to figure something out, and maybe they’re learning about Space science. They’re learning about Earth and Space and trying to figure out “Why do some objects in Space orbit other objects?” …like “What does that mean? How does that happen?” So, one really fun activity that I’ve seen middle schoolers doing is they have these embroidery hoops and these marbles. And so what they do is they put the marble in the embroidery hoop, and they sort of spin it around on the table. And so the marble is swirling in circles and then they lift the hoop and marbles start shooting everywhere. So it’s very funny in a seventh grade classroom, because you got kids running everywhere trying to chase their marbles. And so at first, they’re just having fun, tracking which way the marble goes and trying to figure out when they lift the embroidery hoop which direction will the marble head, and then eventually they start realizing, “Oh, well, the marble kind of wants to go straight, but the embroidery hoop is keeping it going in a circle.” So, if we think about the sun, with the planets orbiting it, if the sun suddenly disappeared, Earth would kind of want to go straight out in whatever direction it was headed. But because the sun’s gravity’s in the middle, it’s keeping Earth going in a circle around the sun. And so they start putting these pieces together and eventually they come up with this idea of the relationship between inertia, which keeps the earth going, and gravity, which is what keeps it in that same orbit. When they think about what is the core idea they’re learning about, well, they’re learning about orbit, but the way they’re figuring it out is by looking at this small model of what is actually happening at the planetary level. And that’s really reflective of the kinds of things that scientists do in their labs. We’re running models that try to simulate what’s happening in space, or what’s happening in the political world, or whatever discipline we’re doing. We’re trying to create these models to help us understand it. And so that’s what the students are doing, too.

John: That reminds me of a talk that Eric Mazur has given in several places, including at Oswego, where he talked about the Force Concept Inventory, and how, while students were able to plug numbers into formulas and solve problems very well, when they were asked about questions like that, specifically, if I recall, “Suppose that you’re swinging a rock on a sling, and you release it, what would the motion look like?” And basically it ends up flying in essentially a straight line… well, other than the effect of gravity. But when people were asked that, they would bring up things that they had seen in cartoons where they expected it to loop through the air, perhaps as it’s moving. That’s actually one of those things where people in really good institutions who had taken a college class had some really poor intuition. And this type of practice can help prepare them with better intuition on which to build later.

Kristina: There was also a video at, I think it was Harvard’s graduation, where they asked a bunch of STEM majors who had just graduated if they thought they could make a little circuit that would light up a light bulb. And so they handed them everything they would need to do, and everyone’s like, “Oh, yeah, yeah, I got this no problem.” And they couldn’t, they couldn’t figure out how to light the light bulb up, because as much as they had done the math in class, they just had never really done the practical aspect. And so getting students hands-on to do the things with those science and engineering practices in whatever discipline we’re in. It’s really important to get our students in the driver’s seat to start practicing what they’re going to be doing when they leave the classroom.

Rebecca: It also seems like having multiple pathways to the same information is a good way to play with our memory, and make sure that it sticks and it stays there. So, something that’s embodied, something that you memorize, something that’s a couple different kinds of examples.

Kristina: Exactly. Maybe it can move it from our short-term back to the long-term memory to help us keep that knowledge.

Rebecca: So we always wrap up by asking “What’s next?”

Kristina: So I think I’d really like to start exploring what this does look like in a classroom setting for myself. So rather than just focusing on what it looks like for students in K-12, I’d like to see if I can use a similar style of teaching in my political science classroom, and just see what kinds of evaluations I get and how the students like it. I think the idea of getting rid of these silos and recognizing that we all use the same practices and concepts could help us with keeping our college experience for our students interesting and consistent. And we start realizing that they’re going to learn in each of our disciplinary core ideas, but there are a lot of things that we all have in common. So, I’m really going to try this semester, maybe my student evaluations will suffer greatly, but we all know from my past talks that they’re biased anyway. But I just kind of want to see what it looks like if I let my students take a little bit more of a driver’s seat in asking the question, “What are we going to figure out? What do we want to know about the world?”

Rebecca: Do you have a piece of this semester that you’re most excited about that you already have planned in this domain?

Kristina: Well, I’m doing the research methods class this semester, which of course, involves some math. And I think that I would like to use their ideas about what kind of data we should be looking at and what kind of questions we should be answering. Because I think that’ll make it a lot more meaningful for them, rather than if I say, “We’re going to look at the American national election study,” letting them figure out “What question do you want to answer?” And then I’ll teach them whatever method it is that they need to know in order to answer that question. So, we’re going to try it. We’ll see how it goes.

John: In a past podcast, Doug Mckee talked about a similar situation in his econometrics class where he was using a time-for-telling approach. Where basically you face students with problems and let them wrestle with it a bit before giving them some assistance and helping them resolve things, and there’s a lot of evidence that those techniques can be really effective.

Rebecca: So, it sounds like well wishes on your new adventures. [LAUGHTER]

Kristina: Thank you.

Rebecca: Thank you so much for joining us.

Kristina: Of course, this is great. It’s always great. I think eventually I’ll have to come visit y’all.

John: That would be great. Well, thank you.

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John: If you’ve enjoyed this podcast, please subscribe and leave a review on iTunes or your favorite podcast service. To continue the conversation, join us on our Tea for Teaching Facebook page.

Rebecca: You can find show notes, transcripts and other materials on teaforteaching.com. Music by Michael Gary Brewer. Editing assistance provided by Brittany Jones and Savannah Norton.

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110. Fostering a Growth Mindset

Some students with fixed mindsets enter our classes expecting to be unsuccessful while others believe that they have a natural talent in the discipline. In either case, these students often get discouraged when they experience challenging tasks. In this episode, Sarah Hanusch and John Myers join us to discuss how they have revised their classes and used metacognitive exercises to help students develop a growth mindset and to recognize the benefit of learning from mistakes. Sarah and John are both Assistant Professors in the Department of Mathematics at SUNY Oswego.

Show Notes

Transcript

John K.: Some students with fixed mindsets enter our classes expecting to be unsuccessful while others believe that they have a natural talent in the discipline. In either case, these students often get discouraged when they experience challenging tasks. In this episode, we examine how two faculty members have revised their classes and used metacognitive exercises to help students develop a growth mindset and to recognize the benefit of learning from mistakes.

[MUSIC]

John K.: Thanks for joining us for Tea for Teaching, an informal discussion of innovative and effective practices in teaching and learning.

Rebecca: This podcast series is hosted by John Kane, an economist…

John K.: …and Rebecca Mushtare, a graphic designer.

Rebecca: Together we run the Center for Excellence in Learning and Teaching at the State University of New York at Oswego.

[MUSIC]

Rebecca: Our guests today are Sarah Hanusch and John Myers. Sarah and John are both Assistant Professors in the Department of Mathematics at SUNY-Oswego. Welcome, John and welcome back, Sarah.

Sarah: Thank you.

John M.: Thank you.

John K.: Our teas today are?

Sarah: None today

John M.: Yeah, imaginary tea. No tea for me.

Rebecca: The imaginary tea…that’s what my daughter likes to drink. That kind.

John M.: Yeah, I’m in good company there&hellp;

Rebecca: I have English afternoon.

John K.: And I have a ginger tea.

Rebecca: We invited you here today to talk a little bit about how you’ve introduced a project on metacognition in some of your mathematics courses. Can you tell us a little bit about the project?

John M.: Sure, this began, I believe, in the spring of 2018 in a Calculus I course. And the idea was that, Calculus I is known across, basically the entire country…every school in the country…as being a very difficult course. So, you have a lot of students who are coming in, especially in the spring semester, who had bad experiences with calculus in the past. And in particular, I’ve been told by some colleagues that there’s going to be some students in there that more support than I suppose you would imagine. The situation was that on the very first day of class, I had students coming in who have had bad experiences with it in the past. And then at the same time, I have the students that are typically high performing. And they have difficult times also with perfection, you know, being obsessed with 4.0s and grades and that type of stuff. So the idea was that I wanted to simultaneously address failure with the students and perfection at the same time. And I was sort of led to think about this metacognition project, actually, funnily enough, on a flight back from San Diego. I was at what are called the joint meetings for mathematicians, and a lot of progressive newer teaching techniques are talked about at this conference. And I’m flying back from the conference on the airplane and I’m getting really introspective and I’m thinking like, I really need to do something to talk to my kids about failure and perfection. And then it occurred to me that there was this blog post that I had just read a couple weeks before by a mathematician by the name of Matt Boelkins at Grand Valley State University. And he had this idea for a metacognitive project that addressed all sorts of things like growth mindset, fixed mindset, productive failure, and all these different things. And I decided about a week before classes started that this is what I was going to do.

Rebecca: That’s when all the best ideas happen.

John M.: I know…right before class and on an airplane. I get really introspective when I’m on airplanes and staring out the window and thinking of all the big things in life and stuff.

Sarah: And essentially, John came to me and said, “I’m thinking about doing this project.” And I said “Well, that sounds cool. And let’s see if we can measure if it has any positive effect or not.” So, I sort of came in on the research side of it…of “let’s see if this is effective for changing attitudes towards mathematics.” And since then, I’ve stolen the project to use in my own classes. But, it really started as I came in sort of more on the research side of things

John M.: I think stolen might have been a strong word, but…

Sarah: I didn’t ask…I just took it. [LAUGHTER]

John K.: For the research project did you do pre- and post-tests on attitudes?

Sarah: We did a pre- and post-test, we use an assessment called MAPS which is the Mathematics Attitudes and Perceptions Survey. It’s a 31-item survey. It assesses, I think, it’s seven different dimensions. Some of them are growth mindset. Do they view mathematics as being answer focused or process focused? The categories were growth mindset, the applicability of mathematics to the real world, their confidence in mathematics, their interest in mathematics, their persistence in mathematics, their ability to make sense of mathematics, and do they view mathematics as being answer focused or process focused?

John K.: Sounds like a good instrument. Before we talk about the results, let’s talk a little bit more about how you implemented it. How was the project structured in terms of what activities did the students do during the class?

John M.: So the idea was that over the entire semester, they would have a selection of articles online to read, they would have a selection of YouTube videos to watch and it was essentially experts that are addressing these various topics. So, like for example, there is a clip by Carol Dweck, one of the originators of the theory of growth and fixed mindsets, and they were to watch these clips and read these articles across the semester. And then I think it was probably with two weeks or three weeks left in the semester, they’d have to write a reflective essay. It was an attempt to sort of shift the culture in the classroom towards viewing mistakes and failure as productive and as opportunities for learning. Because I think in wider culture, everybody believes that math is just about the right answer. And that if you can’t get the right answer, then there’s no worth in whatever effort it was that you put in to get to that point. And I wanted to provide sort of a counterpoint to that, so a counter narrative. Being honest about how many times per day mathematicians actually do fail, you know, that type of thing. So yeah, the main component was this essay that was reflecting on the stuff that they read and watched over the semester, and then there was sort of like daily conversations.

