Abstract concepts can be really difficult for students to grasp. In this episode, Matt Anderson joins us to discuss how simulations can be used to make statistical concepts more tangible. Matt is a lecturer in the psychological sciences department at Northern Arizona University. He was a recipient of the 2020 College of Social and Behavioral Sciences’ Teacher of the Year award at NAU.

### Show Notes

- Geoff Cumming (2013).
*The Dance of the P Values* - The R Project for Statistical Computing
- RStudio
- Shiny
- Rice Virtual Statistics Lab
- American Statistical Association.
*Guidelines for Assessment and Instruction in Statistics Education (GAISE) Reports* - Beth Chance and Nathan Tintle (2020). “Teaching Statistics with Simulation-Based Inference.” April 3.
- NAUFlex
- Blackboard Ally
- Universal Design for Learning (from CAST.org)
- John Marden Stat.istics.net
- Vigen, T. (2015). Spurious correlations. Hachette books.
- Vigen, Tyler. Spurious Correlations web site

#### Additional simulation resources:

- Why Teach with Simulations? (Science Education Resource Center at Carleton College)
- Teaching Stats with Simulations (Paul Velleman)
- Using R as a Simulation Tool in Teaching Introductory Statistics (International Electronic Journal of Mathematics Education)
- Guidelines for Assessment and Instruction in Statistics Education (GAISE) Reports (American Statistical Association)
- StatKey (Lock, Lock, Lock, Lock, & Lock)
- Data Sets & Utilities from Project MOSAIC (Project MOSAIC)
- Sampling Distribution Applet (Rice Virtual Lab in Statistics)
- Estimating Correlation Coefficients (John Marden)
- Interpreting Cohen’s d Effect Size (Kristoffer Magnusson)
- ActivStatsTools (Vellemal et al., from ActivStats textbook)
- Introduction to Statistical Investigations (ISI-stat.com)
- Simulation-Based Statistical Inference (Blog) (causeweb.org)
- Consortium for the Advancement of Undergraduate Statistics Education (causeweb.org)
- Rossman/Chance Applet Collection (Allan J. Rossman & Beth L. Chance)
- Journal of Statistics Education (Taylor & Francis Online)

### Transcript

John: Abstract concepts can be really difficult for students to grasp. In this episode, we look at how simulations can be used to make statistical concepts more tangible.

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

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

John: …and Rebecca Mushtare, a graphic designer.

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

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John: Our guest today is Matt Anderson. Matt is a lecturer in the psychological sciences department at Northern Arizona University. He was a recipient of the 2020 College of Social and Behavioral Sciences’ Teacher of the Year award at NAU. Welcome, Matt.

Matt: Thanks very much, John. It’s a pleasure to be here. And I’m really excited to be talking about the use of simulations in introductory statistics classes.

Rebecca: Today’s teas are:

Matt: Today’s tea is lemon ginger.

Rebecca: Well, that sounds good.

Matt: Yeah, that’s a fave.

Rebecca: How ‘bout you, John?

John: I have Christmas tea…

Rebecca: Aha.

John: …with a cinnamon stick.

Rebecca: That’s only because I was drinking it last time.

John: You inspired me to buy some Christmas tea, which I’ve been drinking for the last couple of weeks.

Rebecca: I almost sent you some. And I have a Scottish afternoon tea today.

John: We’ve invited you here today to talk about how you’ve been using simulations in your courses. But first, could you tell us a little bit about what courses you normally teach?

Matt: Absolutely. My main mission is to teach the labs for the undergraduate statistics courses, the introductory statistics courses that are taught within the Department of Psychological Sciences. And so I teach about six to eight of those a semester. And I think it might be useful to just contextualize the labs. They’re one-credit labs, and they’re embedded in four-credit, introductory statistics classes. And all of our faculty use the same schedule, and we use the same textbook, and so there’s a lot of coherence among the sections that we have. So, the thing I love about the lab the most is that, because I’m getting all the psychological sciences majors, I have a chance to meet almost all of them. And I have a chance to do that early in their academic trajectories. And that provides an opportunity to get things on their radar for those who are going on to graduate education such as the graduate record exam and things like that. We have a little bit of a focus on SPSS in our lab, in addition to the normal course content that we would see aligned with the textbook. In addition to the course faculty teaching the lecture portions, and I’m teaching the labs, we’ve got some wonderful tutors, and those tutors come from our Academic Success Center. And we’ve also got a tutor who’s a second year graduate student in our Master of Arts in Psychological Sciences program who adds a lot to the course delivery. So it’s a really wonderful place for me to be teaching. I feel very well supported, and I love the mission, even though I understand that statistics may be, to be contemporary, not everybody’s cup of tea. [LAUGHTER]

John: So how many students are there in these classes? And what level are they? You mentioned they’re fairly early in their career, are they mostly sophomores?

