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.

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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.

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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.

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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.

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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 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.