John K.: Were the conversations online or were they in class conversations?

John M.: In class…in office hours, just kind of whenever they popped up. I remember a couple conversations that happened after I gave back exams, for example, or rather right before I gave back exams. So for example, I would say, you know, I’m about to hand back exams. And I want you when you see the score, when you put the paper over and see your score, I want you to immediately think how are you going to frame this result in your mind. Are you going to look at that score and be happy with it and chalk it up to just your natural talents? Or are you going to say, “Oh, this is a result of hard work?” And then if you’re not happy with your score, are you going to put it away and never look at again, or are you going to engage with your mistakes and make them productive mistakes? It was sort of intervention through conversation that happened on an almost daily basis.

Rebecca: Did you notice a difference in the kinds of conversations you were having in class because they were doing these readings and watching these videos, maybe conversations you hadn’t experienced before in the classroom?

John M.: Yes. In particular, I had students come into office hours and they were relentless with trying to understand the material because they knew that they were going to have another shot to get it right. And I had never experienced that before. In fact, in one of my student’s essays, I had a student tell me that when she’s not done well on exams in the past, she would just take the exam and stuff it into her book bag and never look at it again. And she told me that just because of because of how I was structuring the course that she doesn’t do that anymore. She actually pulls it out and engages with the mistakes and the comments that I put on the exam and comes and talks to me about the exam and everything. So I did see a change in the students.

John K.: Was some of it based on the reflections or was it also partly based on a restructuring of a course to give students more opportunities to redo things or to try things again?

John M.: I believe the latter had something to do with it. Because the idea was that I could say these things out loud to them. But I wanted to actually build components into the course in addition to the essay that sort of reflect the themes that I’m trying to communicate to them.

John K.: Telling them that they can learn from mistakes, if you don’t give them the opportunity…

John M.: Right.

John K.: …to learn from mistakes might not be as productive. I think both components are really valuable. I just want to make sure we were clear on that, too.

John M.: I think that you risk sounding like a cliche motivational poster, if you don’t actually put some meat on the bones with it.

Rebecca: Can you talk about some ways that you actually built that into the course?

John M.: I did test corrections. I don’t remember exactly, I think it was get back half the credit they missed or something like that. So, the idea was that they had to engage with the mistakes on their exams and correct them. And it had to be perfect. So they had a week to turn in their test corrections, and then I would re-grade them. This was very time consuming, as you might imagine, but the students I believe, really responded to it. It really sort of hooked in with the theme that I was trying to send.

Sarah: And since then, we’ve both moved to more mastery based grading. John before I did, but a system where students keep trying things until they get it right. And that really helps sort of drive that “learn from your mistakes” message home.

John K.: Are you able to do some of that in an automated way? Or is this all involving more grading on your part?

Sarah: The way I’m doing it, unfortunately, it’s more grading on my part. Although I will say this semester I’m doing these mastery based quizzes, but I’m not collecting homework. So, it’s kind of a toss up in terms of how much…it isn’t really extra grading. I’m just grading more things in another category.

John M.: Right, I would not do test corrections again. Not only was it a lot of time to grade, but then I had issues with academic honesty. The mastery based thing I have found is, I believe, much more effective.

John K.: Another thing you may want to consider that we’ve talked about in a couple of past podcasts is having a two-stage exam, where in the first stage, they do it themselves. And then you have them break up into groups and do either all the questions or a subset of those as a group. So, you’ve got some peer instruction going on as well…and that way it’s done right in class and it can be done, if the exam is short enough or the class period is long enough you can do both of it. A common practice is to do two-thirds say individual and then one-third for the group activity, which has many of the same things. They don’t know what they’ve gotten wrong, but when they’re sharing with their peers, they’re talking it over and it means you only have to grade the group exams on the second stage, which makes it a whole lot easier than individual ones.

John M.: Right. Yeah, I have a friend I believe he has done that stuff like that. So yeah,

John K.: The Carl Wieman Science Education Institute, I believe, has a lot of information on that. I’ve been doing it the last couple of years, and it’s been working really well. Doug Mckee was a guest on an earlier podcast, we talked about that as well. Are there other things we want to talk about in terms of what you’ve done in the courses?

Sarah: One thing that we’ve both done since this initial project is we’ve taken some of the ideas of this project, but interspersed it more throughout the course. One thing I know at the time that John observed was that he felt like a lot of the students started the projects in the last week, right? And so what I’ve done instead of doing a big project of these topics is I’ve taken these articles and done the second week of class, you have to read one of them and respond on it. And then the fourth week, you have to do another one, and so on. So it’s a little bit of it throughout the whole course instead of all loaded at the end. I think it helps having some of those conversations with the students as well because they’re not just seeing the ideas in the conversations. They’re not just seeing the ideas in the paper. They’re kind of seeing both and it just helps intersperse it a little bit throughout the semester. I know I’ve done that a couple times now. I think you’ve done that since as well.

John M.: I did a pre-semester sort of essay and then I did a post-semester essay. But it was in response to the first time we did that, which is referred into the paper, and one of my students actually told me in their essay, he was like, ‘Hey, I wish I had this at the beginning of the semester.” So yeah, it’s definitely like a “duh” moment. Like, I probably should have done something earlier in the semester, instead of waiting all until the end. But, you learn as you do these things, so. But the essays that the students wrote… I provided them with prompts just to alleviate any sort of writer’s block that they may have. But, the students who basically ignored my prompts and told me their personal stories were the essays essentially that I still remember. I had students that were straight A students that were telling me exactly what I thought was going to happen: that they’ve been the smart person their entire life, and they kind of feel trapped by being a smart person. They don’t want to take any risks because if they risk something and fail, then that’s their identity as a smart person, right? They’re not smart anymore. I’ve had students from the other end of the grading spectrum who basically told me that the first day they walked into the class before I even said anything, they were already convinced that they were going to fail the class. I had students tell me about mental health problems. I had adult learners talking about balancing life and school issues. I mean, it’s just absolutely amazing what they told me, they opened up basically. That made a big impression on me.

John K.: Tying into an earlier podcast, Judie Littlejohn and I had introduced something really similar where we have weekly discussion forums. And I also noticed the same sort of thing, that I got to know the students much better because when they were talking about some of the barriers or the issues they face, they were sharing a lot of details about their life. And you get to know them better and they also seem to form a little bit more of a tighter classroom community because they also got to know each other a little bit more.

Rebecca: It is kind of interesting how when students are talking about their process or who they are as learners, is very different than talking about the subject matter. And it does get them to open up and may be engaged with faculty in a way that they wouldn’t otherwise.

John M.: And I have found being honest about my own failures in the past has been a catalyst for conversation, right? Because they view us as professors, they view us as the authority figures, the experts in that we never fail. And basically telling them how many times I fail on a daily basis in my own mathematical research. It goes a long way, I think… finding common ground with them. And acknowledging how difficult the subject material is. I mean, there’s a reason that calculus has a high failure rate because it’s a hard course, among other reasons. Yeah, just having the humility with the students and kind of stepping down off of the pedestal in front of them, I think that it helps.

Rebecca: So do you want to share some of the results that you got from your study?

Sarah: We saw some very significant quantitative results. I mentioned the MAPS instrument is what we use. It’s a 31-point scale. Its reliability and validity has been established pretty well, especially in calculus classes. One of the things that they did was they looked to see if the items were consistent with expert consensus…. So, with how mathematicians view it and all of the items were valid with the attitudes of mathematicians except some of the growth mindset scales. Research says that that’s an important scale as well. And on this 31-point scale, we saw an almost 4-point improvement from pre-test to post-test…of the students becoming more aligned with the expert opinions, which is a really significant amount…I mean, almost 10% improvement, which is even more remarkable, because when this assessment was first validated, they found that there was usually a negative result from taking a Calculus I class. So, the attitudes get worse pre-post in a calculus class and ours had statistically significant improvement. In addition, we saw statistically significant improvement among all of the sub scales. Now some of them were better than others. Some were just barely below .05 in terms of significance and others were much more significant. I mean, we really saw that over the course of this semester, they really did change their attitudes. We also had some evidence, as John’s already talked about, from their essays…where they said how they started to view mistakes as productive, and they started to feel like there was value in making mistakes and learning from them.

John K.: You mentioned alignment with an expert scale, can you explain that for our listeners?

Sarah: Essentially, what the original authors and it was Code et. al. that did this paper and develop this instrument. They gave this survey to students and they gave it to mathematicians and looked for alignment. Particularly they were looking for whether or not the mathematicians agreed on the items. And the idea was our goal is to get math students to have attitudes more like mathematicians, because that’s our goal, right? …is to develop future mathematicians. And so we would like those attitudes to get closer to how mathematicians view mathematics. They had high agreement among the mathematicians on every item, like I said, except one or two of the growth mindset questions. So, in other words, this survey reflects how mathematicians view mathematics. And that was how they determined the right answers on the survey, whether a particular item is something you should agree with or something you should disagree with. They went with the expert consensus.

John K.: So now, I may be misconstruing this, but are you suggesting that perhaps a lot of mathematicians had adopted a fixed mindset? So, there was a bit more variance there on that?

Sarah: I will say that was what the results of their validation showed.

John K.: Okay.

Sarah: And leave it at that. [LAUGHTER]

John K.: It does remind me of that study a few months ago, that found that when instructors had a growth mindset, the achievement gap narrowed and the drop-fail-withdrawal rate was much lower in courses, then for those instructors who had a fixed mindset. I think that maybe even more of an issue in the STEM fields than it is in humanities and social sciences, but I think it’s not uncommon everywhere.

Rebecca: I say it’s a common problem everywhere.

John M.: I’ll say it…mathematicians suffer from fixed mindsets. I’ll just say it, right? [LAUGHTER]

John K.: Many academics do.

Sarah: Yeah.

John M.: Yes, of course.

Sarah: I mean, the people who choose to become academics are often the people that were successful in school and they decide to continue with it. I mean, it is less likely that people who felt unsuccessful decide to keep going and to go into academia.

John K.: Selectivity bias there and that reinforces a belief in a fixed mindset, perhaps.

Sarah: Precisely.

Rebecca: What kind of response have you seen from students from…I mean, it sounds to me like this one study lead to good results, and then that changed many classes in that you’ve taught or the way that you’re teaching, how have students responded?

Sarah: Generally positively. I think doing the projects at the end of the semester wasn’t the best idea because they just feel so overwhelmed at the end of the semester with exams and projects and everything coming due. So, I did get some responses of “W hy do I have to do this now.” But generally, I think they appreciated learning about learning.