Matt: Well, it’s a mix. Yeah, I think that the tendency is that we’ve got sophomores and juniors, we do have first-year students, and we also have seniors, but most students are sophomores, or juniors. And in each section, I’ve got maybe 30 students. So you can see when I’m teaching eight of those, that’s a lot of folks. And that’s complicated a little bit by the online delivery that we’re using right now as well. I also teach a thing called an undergraduate teaching apprentice class. And in this very small class, I’ve got students who are interested in learning more about the science of teaching and learning. And we focus on statistics, and they have applied assignments where they might help me with our learning management system. I think I’ve been inspired by all of the great simulations out there, and I’m going to add an assignment related to those as well. And then I also teach a fully online statistics lab for undergraduate students who are transfer students, who might not have had a lab experience when they took their lecture. And so this uses the same materials that we use in the face-to-face labs or the labs that we use for our basic introductory classes.

Rebecca: So, you participated in a redesign of your introductory statistics classes, can you talk a little bit about this redesign, maybe where it started, and now where it’s ended up?

Matt: The redesign that I was involved with had to do with the lab portion of the class. And it started around 2013, when I was hired to teach the labs for these courses, and also for our research methods in psychology classes. And up to that time, the labs were taught quite capably by graduate students, but there was variability in content and delivery and things like that. And so it was in the interest of the department to consolidate those into a single uniform experience. And that’s what I had the pleasure of putting together. And so what I started doing was building these what I called lab modules, and they would be used in each of the classes. And when I first started doing those, the version I used on Thursday was much different than the version I used on Tuesday. And there’s a lot of evolution that took place. And teaching eight of these labs a week, it was nice to have some development take place that was meaningful over the course of a single semester. And right now that lab manual is still being used. It’s fortunately not something I have to stand at the copier and print, but it comes in a bound book through our NAU bookstore. And it’s got modules that are aligned with each of the chapters in the textbook that we use, as well as very specific freestanding modules related to things like SPSS assignments and power analysis, and a little bit of Excel that’s built in there as well. And the fun thing about putting this thing together, I just loved the creative process. And I benefited enormously from the input from instructional designers at NAU. We’ve got some just phenomenal folks there who had some really important insights to provide that we put into the lab manual. So, it’s got QR codes, for example, in it. And so if a person gets to a particular part in an SPSS assignment and can’t remember how to do this, they can just use the QR code to see a very short little tutorial on how to do that. And I think being able to build those kinds of resources in something like this, make it interactive, I think is useful for the students and for me. It’s a really fun part of the creative process.

John: When you started working with constructing these labs, did you start using simulations right away? Or was that something you’ve gradually been adding since then?

Matt: Well, I started adding them soon after I started building them. But it wasn’t until maybe a year later that I started embedding simulations in as assignments. I was one of those students who really struggled, I probably shouldn’t say this out loud. My first stats class, it was very abstract. It was early in the morning, which complicated things for me. But, what I found was that I really benefited from seeing things to help marry these abstract concepts to real data. And about the time that I started teaching, there was a series of videos that were put out one was called “The dance of the P values.” It was by Dr. Geoff Cumming and it had a beautiful simulation attached to it. And so I was just starting to learn R at the time. And so I started seeing if I could replicate his findings using R and was able to, and that gave me a little bit of encouragement about building them. And at the same time, in 2014, our mathematics and statistics department helped host a International Conference on the Teaching of Statistics here in Flagstaff. It’s a huge international event. And it brought people together who were just marvelous at explaining and had these beautiful simulations. And they also talked about how to teach courses using R. And I just found that whole thing inspirational, in addition to having the pleasure of meeting some of my colleagues in the math department that I might not have met otherwise. And so that opened a whole new window into what simulations are out there, created by these really incredibly bright and capable and devoted teachers to the introduction of statistics and psychology,

John: I have to ask, what does “The Dancing P values” do as a simulation?

Matt: Well, they don’t actually dance. They do move. This is very similar to the way that I dance I suppose. But what it shows was that with small sample sizes, the P values just really were not consistent. And that was a message that was really central to what he was trying to put across. And the way that it was articulated and illustrated, I thought, was really compelling.

Rebecca: And who can argue with that title. That’s the hook. You have a good stimulation with a good hook, you got your attention.

Matt: It is a hook, right? Yeah, even if you didn’t have an interest in statistics, there might be dancing involved. Yeah.