John M.: I think that given the opportunity to talk about their past experiences, I think they appreciated that. For the most part, I’ll agree with Sarah. I think that the message landed with an awful lot of students like I wanted it to. Some of my favorite essays were students who told me that they thought I was crazy on the first day. I mean, you go into a math class to learn math, you don’t go into a math class to study metacognition, or whatever it may be. I had one student the first time around, who basically told me it was all a load of crap, like why this is not working at all. And I had a student the last time that I did this, she was very skeptical towards the end even. Basically, aliken it to just some cheesy self-help stuff. I think that most students responded positively.

Rebecca: Have you seen the response impact other faculty in your area? For example, if they really liked having those techniques and things introduced in your class, have they asked other math faculty to do that in future classes or are you finding that its not many math students who were actually in that particular class?

Sarah: We haven’t done any tracking, so I don’t know where his students have gone. I mean, I’m sure some of them went on to Calc II…I’m sure some of them did not. Right. I mean, I guess most of them would have had Jess the following semester, right? Did she say anything?

John M.: No, she didn’t say anything. I’m teaching Calc III right now, and I have some of my former calculus students that were in this and they’re doing well.[LAUGHTER] Small sample size, but yeah, they’re doing well.

John K.: That could be an interesting follow up though to see how successful they were in the subsequent classes.

Sarah: Yeah.

Rebecca: Sometimes we’ve heard anecdotes, of departments and things when there’s been change that if students really respond well to whatever the techniques are, that they will demand it of other faculty members, and John’s talked about this before in economics.

John K.: Yeah, when you can show results…

Rebecca: Yeah.

John K.: …that there’s been some gain, and especially if it comes from students at the same time, it often puts pressure on other people in the department because if you’re able to show people that your technique has been successful and students are coming in and saying, “G ee, I wish you would consider doing this. I did this in my intro classes, and it was really helpful.” That sometimes helps make change much easier.

Sarah: Yeah, so one of the things that we did look at was we compared the final exam scores of John’s sections to the other sections of calculus that semester. Now, there was some other issues that clouded that data a little bit. His scores were a little bit lower than the other instructors. But what was really surprising, essentially, if you look at, I don’t remember if it were just the final exams or the semester grades. The DF rates were the same among the sections, but the withdrawal rates were significantly different. And that almost no one withdrew from John’s sections. I think there were two if I remember the data correctly, whereas there was like five or six on average from the other sections. And so the DFW rates were different, but the DF rates weren’t. So I just thought that was an unusual circumstance. So, it seems like the students were sticking with his class… and pushing through.

John K.: And if there is a larger portion of students staying with the class, then perhaps a slightly lower average grade is not necessarily a bad sign…

Sarah: Exactly.

John K.: …because student success is partly measured for persistence to completing the course.

Sarah: Exactly. I think because there were more students who stuck it through to the final exam, then his final exam scores ended up being a little bit lower. But again, if you looked at like overall course grades, they ended up being pretty consistent, other than the W rates. I wanted to make sure that there weren’t significant differences in the rates and I think it was just shy of being statistically significant. Like, if you had one more student that would’ve been significant. But just to make sure that, especially like adding the test corrections in wasn’t substantially making the class too easy, right? Because that’s often a critique that, you know, “Well you make these changes, but is that just making the class too easy and people who aren’t really prepared, are they passing?” And so I just did this analysis of the, like I said, it was really just a t-test analysis, but just to see whether or not it was significantly lower and it wasn’t significant. It was lower, right, just not significantly. And then like I said, I looked at retention rates just more as an explanation for why the average was lower.

John K.: In a lot of studies of interventions, the dependent variable is the drop-fail-withdrawal rates, because that’s a measure of success in completing the course. That by itself could be an interesting focus of a study. I’ve been running this metacognitive cafe in my online classes for a while and I did have a student in the class who wrote a few times about the metacognitive development that was introduced in one of your classes. They didn’t specify who but they said, we’re also doing some work on metacognition in the math class, and they said it was really useful and it was nice to see it in two classes.

Sarah: Yay!!

John M.: Good.

John K.: So there’s at least one positive data point there or one additional data point there. So are you going to continue this in the future? And if so, what might you do differently?

Sarah: Well, I think we’ve mentioned already that we’ve worked on including some of the ideas at the beginning of the semester and throughout the semester, rather than one project at the end. For the reason that it really benefits them most at the beginning of the semester when things are getting started. I think we’ve also both changed different things about our grading systems to incorporate more opportunities for growth.

John M.: The last time I did this, I introduced some articles that were a little bit more rigorous with the data and the science, because I sort of wanted to counter that kind of criticism that all this “Oh this is just a bunch of TED Talks…” that kind of thing. So, I really wanted the students to see some of the science behind it, the science of learning, because I really wanted to send that message that “No, this is not me just standing up here saying, ‘Oh, this is going to help you or anything, right?’ This is actually stuff that researchers have thought about before.”

John K.: I had a very similar response the first time I did this. I had a video I posted which was a TED talk by a cognitive scientist who talked about research that showed that learning styles were a myth. And some students had come to believe in the existence of learning styles because they’ve heard of them and often been tested, multiple times in multiple years, on their learning styles. Sometimes even through college and that’s rather troubling. The students said, “Well, this is just one researcher, I’m sure there’s lots of other studies. I don’t believe it because it’s not consistent with what I’ve always been told or what I’ve heard.” So I decided to modify it then and I added to that discussion, five or six research studies. In case you don’t believe this TED talk by someone who’s done a lot of research on this, here’s a number of studies, including some meta analyses of several hundred studies of this issue, and that has cut much of that discussion. They’re less likely to argue against it when it’s not just a talking head or not just a video when they can actually see a study even if they don’t understand all the aspects of it.

Sarah: Yeah. So I think that’s one thing we’ve tweaked what articles and what videos are we showing. I know the semester I gave my students a article that had just come out this September, that students perceive active learning as being less efficient, even when they’re learning more. In some physics classes at Harvard, they gave two weeks at each thing… two weeks of active and two weeks of lecture, and then they had them switch. And the students learned more with the active learning, but felt they learned less. And my students have been feeling frustrated because they feel like they’re not learning enough and that I’m not telling them what to do.

Rebecca: You’re not “teaching” them.

Sarah: I’m not teaching them. And we spend the class period, letting them vent. So all their feelings were out in the open. But, then I sort of countered with this article saying, “Look, I promise you really are learning things. You just don’t feel like you are. But you really, really are. And you’re actually learning it better than if I were using a different style.” So, that’s one way that we’re tweaking the articles because sometimes the research comes out that’s pertinent.

John K.: We refer to that Harvard study in a few past podcasts. We touched on it in a podcast that will release on October 9th. I haven’t shared it with my class yet, but I’ve been tempted to.

Rebecca: What was the discussion like talking about that particular article? Given that they were frustrated?

Sarah: I mostly was just trying to acknowledge that I understand their frustrations…and that, yes, the way I’m teaching this class can be frustrating. I agree. Sometimes I get frustrated about it. But I know that ultimately, they are learning things and that they are going to be stronger writers and stronger students of mathematics by using this structure. And so I kind of use it as evidence of I’m not changing.

Rebecca: So I hear you…

Sarah: Yeah.

Rebecca: …nut…

Sarah: I hear you, but…

John K.: I had this very conversation with my class today. They’re coming up for an exam very shortly. And I asked them, how did they review before an exam and the most common answer was they like to reread the material over and over again. And I mentioned some of the research on that. And I said, the best way to review is to work on problems with this. And I gave them several ways in which they could do that, that are built into the course structure. And I said, “But that doesn’t feel as effective. Why?” And one of the students said, “Well, I get things wrong.” And I said, “And when would you rather get things wrong, when you’re reviewing for an exam, or when you’re taking exams?” And I think some of them got that message. So I’m hoping we’ll see when they take the test next week.

John M.: Right? It seems like anytime you do anything that’s just not a standard straight lecture, there’s a certain amount of buy in that you need to get from the students. And sometimes that can be very difficult. There’s almost a salesmanship that you have to do throughout the semester to make sure that everybody’s on the same page and to kind of fight those feelings where the students give you a lot of pushback. Yeah, that’s the great fear is that when you innovate or you experiment that’s going to go horribly wrong. And sometimes it does, but, you know, we still keep going.

John K.: Because students are creatures of habit. They’ve learned certain things and they want to keep doing things the same way. And anything new can seem troubling, especially if they’re getting feedback along the way that says they need to work more on things…that’s not as pleasant as rereading things and having everything look familiar.

John M.: Right

Rebecca: Passively sitting in a lecture when things all seem like it makes perfect sense to you, because an expert is describing it who knows what they’re talking about, right? Always feels easier than trying to apply it yourself. And I think that students, even though the lecture might feel better, and learning is hard…over time…at the end, when they’ve seen how much they’ve accomplished, and you do have them reflect…many of them appreciate or come around. Sometimes, it’s not in that same semester, sometimes it’s emails, months or years later.

John K.: Yes.

John M.: Right. Right, right.

Sarah: If only if we could do course evals, you know, a whole year later,

John K.: Or five years later. That may not work too well in my tenure process, though.

Rebecca: We always wrap up asking what’s next?

Sarah: Well, the first thing is we’re hoping our article gets published. It’s been submitted. We’re waiting for reviewers. I’m going on maternity leave next semester…that’s really what’s next.

Rebecca: Sounds like a new adventure.

Sarah: It is a brand new adventure.

John M.: Wow, I don’t think that far ahead, I guess. Yeah, I guess I’m that unoriginal, huh. But, yeah, no I’m just trying to…

Sarah: We’re moving to a new building.

John M.: Yeah, moving to a new building, and getting a new department chair. Yeah, that’s right.

John K.: A new desk to go with the chair?

John M.: No. Ah… Yeah, funny, funny, funny.

Sarah: if only…

Rebecca: Well, thanks so much for joining us, this has been really interesting.

[MUSIC]

John K.: If you’ve enjoyed this podcast, please subscribe and leave a review on iTunes or your favorite podcast service. To continue the conversation, join us on our Tea for Teaching Facebook page.

Rebecca: You can find show notes, transcripts and other materials on teaforteaching.com. Music by Michael Gary Brewer.

John K.: Editing assistance provided by Brittany Jones and Kiara Montero.

107. Project NExT

Faculty beginning their teaching careers often rely on the teaching methods that were inflicted on them when they were students. These practices are not always consistent with evidence on how we learn. In this episode, for Assistant Professors from the Math Department at SUNY-Oswego join us to discuss how our math department is transforming its instructional practices through the use of professional development opportunities provided by the Mathematical Association of America.

Show Notes

Transcript

John: Faculty beginning their teaching careers often rely on the teaching methods that were inflicted on them when they were students. These practices are not always consistent with evidence on how we learn. In this episode, we examine how one department is transforming its instructional practices through the use of professional development opportunities provided by its national professional organization.

[MUSIC]

John: Thanks for joining us for Tea for Teaching, an informal discussion of innovative and effective practices in teaching and learning.

Rebecca: This podcast series is hosted by John Kane, an economist…

John: …and Rebecca Mushtare, a graphic designer.

Rebecca: Together we run the Center for Excellence in Learning and Teaching at the State University of New York at Oswego.

[MUSIC]

John: Today we are joined by four assistant professors from the Department of Mathematics at SUNY Oswego. Our guests are:

Sarah: Sarah Hanusch.

Rasika: Rasika Churchill.

Jessalyn: Jessalyn Bolkema.

Zoe: And I’m Zoe Misiewicz.

Rebecca: Welcome everyone!

John: Our teas today are:

Rasika: I’m having Earl Grey.

Jessalyn: I just poured myself a cup of lemon ginger.

Sarah: I’m not having any tea today. I’m not much of a tea drinker.

Zoe: I’m not having any tea today either. I just haven’t unpacked to that point yet.

Rebecca: And I have… English afternoon.

John: And I have Bing Cherry Black Tea. So, we invited you here to talk about Project NExT, which is something that people in our math department have been involved with. Could you tell us what Project NExT is?

Sarah: So, Project NExT stands for New Experiences in Teaching. It’s a program that is sponsored by the Math Association of America that brings new mathematics faculty…so you have to be in your first or second year of a full-time job…but they bring these new mathematicians in from all over the country to teach them about active learning.

Rebecca: How did your involvement, or the department’s involvement, with Project NExT get started?

Sarah: I learned about it as a graduate student, and was highly encouraged by a lot of people to apply. And so I kind of brought it into the department by saying, “Dear Department Chair, will you pay for this?” And since then, in part because of my starting it, we’ve encouraged everyone we’ve hired to apply. And as a result, there’s now five members of the department that have either completed or are still in Project NExT.

Jessalyn: Yeah, I will echo that experience. It was something that I was aware of as a graduate student, in part because some of my mentors had gone through Project NExT…it’s now 25 years old…just celebrated 25 years. And so for me, it was something that I knew I was interested in. And in fact, when I visited Oswego for a campus interview, and the department said “Oh, yeah, we have Project NExT fellows on the faculty, and we would be happy to support you in that,” that was a really exciting and encouraging thing about the department.

Rasika: For me, actually, I didn’t heard about that before. But, when I got the job offer, it came with that. I said “Yeah, sure.”

Zoe: I was just hired this past year and so I’m doing Project NExT, but I think I can already see the effects that it has had. It was a program I already knew about, I really wanted to participate in. So, as I was going through the hiring process, one of the first things I would ask the chair at a place was “Would you support an application for Project NExT?” …because it does require a bit of funding. And so seeing that there were already multiple Project NExT fellows in this department was also a good sign for the department as a whole when I was thinking of what sort of department I’d want to be at. And so I think it’s just showing that it’s already been recruiting people who are interested in it already, at this point.

Sarah: I was just going to clarify a little bit about how the funding for it works. There’s actually no fee to participate in Project NExT. The way it’s organized is that you attend special sessions at three of the national conferences in mathematics. So, you attend two math fests in the summer, and then the joint math meetings, which is in January. And so these are big nationwide meetings in mathematics. And so the idea is that you’re going for some special sessions during the meetings. And then your first year, you go for a couple days pre-conference for the really heavy duty workshop. So, the financial commitment from a department is just the funding to go to those three conferences.

Rebecca: You mentioned active learning. Can you talk a little bit more about how those workshops and things are structured?

Zoe: There were a lot of workshops about active learning and just using evidence-based pedagogy, so saying not only active learning is good, but we have evidence to support it and here are some of the things that you could do in terms of active learning. And all the sessions obviously are structured with that in mind. So, we’re not just sitting there listening passively to someone tell us about active learning, but they really make sure you’re doing something, whether it’s a fun little game like building a marshmallow tower, or some other interactive activity in each session. The sessions aren’t only about active learning, there’s a lot about inclusivity and diversifying the profession. So, a lot of sessions on that, or maybe I just chose sessions on that. But, there’s also a whole professional development stream. So, there’s stuff about how to get started in your career in terms of grants and so on. It’s really a lot of everything in there.

Rasika: It’s categorized like if you interest on the tactile learning, so are you interest on the group work, are you interest on some other…you know, inquiry based and mastery grading and so forth. So, depending on your interest, actually, they give more opportunity to listen, go talk with people and have a conversation: what they had, what they tried and what failed and what succeed. Which is like a really nice thing for us, as a beginner, to see what people have gone through and what I should expect, and so forth. Actually, I was interested about the whole program.

Sarah: So, they do some three-hour breakout workshops where you get to go based on what your interests are. So, I did one that was focused on teaching future educators because that’s my background, but I doubt any of these other ladies chose that same session because that’s not their expertise and not what their job is going to be about fundamentally.

Jessalyn: I will add, I attended two workshops that stand out to me in retrospect. One on making active learning intentionally inclusive. That was all about inclusive pedagogies and ways to incorporate group work in the classroom in a way that benefits all students and allows all students to participate fully. I also did a longer breakout workshop that was building a toolkit for student-centered assessment, that was all about learning objectives and exam structures from a more experienced instructor. And then there are also facets of Project NExT that extend well beyond the physically meeting in person. So, as Rasika mentioned, there are lots of ways that you can navigate the workshop according to themes that are of particular interest to you. So, if tactile learning or kinetic activities are of interest, or you’re really focused on educating future teachers or whatever that might be, you might be encouraged to declare a goal for yourself in your first year related to one of those areas of interest. And then we’ve got little email exchanges that go on for people who’ve declared interest in one of those goals like “this email list is all about mastery based grading, check in when you’ve tried something. check in with your questions.” So, there’s a little bit of accountability built into that structure that these people know what you’re trying to do, and they’re going to check in with you on it. But, then just the larger structure of email lists is that you have this cohort of other new instructors who will fire off questions like, “Oh, I’m teaching this class next semester I’ve never taught before, what textbook might I use?” or “I had this really strange interaction in my classroom, and I’m not sure how to handle it” or “I think this part of my syllabus is just crashing and burning. Help! Has anyone been here before?” And so you have this sort of communal resource and the community experience of brainstorming and problem solving together.

Sarah: …and included in that they assign each of us a mentor. So, a more experienced instructor that’s a mentor is assigned to each person in the program currently, and it’s always someone that is outside of your department. In fact, they will not allow anyone to be a mentor who has a fellow in their department. So, as long as we keep having fellows, we won’t have any mentors here. But, what’s nice is when you do send emails out on that list of “I’m trying this and it’s not going well, help!” you do get responses from your peers. You also see responses from all of the mentors for that cohort, which I think is also valuable because sometimes they have a little more experience than your actual cohort.

Rasika: We have a group that people who are interested on the inquiry based or tactile work, they have their own little Zoom conversation whenever they have time together. You get to know all different schools, what they’re doing and, you know, share your experience.

Rebecca: Would you all like to talk a little bit about how Project NExT has influenced your own teaching?

Rasika: For me actually, I was really interest on the tactile experience from this Project NExT. So, I decided to do some activities this semester starting as a beginner and also some group work. And also something that… not exactly what I’m getting from the Project NExT, but it’s like I will say, part of the SUNY Oswego Reading Group, that I was so interested on the book that we are reading. And I decided to give a couple of pages for the students every week to read, and I assigned them 5% for the final grade that they have to read and write half a page to one-page report for me and tell me what they think. Do they think like it’s feasible for them to change and try and do the things in that nature? So far, it’s really going well, and I have good comments from students saying that “you are opening up different ways of thinking…that we were stuck and never complaining about everything. But, we are now having, you know, in a broader way of looking at the things about growth mindset and so forth.” So, I was speaking here and there like chapters from some interesting books. So, that’s what my experience so far this semester, as a beginner.

Sarah: I think for me, it just gave me a lot more lesson plans and ideas to draw from. I already had a pretty active approach to my teaching, but it just opened a broader view of what kinds of things could work well. Especially in some of the more tactile things available that can be helpful for helping students to learn.

Jessalyn: Within my own teaching, I think it’s been really easy or natural to draw on resources from Project NExT in setting up my class or setting up lessons. When I taught Calc I, on day one, we made zip lines out of ribbon and key chains and measured average velocities and it was fun and it was memorable and it got students working in groups and they reported at the end of the semester. “Hey, remember when we did zipline? That was fun!” and I 100% would not have pushed myself to do something that involved or non standard, I’ll say, without thecontext of Project NExT saying “Oh, just try one new thing each semester.” I completely overhauled the Calc II class to be entirely mastery based grading in response to some of my own frustrations with how I had been setting up my class. And Project NExT supplied a whole lot of resources, a whole lot of people, a whole lot of information and motivation to try something like that, which I think was helpful. As far as department culture goes, I think the fact that we’ve had this many Project NExT fellows and continue to have Project NExT fellows gives us a shared language to talk about teaching. Some shared frame of reference on “Oh, yeah, you know, this person who tried this technique,” or “Have you heard anything about…. “”…Oh, hey, this came through on my Project NExT list.” That I think has encouraged just our conversations about teaching and being intentional in how we’re structuring our classes, or how we’re handling things.

Sarah: I’m experimenting with mastery based grading this semester because of the information you and John got, from your experience in Project NExT. And so your experiments with it last year has led me to experiment with it this year. So, it definitely has changed just how we even hear about new things to try.

Jessalyn: That’s delightful. I appreciate that it’s trickling around.

Sarah: It is trickling for sure.

Zoe: So, I’d say it’s still obviously fairly early. We’re only one month into my first semester after going through the first part of Project NExT. But, I’d say a lot of it has been both an affirmation of things that I have been doing and also it’s sort of given me the confidence to do the things that I was doing even more fully and to advocate for these approaches, even though I am brand new in this department. So, I’m not afraid to send to the whole department email list like “we need to be more positive toward our students and not say that it’s all their fault if they’re struggling. we need to take responsibility for that.” Or just to try things that may or may not work well. For example, I’m doing mastery-based grading just of the homework in my general education math course. And I’m using an online system that,it turns out, is not that great for mastery-based grading of that course, even though I’ve used it for other courses. Students, I think, still benefit from it, but it’s not quite as effective as I might have hoped. But, I’m just willing to try these things and willing to speak up about things, so those are the main impacts in my courses.

John: Could you tell us a little bit about how you’ve implemented mastery learning technique?

Sarah: I think we’ve all done it a little different. Why don’t you start, Zoe, since you were just talking about it.