John: And p-values is a concept that students often have trouble with. So, having that practical application, I would think would be helpful.

Rebecca: For those that aren’t familiar. Can you describe what R is?

Matt: Yes, R is a statistical software package that was built from the ground up to do stats and represents statistical graphics. It’s incredibly powerful. It’s free. And it’s also open source in the respect that people build these things called packages for them, which extend their capabilities quite a bit. And so if you can think of almost any esoteric statistical procedure that you would like to implement in your own lab, for example, there’s probably a package out there to do that. And the thing that I liked about it was that it was able to be paired with a thing called Rstudio, which I thought was a nice integrated development environment, which has some additions that allows you to take some of the things that you do on your local machine and put them on the web. So it was really a nice match between what I wanted to do in the lab and what I wanted to put out on the web for people to be able to see.

John: How do your simulations use R.

Matt: That’s a great question. They basically are simulations that I’ve built in R in this add on called Shiny. And so the students don’t see any R code at all. That said, in the labs themselves, I do think it’s useful for them to be able to interpret statistical output from different software packages. So I do give them some R output and ask them to make meaning out of it. But I don’t ask them to do any coding at all.

Rebecca: Can you talk about the difference in students experiencing simulations versus different kinds of exercises you might have had them complete prior to introducing the simulations into your course.

Matt: Maybe right now, I should just define what I think a simulation is. And so this is a very wide net. And I think it’s basically any visualization that allows you to “What if?” questions, to explore and demonstrate connections between abstract concepts and real data. Some of the simulations that I’ll talk about allow you to do statistical inferences as well… so, incredibly powerful. So I think these simulations and the use of the simulations exist across a continuum. I think there are some environments, such as the one in which I am operating, where we use simulations to try to reinforce critical points. So, Central Limit Theorem comes to mind. But there are also some courses where they build the entire semester around the use of simulations, they start them very, very early in the course, leveraging people’s natural inquisitiveness and their desire to see patterns and use that over the course of the semester to develop this deep understanding, not only of the details regarding statistics, but the big picture, how these things are all wired together.

John: Going back to Rebecca’s question, how have students responded to the use of the simulations compared to what you’ve done earlier in some of these lab assignments.

Matt: One of the simulations is one that’s done by the Rice virtual statistics lab. And it’s one that has to do with sampling distributions, which for me, when I was learning it and teaching it and for students still, a difficult concept. Imagine, if you will, just this normal population at the top of your screen, and then three boxes below, and the box immediate below, you have the mean of a sample that’s drawn. And then below that, it gets pushed into what emerges as a sampling distribution based on that sample size. And then the fourth box, the one at the bottom, would allow you to do a different sampling distribution. So you can do two at once, if you will. But this is visually really appealing, because it allows you to see the random sample being taken and where that winds up being put and how those samples aggregate to develop the sampling distribution. So that’s one that I built an entire assignment around, because you can predict some of the values of the sample distributions based on the math. And so it was nice to be able to put all those things together, I think, and the added beauty of this is that you can take that normal parent population, and you can make it one that’s non-normal. And you’ll see when you rerun the sampling distribution that you wind up with, in most cases, a very normal looking sampling distribution that allows you to run those inferential statistics. So it helps connect some of the dots that might not be connected otherwise. And so, while I don’t have any p-values myself to evidence how successful this has been, I have heard a lot of “a-has” when I’m talking to students about this, which to me is the Holy Grail. And they seem to get it with these simulations. As I researched simulations in preparation for this particular conversation, that was something that was echoed in all of the presentations was just the students really getting it and being able to leverage previous knowledge and being able to put all these things together so they can anticipate what happens in the future, when they do other simulations.

Rebecca: There’s something really powerful about being able to observe something and make that rule for yourself rather than just being told the rule that you have to follow. Otherwise, it seems really arbitrary.

Matt: Rebecca, that’s absolutely true. And it’s kind of fun to see these things played out with real world data that is much more compelling to students.

John: Inferential learning about inferential statistics.

Matt: [LAUGHTER] Absolutely, yeah.

John: But those are things, again, that students do have trouble with. They have trouble understanding that the estimators themselves have distributions. And this should make it a whole lot easier for them to see it. I’m getting a lot of ideas here, because I’m teaching an econometrics class this spring, and many of the things you’ve mentioned are things that my students have trouble with.