Zoe: I’ve done it only in the homework, so not in their exams. So, the homework is done online, it’s 15% of their grade. And so for each little subtopic, they have to do a little quiz. It’s five questions: three medium, one easy, one hard, and they need to get at least 90% on it. And they can try as many times as they want, but they do have to keep trying. And so, in courses like college algebra…is the one that’s most similar to where I’ve done it before…the material all builds on itself and it divides nicely into little component and there, I’d say it’s going well. The students complain about it at the beginning, but already after I asked them to reflect on their first test performance, a lot of people said, “Oh, it’s actually really helpful that I had to go back and keep learning these things until I fully understood them.” Whereas in the first couple of weeks, there’s always a bit of pushback about “Why do we need to get 90% on this. It’s too hard to get 90%…couldn’t it be lower?” And then once the results come in, they see it’s worthwhile. The other course I’m doing is similar, the gen ed math course…it’s also their online homework…15% of their grade, but that textbook just doesn’t break down the material into as nice sections and the questions are longer and the grading of the online system is pickier. So, that one has some issues, but the same basic idea.

John: Are you using publisher provided questions then, and tools?

Zoe: Yeah, publisher provided questions and tools.

John: Are you allowing unlimited attempts or is a limit on the number of attempts?

Zoe: Yeah, unlimited attempts, and flexible deadlines too. So, I do say they need to achieve a certain amount before each of the test. But, the idea is that if you haven’t yet mastered something, you can still go back and do it several weeks later. As you keep practicing the material, we keep building on it. So, it’s not that you have just one chance and you’re done. The goal is to get them all to understand it fully by the end of the semester.

Jessalyn: My approach to mastery based grading in my first implementation was to go totally off the deep end, and just structure the whole class with a mastery-based grading scheme. So, what this meant was that I did away with midterm exams, everything was broken down into learning objectives roughly correlated to the sections that we were intending to cover in the textbook. And the primary mode of assessment was quizzes. So, my students had quizzes that they could retake as many times as they needed to. And each quiz had three questions and I wrote problem banks of many many questions for each quiz. And in order to earn an A at the end of the semester, the expectation was something like, “Oh, you need 18 of your quizzes to be three out of three and the rest of you two out of three.” So, it was not a points accumulation scheme, it was just quizzes and repeated quizzes. They also had online homework through web work and that was unlimited attempts. There were deadlines, and they just needed to… there was sort of a threshold percentage associated to an A or a B, or a C. And then I had a few more other activities and elements going on. But, primarily, the structure involves these mastery quizzes. And I owe a great deal in the structure of this class to Laura Taalman from James Madison University, who shared a lot about how she structured her class that way and so I sort of borrowed and adapted from her setup for my experiment.

Sarah: So, my class is pretty similar to Jess’s. The main difference is I’m doing it in a proof-based course, so it’s fewer questions. She had three questions per objective. I have one, because they’re a little bit longer questions. The only exam in my class this semester is the final and that’s only because I’m required to have some common questions on a final exam. So, I had to have a final exam…instead I’m doing weekly quizzes. Each week, we add one to two new objectives. There’s about 20 for the entire semester. So, our first week we had two questions on the quiz. The second week, we had four questions on the quiz, but questions one and two were the same objective as one and two from the first quiz. So, the questions are just going to grow cumulatively…so our last quiz will have about 20 questions on it. Although I did tell them once everyone has mastered a question, it’s just going to say mastered, it’s going to be no new question writing and at some point, I’m going to recycle some of the early ones.

John: Your building in some interleaved practice and spaced practice as well.

Sarah: But, the idea is that once they have mastered a question, they no longer have to do it again. They’ll have the questions for practicing and for getting ready for the final. In addition to these mastery quizzes, I’m having them write a portfolio, which is going to have a little bit more of that interleaving practice and making sure that at the end of the semester, they still remember how to write some of these early proofs and it’s also to focus on the writing aspect. So, to help make sure they’re really using the language precisely. Sometimes with a quiz when it’s timed, you’re a little more flexible, but I want to make sure that they have that precision of language down by the end of the semester. So, I’m sort of balancing those two aspects of it that way. They have “unlimited attempts” in air quotes…restricted by what? …there’s 12 times I could quiz during the semester…13 for something…So, restricted to…they need to do number one all semester long. They can have all semester to do it, but we are eventually going to run out of time.

Rasika: So, for me, I haven’t tried to mastery based grading yet. Maybe in the future.

John: Are there any other new techniques any of you have used in your classes?

Sarah: I’ve done a lot of experiments with this idea of embodied cognition, where you actually have students sort of using their bodies to experience things mathematically. One way that we did this with my pre-service elementary school teachers, I give them a bunch of clothesline, and I have them make a circle. So, you may think, “Okay, no big deal.” But, what happens is, it’s not good enough until it’s a perfect circle. Part of this is to elicit the definition of a circle, because to non-mathematicians, I’m going to pick on you for just a moment, Rebecca, how would you define a circle?

Rebecca: One continuous line that’s in a loop.

Sarah: So, a lot of times they come up with something like that. Well, how does that distinguish, though, a circle from an oval. So, it’s not really a precise definition of a circle, right? With the precise definition is being it’s all of the points that are a fixed distance from the center. But, what happens is, by forcing them to make their circle better and better and better and better, they actually all know that’s the definition of the circle. Maybe they don’t remember it, but they know that there’s this radius thing involved. And so by not allowing them to sort of quit until they actually are in a perfect circle, the only way to do that is you have someone stand in the center, and you take another piece of clothesline to measure your radius, and you move everyone in and out as appropriate. So, that activity of physically making the circle and by having to have that person in the center, and that radius gets them to say the definition of the circle properly, first of all, but they get to experience it in a way that they don’t get to otherwise. And that’s an activity that I never would have thought of without going to Tensia Soto’s session at my first Project NExT meetings.

John: It is certainly safer than giving them all compasses with sharp points where they can stab each other, which was how people used to do it.

Sarah: We still do compass and straightedge constructions in geometry, but again, that doesn’t actually help you really understand what the definition is. I think doing this physically actually helps them understand why a compass works. I know that sounds silly, but it really helps make those kinds of connections. I have another activity where we take clothesline and I make a triangle on the ground, and I make them walk the interior angles of the triangle and you spin 180 degrees and it, again, helps them experience that the sum of the internal angles of a triangle is 180 degrees. And again, that’s something that, the first time I did it, it was baffling because first of all, it’s hard to turn the interior angles. Your instinct is to turn the exterior ones, but you end up backwards. From a geometry standpoint, it makes sense, but somehow that physical aspect just really changes things.

John: It makes for a much more memorable experience, where they’re seeing things from a different perspective. And I think that’s really useful.

Sarah: I agree. That’s why I do it.

Rebecca: Does anyone else want to chime in about how having so many fellows from Project NExT has influenced the larger department? Because you’re not just five people in your department, you’re how many?

Sarah: There’s 14 of us tenure/tenure-track now. I do think it’s changing the way some things are done. It’s slow going. I think everyone would concur with that. Jessalyns’s smirk is definitely confirming that. It’s slow going, some of us would like change to happen faster. But, I do think change is happening. I think there’s a lot of respect from our colleagues that we are trying new things. I think a lot of them have a “You can do what you want, but don’t make me change yet.” But, I think we’re starting to get them a little bit, too.

John: If your students are more successful, that often convinces people and sometimes when students say, “I did this in this other class and was really helpful,” that’s often really persuasive to other faculty. But, it’s convenient that you had so many people all come in at once, because that’s not typical in most departments that have such a large cohort, in a short period of time.

Sarah: We have had a lot of retirements, one right back on top of each other. So, we have had an influx of young faculty in our department, which…that alone…to have so many in this program as well. Definitely.

Rebecca: I think it really helps to have models of ways that you can do things because if you didn’t learn using these methods or you didn’t have exposure to that as a student, you have no way of knowing how those really play out unless you have examples. So, it sounds like Project NExT played that role for you, but then you are playing that role for other faculty in your department.

Jessalyn: Thinking about department culture more broadly, not just among discussions and relationship among faculty, but in terms of the student experience, and this engagement that we’re having from our majors and the sort of activities that we’re involving them in. I think there has been a Project NExT influence there as well. Sarah, you and John started the Putnam Competition before I came even and a lot of other conversations and gatherings have come out of that, like we’re getting together with our majors and talking about preparing them for graduate school if that’s something they want to do. The math club or other organizations have taken on a different role in the department and I think a lot of that comes out of some of the ideas in Project NExT, like hearing about how another department celebrates their students participating in something like the Putnam Competition. But, it also comes out of the relationships you build in an active learning classroom and the way that we connect with students when we are trying new things. And we’re being honest with them and saying, “Hey, I’m trying something new. And I’m going to want your feedback.” The community that you build in a classroom flows into the community that we support and foster as a department.

Zoe: So, it’s a bit hard for me to talk about departmental culture change in the one month that I’ve been there not having seen it before I did Project NExT. But, I can certainly talk about how the department seems different from other departments, just in the willingness to embrace new ideas. And there’s also a sense that these ideas are just supported. Even if we haven’t had an explicit conversation, I know that there will be support for trying something new that was suggested in Project NExT. And it seems, when it comes time to make policies, that we have almost a majority just of Project NExT people. Obviously, we need a couple more people, but there are other people who haven’t participated in the program who would still support these sorts of initiatives. Knowing that that base of similar views is there, makes a big difference in what sorts of ideas we would even suggest or consider.

Sarah: I think a lot of our Project NExT fellows have also been very active with doing undergraduate research with students.

Rasika: I think even like talking to colleagues. For me, like I have a personal experience, because my husband is also a mathematician and teach at SUNY Oswego. If I learn something new, I share with him of course, he’s not a Project NExT fellow, but…

Rebecca: So, it sounds like the program’s working really well. You’re all really excited about it. It sounds like it’s engaging all of you. So, glad that you’re able to share it with us.

Sarah: The MAA has definitely done a lot to support improving teaching in mathematics and I do think it is a program that other disciplines could look at and possibly model. I will say they have put a lot of money and a lot of investment into making this a success. It is well run and has been well funded, which is a testament to how important professional organization views it.

John: We always wrap up by asking, what’s next?

Sarah: Well one thing that’s next is we’re trying to get one of our other new faculty, his application was rejected last year. We’re also hiring two people, hopefully this year…So, possibly trying to send them next year as well.

Jessalyn: Another immediate thing that’s next is that our two current NExT fellows will be attending the joint math meetings in January and maybe organizing some Project NExT sessions or at least attending some sessions.

Zoe: I’ll be helping to organize a session on getting started in math education research, which I was made part of because I said it was something I wanted to do, but it’s not something I have any background in. So, I’m finding it a bit of a challenge to assist in this organizational process. But, I also, possibly for Math Fest next summer, helping organize a session on reducing math anxiety, which is something that a previous NExT fellow who I follow on Twitter help organize this session. So, having attended NExT, I think, gave me the confidence to respond on Twitter to this senior mathematician and say, “Oh, yes, I’m interested in this topic.” And so that will come later. And that’s something I actually feel like you could contribute to in a meaningful way, unlike math education.

Rebecca: Well, thanks so much for joining us. This has been really interesting.

Sarah: It’s our pleasure.

Jessalyn: Yeah, thanks for having us.

Zoe: Thank you very much.

[MUSIC]

John: If you’ve enjoyed this podcast, please subscribe and leave a review on iTunes or your favorite podcast service. To continue the conversation, join us on our Tea for Teaching Facebook page.

Rebecca: You can find show notes, transcripts and other materials on teaforteaching.com. Music by Michael Gary Brewer.

John: Editing assistance provided by Brittany Jones and Kiara Montero.

59. Gatekeeping in Math Ed

Teachers at all levels often play an important role in influencing the educational and career paths of our students. In this episode, Dr. Marcia Burrell joins us to discuss how math teachers play a critical role as gatekeepers who may either welcome students to or provide a barrier to student success in all STEM fields. Marcia is the Chair of the Curriculum and Instruction Department at SUNY Oswego.

Show Notes

  • National Council of Teachers of Math (NCTM)
  • Budapest Semesters in Math Education
  • Polya, G. (1973). How to solve it: A new aspect of mathematical method. Princeton: Princeton University Press.
  • The Polya Approach Used at the University of Idaho
  • Bjork, R.A. (1994). “Institutional Impediments to Effective Training”. Learning, remembering, believing: Enhancing human performance.
  • Bain, K. (2011). What the best college teachers do. Harvard University Press.
  • Brown, P. C., Roediger III, H. L., & McDaniel, M. A. (2014). Make it stick. Harvard University Press.
  • Miller, M. D. (2014). Minds online: Teaching effectively with technology. Harvard University Press.
  • Miller, L. & Spiegel, A. (Hosts). (2015, January 23).Invisibilia: How to become Batman pt. 1 [Radio broadcast episode].
  • National Research Council, & Mathematics Learning Study Committee. (2001). Adding it up: Helping children learn mathematics. National Academies Press.
  • Brandsford, J. D., Brown, A. L., & Cocking, R. R. (1999). How people learn: Brain, mind, experience, and school. National Academy Press.

Other resources:

  • Larson, M. (2016). The Need to Make Homework Comprehensible. National Council of Teachers of Mathematics.
  • Stinson, D.W (2004). Mathematics as gate-keeper: Three theoretical perspectives that aim toward empowering all children with a Key to the Gate, The Mathematics Educator14 (1), 8–18.
  • Burrell, Marcia (2016) Gatekeeping in Mathematics TEDx talk at OCC. January 29, 2016.

Transcript

John: Teachers at all levels often play an important role in influencing the educational and career paths of our students. In this episode, we examine how math teachers play a critical role as gatekeepers who may either welcome students to or provide a barrier to student success in all STEM fields.

[MUSIC]

John: Thanks for joining us for Tea for Teaching, an informal discussion of innovative and effective practices in teaching and learning.

Rebecca: This podcast series is hosted by John Kane, an economist…

John: …and Rebecca Mushtare, a graphic designer.

Rebecca: Together we run the Center for Excellence in Learning and Teaching at the State University of New York at Oswego.

John: Our guest today is Dr. Marcia Burrell, the Chair of the Curriculum and Instruction Department at SUNY Oswego. Welcome, Marcia.

Marcia: Thank you.

Rebecca: Welcome. Today our teas are…

Marcia: Earl Grey with caffeine.

Rebecca: Extra caffeine. [LAUGHTER]

John: Mine is just a pure peppermint tea today.

Rebecca: And I have a jasmine green tea.

John: We’ve invited you here to talk a little bit about the work you’ve done on math instructors as gatekeepers. What does it mean to be a gatekeeper?

Marcia: Well, I like to use the word gatekeeping because sometimes gatekeeping has to do with an open gate, where you can just slide right through, or someone gives you the key, or they’ve given you the secret password, or it’s a barrier, where if you don’t really know what the hidden curriculum is about passing through the gate then you could stay there and be turned away. And in mathematics a lot of times people are afraid of math or they’ve been socialized to think they cannot do math and it’s really a gate that’s been created either by themselves through socialization or it’s been created by a math person or by someone like a parent who said, “oh, don’t worry, I wasn’t good at math either.” So, when I think about gatekeeping and mathematics it’s really about barriers that are created by us or barriers that are created by others, or for people who are really successful in mathematics, they have an opportunity to open the gate; there are certain things that they can do that will make people pass through the gate more easily.

Rebecca: I think our students can empathize with the idea of gatekeeping when it comes to mathematics—you hear them talking about these stories of certain situations where the barriers have been in place for them, or sometimes that’s faculty. For example, I’ve heard many times in creative fields where the creative faculty might say, “yeah, we know you’re not great at math but you have to take math,” or I had a situation when I was a kid in middle school—I remember distinctly middle school teachers saying “the women in this class aren’t going to do as well” and then I remember the few of us banding together and then we got really good grades on this final exam that we were told that we wouldn’t do well in. I think that those narratives are certainly there and it’s interesting to think about it not only from the person coming to the gate but also from the gatekeeper perspective, which leads me to the question of, what are some things that gatekeepers do that keep people out?

Marcia: I’m gonna focus on math people mostly, where sometimes they say things like maybe in a beginning level math course, “Why didn’t you know that? You should’ve learned that before. I don’t understand why you can’t do fractions.” So, there’s vocabulary built into a lot of us where we send out messages which get people to realize, “Oh, there’s something wrong with me; I should know how to do this.” So, they start imposing those same messages on themselves. The other thing that I think is important is in mathematics there’s always been a stratification about who can do math or who should do math and who can be successful in math. Often, as you just said, women have stories about fighting to get into a advanced math class because they didn’t do very well on some class but they were willing to work hard. So, certain populations are harmed because they’re socialized that way that when women have trouble in mathematics we say, “Oh, we should make it easier; you should do a group of courses that are not gonna lead you to calculus in high school,” but sometimes when men struggle we go, “Oh, struggles perfectly fine.” In the U.S., teachers make it easier for students to learn; they give them answers, they work out all the details. When I say give answers, I mean they work out all of the problems so that it’s really just rote, as opposed to in other countries, struggle is actually honored—hard work and struggle is part of the mathematics learning process, where in the U.S. sometimes we don’t allow people to struggle. If you got a B in Algebra I, well, you don’t really need to take Algebra II because the minimum requirement in New York state is Algebra I, and the fact is struggle is a part of the learning process. Historically, we’ve always stratified who is successful in math or who can take math and the level of courses that people can take. Plato 2,300 years ago believed that everybody needed arithmetic, but the advanced math was relegated to philosopher guardians, and in the 1920s the National Council of Teachers of Mathematics argued to have mathematics part of the curriculum, and between 1890 and the 1940s there was a growth in public schools and the perception was that sometimes they weren’t sure that students had the intellectual capability of doing some of the mathematics that NCTM thought was important. But remember in the 1950s the business world and industry said, “What are you guys doing in schools? The people that you’re putting out there can’t do mathematics.” Well, that was mathematics for a purpose and then Sputnik happened and all of a sudden math became this subject that we wanted to make sure people had. But think about how many English classes do people take—one or two in high school, but in high school students often take four or five math courses. I’m not saying they’re not important, but it really forces us to think about mathematics as an elite subject when gatekeeping from my perspective is it’s not about an elite subject, it’s everyone can do math; people are born mathematical and everyone should have an opportunity to do the subject and not fail at it, but struggle and make movements towards whatever learning they need to do.

John: So a lot of this sounds like our society is creating or emphasizing or encouraging the development of fixed mindsets in math where many messages coming through (as you both have mentioned) in early childhood discourage people from thinking that they’re able to do math and only the elite can get through. Is that common in other cultures?

Marcia: I mentioned earlier that in other cultures hard work and struggle are honored and I witnessed in Budapest, when I was visiting there as part of my sabbatical, that students were asked to go up to the board and struggle through a problem, even if they had no idea. And we do a lot less of that because either you know the answer or you don’t; that doesn’t really work that way—it is an iterative process. I used to work on problems and maybe get a little frustrated, put it away and the next day I’d look at it and I go, “Oh, now I get it.” It’s really about process. The NCTM standards talk about process and product, and if you want people to learn mathematics then you really have to emphasize process, working in teams, giving people a chance to try things and fail but also collaborate with others to ensure that maybe there are multiple ways of approaching a problem, but if you’re not allowing students to talk with one another and work it through, then sometimes they think there’s only one way to do it and it really doesn’t improve their mathematical abilities. Mathematicians are about process—there are certain skills that mathematicians use. Good mathematicians persevere through problem-solving. They check their answers using different methods, they plan how to solve a problem versus jumping into a solution, and they justify the answers and communicate with others. Good mathematicians don’t just know the answer; it’s a process, and there’s even collaboration between mathematicians, but when we teach it on the K-12 level, we say, “This is what you need to learn and you need to learn it in a specified amount of time,” and so a lot of times students are turned off by the way we teach mathematics. Opening the gate is really about helping teachers rethink how they actually teach mathematics. We have a lot of data about how to successfully teach math, and it’s about problem-solving, reasoning, communication, connections and representations, but if you’re just gonna stand at the board and write the answer to a problem, that doesn’t help people really connect to how you came to that problem. So, gatekeeping is about getting teachers to rethink how they’re teaching mathematics and what they think is important. Process and products are important, but process is actually more important.

Rebecca: You mentioned mathematics as a collaborative process, but in my experience in K-12 I don’t think I ever worked with another person once.

Marcia: It’s funny you mention that. Again, the stratification stuff is huge. I attended a program called Budapest Semesters in Math Education and it’s geared for Americans, Canadians to come to this program. They’re interested in both juniors and seniors to come and learn about the problem-solving approach to mathematics. These are students who are mostly math majors, but they could be math ed majors, and they are sent to these schools where they’ve selected the top students in mathematics to use a problem-solving approach and what happens is they give them a problem with no background and they ask them to work out these problems. They can use their textbooks, they can use calculators, but the fact is our students—Americans and Canadians—get to witness students almost trying anything to work out these high-level mathematics problems—sometimes they’re theoretical, sometimes they’re applied. But what the students say who are in this particular program—and I got to be in these classes with them—was, “Why can’t we have all students use some of these processes?” And the processes are really just the things we already know that good mathematicians are supposed to do, sort of George Pólya, you know: analyze the problem, look at all the facts, try something, test your answer. But you actually get to witness that. So, when you asked me “None of the classes I ever went to that were collaborative and problem-based and working in teams,” well we seem to have an idea that only the gifted and talented or special programs will allow kids who already show aptitude to do mathematics in that particular way, and the fact is I visited a school in Budapest where this teacher who’s been working with the gifted and talented students got permission from the parents to try this problem-solving approach for a ninth grade through 12th grade. They had to get sign-offs by parents, because of course, in our system, if kids don’t know certain things by the end of certain grades then their opportunities—another gate—for getting into the university and going through the career path are cut off. So, these parents had to sign off that they were going to risk that what she was gonna to do over the next four years was gonna be helpful to their students and that they wouldn’t be harmed by doing this problem-solving approach. I witnessed several math classes where this teacher had been working as part of her dissertation to have students go through this problem-solving approach—it’s not just Pólya; there are other… Pósa there’s a Pósa method—I met this gentleman who, he was in his 80s and he invented the Pósa method and he’s one of the top mathematicians in his age… in his day, but he devoted his life to teaching problem-solving to kindergarten through grade 12. But the point that I’m making is, I witness students who had been through this process, and they were explaining problems to their peers on the board in ways that I haven’t seen good math teachers explain. But they built these kids up from start to finish to be confident about what they knew, to work in groups, not be afraid to make mistakes, and I think that we can do more of allowing students to learn not just at their own pace, but learn what mathematicians do—the process of engaging with one another if we weren’t so afraid of the whole accountability—what do kids know at the end of 12th grade? What do they know at the end of 11th grade? It’s recursive. Some things they learned in ninth grade in Algebra I will come back in Algebra II and when they’re college students they’re gonna pull the algebra and geometry together, if we allow it, as opposed to looking at these areas as completely separate things. One of the things about gatekeeping is that teachers have to think about students as already being competent; they’ve got to provide students with scaffolding so that students that are in different places have an opportunity to demonstrate what they know. I also think that we have to have high expectations, but we have to let students understand that they can extend the learning if they take some risks; that’s what good mathematicians do, and then we have to exhibit in depth knowledge as well as subject matter knowledge. So there are certain things that gatekeepers—math teachers—can do, but they’ve got to trust that students can learn, and we’ve got to keep the expectations high, but also scaffold for them so that they’re successful.

Rebecca: …a lot of evidence-based practices.

John: Yes, I was just going to say a lot of what you’re talking about, there’s a tremendous amount of research supporting that, not just in math instruction but across the board. In terms of providing students with challenging problems—you have the desirable difficulties of Bjork and Bjork, for example, and in terms of learning from mistakes, that shows up in all of the research on teaching and learning and it’s something that Ken Bain talked about when he summarized some of this research in What the Best College Teachers Do, and it’s also shown up in several of the books we’ve used in our reading groups, Make It Stick and Minds Online, for example: that retrieval practice, low stakes testing, where students can make mistakes and learn from mistakes, is effective in all types of instruction. So, these are really good practices that seem to be mostly neglected in math instruction.

Rebecca: I was expecting John to also mention something about growth mindset. [LAUGHTER]

John: I think I already did a while back, but treating math as something you’re either good at or not good at by teachers and by families and by our culture discourages the development of a growth mindset, and that’s really important. This year I’ve completely flipped my large microeconomics class and one of the things I had them do is before each class I asked them to do some readings and then I asked them to work through some problems in the readings; I have students submit a short Google form, where I ask them just two questions before each class. The first question is: “What have they learned from this reading assignment before that day’s class?” And also, “What are they still struggling with or what don’t they fully understand?” And half to two-thirds of them before each and every class list, “I have trouble interpreting graphs;” “I have trouble understanding graphs;” or that “I have trouble computing these things,” and that’s all basic math, and of course they have trouble doing it when it’s the first time they see it, but they see it as a barrier— “I’m just not good at it,” and every day in class I’ve been trying to encourage them to say, “Well, you may not do it now, but you can get better at this;” “You haven’t yet mastered this;” “You’re not yet good at this, but the more you do it the easier it gets,” and we’re not always seeing that happen, and we see that in lots of areas.

Marcia: Yeah, I think that students are more willing to say “I’m not good at math; I don’t have any experience with math,” but they would never say, “I can’t read; I’m not good at reading.” They might say it, but it’s socially acceptable to say “I’m not good at mathematics,” and the fact is when you look at a group of kindergarteners and they’re in a classroom, they’re all learning for the first time how to add and subtract and they slowly… I’m sorry, through some of their elementary school teachers who often are afraid of mathematics, and they say little things, “Oh, don’t worry about that, it’s okay to not be able to do that, we’ll work on that later on,” but they say it in a way that sometimes gives students permission to say, “Oh, I don’t have to learn that—I’m a girl, I’m a student of color, I don’t have to learn that because the teacher said she doesn’t know it either,” and so one of the concerns that I have for how we train childhood educators is we force them through, at least on our campus, these two math classes where they go kicking and screaming, but the fact is we almost need to reprogram them to think about the things that they can do mathematically and then build curriculum around them. It’s not always about the fact that the way you learn is the same way that all the kids that you’re teaching learn; it’s more about how do you change your perceptions about mathematics. There’s something on NPR, and I’ll have to find the reference a little bit later on, where this young man who was blind learned how to ride a bike, was sent to school, and people couldn’t even really understand why he was able to do all of these things as a blind person—well, his mother decided to treat him like he was a sighted person and it’s a Batman series, where the fact is, if you convince someone that they can do something and you believe it, then all of the things that you do to work on their perceptions about their capacity will come through. But first the teacher has to believe it and then they have to do all of these things to scaffold it. The fact is that, and again, I’ll have to find the researcher, but he did this study where he told all of his researchers that these mice were smart mice… these mice were everyday the same mice… what happened is the researchers came in and they treated those mice like they were smart—they handled them differently, they had them run through whatever people do in psychology with mice, and then he came back later on and said “All of these mice have exactly the same capabilities.” Well, that works in exactly the same way in the math classroom; students come, and if we believe that they’re capable and we come off and treat them with respect about what they have learned and how to build on that, then we’re gonna see better progress in their learning. I have to come back to the gate because the teacher has a lot of power to make the gate accessible or make the gate a barrier, and the barrier is really just the messages that the teacher says to the students and to herself about success in mathematics, and we lose entire generations of people when the gate is closed to them mainly because of perception.

Rebecca: So much discussion of gates it should be important to note that in front of Marcia is this picture of so many different kinds of gates in our conversation. Can you talk a little bit about the gates that you have in front of you?

Marcia: Yeah, I decided to Google different kinds of gates and when you think about the Brandenburg Gate or you think about gates like this one —remind me what this is called; this is in Cincinnati—the arch; this is really a gate, but this shows an opening to something, so when you think about gatekeeping in mathematics, I want us to think about people being gatekeepers for accessibility. So when you look at those pictures you think of when you’re going through the turnstile to pay with an EZ Pass. That is a barrier. If you don’t have money, you don’t have an EZ Pass, you’re not getting through, but if you look at the door to no return like in Benin it’s an opening to the next world just like certain pictures of gates just have you think differently about openings and closings.

Rebecca: There’s some like the dog pen where there is no way in or out; it looks like that one’s just closed forever.

Marcia: Yeah, which one is it? This one or this one? Right, I mean this has a gate, but often people are closed inside of thinking that they can’t do math and they can’t be successful. The job of a teacher would be to help them jump over that particular gate or find a different way to think about opening that particular gate. If you’re a dog and you’re inside of a pen, I think you’re just gonna need somebody to lift you up over that gate, and I think about that with teachers that what they have to do with each individual student is completely different, but their responsibility is to help them understand that they’re all mathematicians and they all have capacity for success in mathematics.

Rebecca: You’ve talked a little bit about how gatekeepers can open the gate or provide the leg up over the wall, or whatever it is, right, that’s there. Can you talk a little bit more about how to be inclusive and how faculty and teachers can really support this environment that would allow for problem-solving and allowing students to fail and try again and to iterate and eventually succeed?

Marcia: I’ve thought a lot about elementary school students and middle school students, where you’ve probably heard about the Montessori Method. The Montessori Method, you work with individuals to build from what their interests are and it turns out that students without a lot of direct instruction can complete whatever the curriculum is for that grade level by mapping to their interests, their strengths, and projects that they do where they’re learning the mathematics in ways that might be considered non-traditional. In the Montessori Method, they’re not just looking at memorizing times tables; they’re looking at multiplication as repeated addition, they’re looking at visualizations instead of just looking at a text. And the fact is that sometimes, I think, that if we allowed students to individualize their learning, especially in middle school and high school, that there’d be more progress than forcing students through the curriculum where each week they’re expected to learn something but they’re not learning it, they’re sort of just being dragged through the mud. And I have a lot of respect for my peers who are math teachers. I was a math teacher where I felt like I know what that kid needs, I need to take time to help that kid through what they need, but I didn’t have the courage to stop what I was doing and figure out how to individualize or make them work in small groups. I was a successful K-12 teacher, but I feel like I started to figure out what was needed when I made the decision to leave. So, part of my job as a math educator is to help our candidates who are gonna be teachers in schools to have the courage to do what they know is right: think about their love of mathematics and give kids problems that are theoretical and have them try it; give them applied problems, give them things where they have to use visualizations and not just know the procedures, but also understand the concept.

John: And also perhaps to use peer instruction, as you talked about, where students explaining things to each other reinforces learning for each student.

Marcia: Yeah, and sometimes the things that we expect of what we call the gifted and talented are exactly the things that other students can do but we’re afraid to take a risk, and I met earlier this afternoon with one of our adjuncts that’s teaching math methods to our graduate students and she said her job is to teach her candidates how to be good teachers, and sometimes that means forgoing what they think they wanted accomplished on that day and building something fun that’s gonna get students to see that math has many openings, not just following things through rote or through memorization. So, I had a really nice conversation with her because she does work in the school systems, but she’s teaching a course for us and she uses constructivist approaches. I have many peers that are still engaged in this math war that it has to be rote, it has to be step-by-step. In the constructivist approach, you care more about the process that students engage in and there’s a program that I listen to on Sunday morning it’s on NPR where it’s a puzzle and the puzzle is usually related to a vocabulary puzzle as opposed to a math puzzle, but the type of thinking that you have to engage to solve those puzzles really is mathematical thinking, so I love those puzzles, but they’re all couched in word puzzles… but it’s really mathematical thinking… and so I think the teachers need to use more of those word puzzles to bring people in so that they understand that they’re engaged in mathematical thinking—it’s just not called mathematical thinking. One of the other things that I wanted to mention before I run out of time is we are heavily tracking students into particular tracks. Sometimes you’re in the track where you’re just going to do Algebra I, and sometimes you’re in the track where you’re gonna get to do Algebra I and Algebra II, and maybe you’ll get to do Geometry, but some of the best learning occurs when there’s heterogeneous grouping and there’s less tracking. This gate stuff, these gatekeeping, really reinforces tracking, which when students come to SUNY Oswego and they’re in a remedial class and don’t know why they’re in the remedial class, because they may have been tracked in a particular way and cut off many, many job opportunities or majors because they were tracked in a particular way, and that is gatekeeping that occurs in fourth grade. And again our responsibility for our childhood educators is to get kids to think more broadly about what mathematics is; it’s not just arithmetic, it’s not just geometry, it’s not just theoretical problems; there are many types of problems that childhood people could engage students in that wouldn’t shut the door to possibilities 10 or 12 years later when students find out that they were tracked in a way that makes it so that they could never do graphic design or they could never do engineering or something else that they didn’t really understand was possible because somebody closed the gate early on.

John: …and that’s really important because most of the growth in income inequality is due to differences in educational attainment and the returns to education. And the returns to education in the STEM fields is far above the returns in other areas as well. So, keeping people out of those areas means that the people with those areas end up doing really well, but the people without those skills end up in jobs that are perhaps overcrowded with lower job prospects, lower prospects of growth and it helps reduce social mobility and economic mobility. It’s a serious problem in our society; it’s the worst we’ve ever seen it in the U.S.

Marcia: Yeah, I can’t connect it completely to perceptions, but a long time ago I taught a remedial math course at Clinton Community College and I had a student in that class and she was a smart person—I think everyone is smart—but I walked through how to study math, how to approach it: you are capable, work hard, keep asking questions, and about 10 years later I got a postcard from her—this flabbergasted me; she was in a remedial class and she had entered a PhD program in mathematics and she said it was just about the fact that somebody finally showed her how to study math—it was read the textbook, try the problems, come to class, listen maybe to the lecture, don’t be afraid to make mistakes; when you’re tired take a break. There are certain things We know that people can be successful in mathematics but we keep thinking that it’s this magic wand thing; it’s not a magic wand thing. We actually know —there’s research from Adding it Up —where we know exactly how people learn math well. The stuff research from Bransford, which how to study mathematics, how to learn mathematics, it’s written in black and white from large-scale studies, but then we return to the rote memorization, follow these steps and that’s not the beauty of mathematics at all.

Rebecca: One of the things that I think is really interesting about what you’re saying is that societally we might think, “Oh, fourth grade teacher… not really gonna have a big impact,” but you’re really talking about this fourth grade teacher is not a gatekeeper of the little gate around the garden; this is like the gate to the universe.

Marcia: Absolutely, and most of our math candidates who are not math concentrates—they’ve got to take these two four-credit math courses—will say, “I just need to get through this class; I hate math.” If you hate math it comes through loud and clear in your teaching; it’s really difficult to mask that. I taught a math for diverse learners course that the School of Education and Arts and Sciences Math Department and Curriculum and Instruction collaborated on and it was a math for diverse learner, so some of the things that I’ve been talking about here was in a full graduate course, and students would say, “Well, I never really thought about that; I thought everybody was gonna learn math the same way I learned math”—you’re a math person, I shouldn’t even say that. You’re a math person—you came through the system and you were successful in the current system, but if you want to build the next generation you’ve got to think about some of these other factors—you’re gonna be in a system, and as we’ve talked about systems, you are part of the system and you do have power to make changes to it, even if it’s perceptions, even if it’s just giving students the perception that you care about their learning and that they can succeed, and so this is really important to me. There are three principles: teachers must engage student misconceptions, understanding requires factual knowledge and conceptual understanding, and a metacognitive approach enables students self-monitoring. If I think about gatekeeping, if teachers kept those three principles in mind, they’re not mine—it’s in the research. This is sort of revolutionary because we don’t want to restrict people to thinking that only certain people can do mathematics, but if math teachers, whether they’re childhood or adolescence, or university teachers think about what good mathematicians do, they’ll follow these three principles and it might move us forward. I know it’s a big deal because the successful people want to keep what they have to themselves, but I think we miss out on the potential of entire generations if we don’t give them access to opening the gate through mathematics. When the Common Core came out teachers had the perception that they had to give these problems to students and parents would call and complain—“I can’t even do these problems; these aren’t the problems that I did when I was a kid”—well, the fact is we weren’t supposed to be sending these problems home; we were supposed to be doing those problems in class, and so a lot of the Common Core mathematics was supposed to be using manipulatives and getting kids to talk about how they think through the arithmetic problem. They were sending home problems and parents were complaining they were spending two or three hours to work through these problems, and there was an article put out—it was an NCTM—where they said what is your problem? No, don’t send these problems home for kids to fight with their parents, ‘cause that’s just gonna reinforce, “Oh, I couldn’t do math either;” it was supposed to be completely done in the classroom in collaborative groups, but we’re still not interested in teaching in that way. So, we sent home the homework—well, you could have been sending home memorize these timetables just as we did 20 years ago or 30 years ago, so finally NCTM put something out to help math teachers in the K-12 area not to send home these problems that would take parents two to three hours, but to rethink the organization of their classrooms where students could work on problems and have fun with mathematics, and the fact is that there are reforms that mathematicians fight about; there are a whole host of mathematicians that said Common Core was bad; Common Core is not bad, the way it was implemented was bad, so now we’ve done some backtracking to think about the fact that when you carry, when you’re subtracting or you’re adding, why do we do that? And the Common Core got students to make sense out of place value and make sense out of what it means when we carry this is about the tens place or the hundreds place and whenever you have new curriculum, Common Core or what was the curriculum in the ‘50s, I can’t remember… the new math… there’s always new math, it’s just an approach to make it more inclusive, but sometimes the way we roll things out makes it difficult, at least for the next generation of teachers, so I’m pro-reform movements, but we have to take the time and the energy to implement it in a way that’s actually gonna be useful—we just keep going back to the way we taught math a hundred years ago.

Rebecca: It sounds like what happened was faculty who knew how to do things a particular way get handed something that’s different but not a way of demonstrating or doing the different, right, like…

John: …without the professional development needed to allow them to implement it effectively.

Marcia: Correct. That’s correct.

Rebecca: The method doesn’t match the material.

Marcia: Exactly. At the same time they were putting out that students have to take a main assessment in fourth grade and eighth grade, but those assessments didn’t really align to this new Common Core curriculum, and so lots of things have changed over the last, I’d say seven to ten years, and we’re sort of coming out of that. When students come to the university level we still expect them to know mathematics. Do you remember twenty-five years ago they changed the math curriculum to be Math A and B, Course I, II, and III? New York state was the only state that was really thinking more globally about, “Wow, it doesn’t always have to be about algebra—it could be about statistics, it can be about more applied,” but the fact is universities didn’t change and we were still expecting students to know this narrow curriculum but it did broaden what people thought about mathematics, but it didn’t really help a lot of those students because then they were closed out of particular career areas because they might have been in a school that embraced applied math or embraced business math or something that might not connect to what they would do at the university level.

John: You’ve also been involved with Project Smart here at Oswego. Could you you tell us a little bit about that and how it relates to math instruction.

Marcia: Project Smart was a thirty-year project where teachers came to SUNY Oswego for summers to do professional development, math, science, technology. There are some teachers retiring over the last couple of years that came to Project Smart right from the beginning. We brought people in like Damian Schofield in the early days to learn about human-computer interaction. We brought people in from music and from art to help teachers integrate other things into their teaching, so they used to come for three weeks, then they came for two weeks, then they came for one week, then we built it into the department where faculty got released time to go into schools and work with teachers from the bottom up to think about how to improve teaching in their classroom. Project Smart really honored the work that teachers did because we would say, “What do you want to improve in your classroom? Are there particular things that you know students are struggling with?” This past year, funding for Project Smart ended, but the institution is still supporting individual faculty to go into schools and work with teachers to build classrooms that connect with the learners that they have in front of them. It’s more connected to what’s called a professional development school, where at the university we have the latest about how to teach, whether it’s math or English or social studies or modern language, and then we go into schools where they’re dealing with kids every single day and we try to help them figure out how to improve as a teacher; we meet them where they are; we build from there, so Project Smart is over—I’m not gonna say it’s dead, but we have a different system to work on professional development schools but just in a different way.

John: So you’re still doing the same thing even though it’s not under that official title?

Marcia: Correct. Correct.

Rebecca: We always wrap up our episodes by asking, what next?

Marcia: Oh my goodness, thank you for asking what next. After returning from my sabbatical, where I had the opportunity to be part of Budapest Semesters in Math Education where I got to see classrooms where students were using Pólya’s problem-solving approach in addition to something called the Pósa method, I worked with Josh McKeown, who’s from international education to reduce the cost of the Budapest program, so we’re working to recruit math students, both childhood and adolescence teacher candidates, as well as straight math candidates to consider going to Budapest over a winter course for one or two weeks over winter session or during spring break. What would they experience if they went to a short course? They would visit classrooms using the Pósa method, they would sit in on some of the math courses at BSME, where teachers are actually showing how to use a problem-solving approach in mathematics, where sometimes our students say “You talk about problem solving, you talk about the constructive approach, but no one is doing it so we don’t really know what it is.” The next step is to work with international ed to get a group of students to do the BSME program.

Rebecca: That’s really incredible.

Marcia: I’m excited about it too and I hope to also re-institute my math for diverse learners course because through that course I reinforce that I believe students should have access to high-quality, engaging math instruction. I believe all students should have mathematically rich curriculum. I believe all students should have high expectations and strong support, and we’re all gatekeepers— we are change agents and we control the gate. I think it’s ambitious because many people don’t agree with me saying that mathematics needs to be more inclusive, but that’s what I’ve been working for my entire career and I hope to continue that way.

Rebecca: Your work is incredible and we’re really excited that you’re doing that work.

Marcia: Thank you.

Rebecca: I know as someone who’s in a field that you don’t always associate with math—I believe in math and so I hope we can all help support your initiative.

John: It’s a major social justice issue.

Marcia: It’s a huge social justice issue because, again, what happens is often students of color, students that come from poor families may or may not have had the best math instruction. I mean, it’s a big cycle, and when they come here we should be able to help not just convince them, but this is a public institution. We should be able to provide access for them to reach whatever goals they hope to. We should be able to take students where they are and help them achieve whatever their focus is, whether it’s math related or not.

John: Well, thank you.

Rebecca: Thank you so much.
[Music]

John: If you’ve enjoyed this podcast, please subscribe and leave a review on iTunes or your favorite podcast service. To continue the conversation, join us on our Tea for Teaching Facebook page.

Rebecca: You can find show notes, transcripts and other materials on teaforteaching.com. Music by Michael Gary Brewer.

John: Editing assistance provided by Kim Fischer, Brittany Jones, Gabriella Perez, Joseph Santarelli-Hansen and Dante Perez.