Rebecca: As someone who just learned some statistics this January, I’m thinking this could have been really helpful. [LAUGHTER]

Matt: Yeah, and so when I look at what I’m doing, I’m really happy to be using simulations. But as I look at the universe of simulations that are out there, I can see that there’s more that I can do, and that I’m really motivated to do after seeing some of these wonderful things. I shouldn’t get too far without talking about some of the wonderful things that are being done on a grand scale with simulations in introductory statistics courses. There are actually textbooks out there, which are built around these. And what they’ll do is they’ll start off early in a semester using simulations, and without giving names to things like sampling distributions and confidence intervals and P values. But they’ll take some real world data. And then they’ll say, what’s the model that you would use to best describe these data and then run some randomization samples to collect data. And then ask, “How likely is it that the original data were from that distribution?” And so that’s a powerful thing because a person doesn’t need to know any statistics coming into that class and being able to make meaning out of a lot of those things. There are multiple textbooks that use this simulation-based inference testing process to great effect and in the links that are going to be associated with this podcast, you’ll be able to go and find those, and just see the rich resources that they have supporting those texts, which actually can be used independently as well for reinforcing specific points that a person might have about their own statistics class or econometrics class. Another thing that I think is useful to point out is the fact that there’s a document that helps guide all of this. And the American Statistical Association has got the Guidelines for Assessment and Instruction in Statistics Education. This is called the GAISE guidelines. And they were revised in 2016. And they provide some very implementable recommendations for improving introductory statistics classes. And some of them are very consistent with what we’re talking about today, increasing the use of technology and the use of simulations, and decreasing that distance between abstract concepts and these students’ real worlds.

Rebecca: Can you talk a little bit about how to get started in implementing these sorts of things into your classes? So if you’ve never used simulations before, how do you start?

Matt: Well, I think, for me, the best thing to do would be to reach out to colleagues who might be doing that. So, for example, here at NAU, colleagues in the mathematics and statistics department are using these. So I would go to them. And I would say, “What have you found most useful, and how might I implement that in the class, given the context I have?” But, you can also do some wonderful internet searches. And I think I’ve curated a few really good starting places for you, in the resources attached to this podcast, I would recommend, for example, just seeing what’s out there by looking at these lists of applets that exists to teach this and to teach this and to teach this. And if you are thinking about something that’s on a grander scale, listen to the video by Nathan Tintall and Beth Chance, about how they implement this simulation-based inference testing in their classes and the rewards they have from doing that. I think getting a real broad sense of what’s available early can be really helpful in figuring out how you might want to do this. But I think that the nice thing is that you don’t have to do it on a grand scale, to start. You can use a single applet to reinforce a point that you might find your students struggling with. There are some other resources. There are journals on teaching statistics that are very, very useful. And I think this cross-pollenization between mathematics and the psych stats classes, is really useful. So I think it’s helpful to get this strong situational awareness of what others are doing to help inform how you might do what you’re doing better.

Rebecca: I think this idea of “one small step” is always a great approach to trying something new, and it seems very manageable. So I can try one simulation and see how it goes, and then feel confident to implement more and more. But that kind of iterative approach seems really helpful. Of course, not everyone has eight sections that they can iterate through all at once. [LAUGHTER]

Matt: Yeah, even if you’re doing it once. I mean, think about the environment that you have. You’re explaining these findings that are very visual in nature, and how all these things are wired together. And I think one of the most important things the faculty contribute to students’ education is not just the facts, but how these things are all linked, and being able to hear from a seasoned faculty member can help develop student’s ability to think these things through in a more expert way, rather than just memorizing simple facts. So I think that not only do we get some sense of accomplishment in putting those things out there for students to use, but the students do as well, because they want to get this too, and they’re much more enthusiastic about content when they think they’re really getting it, or they know they’re really getting it.

John: I think anyone who has been teaching for any length of time knows where some of the pinch points are, the things that students always have trouble grasping. And those would be a good place to start, not just in statistics, but more broadly, in any discipline, where there’s some concepts that students don’t always make the connection between theory and practice or practical application. So those would be the places I would think where people should get started… thinking back on where students are having trouble making connections, because it’s generally the same areas year after year after year. And that information could be used to help us improve our instruction by using tools that make it easier for students to see those connections.

Matt: Those are all good points. And you know, one of the things that was evident when I was looking into this more deeply was the frequency of which these simulations are being used in AP statistics and earlier. And so it’s much more likely now that we’re gonna see students coming into our classes who are somewhat familiar with this way of presenting information. And so they’re going to get it pretty quickly. And so a nice way to make them feel more at home might be to put these things in and, again, to leverage their learning, give them this feeling of self efficacy, that’s going to be really helpful to them as they get into more difficult concepts.

Rebecca: How have you adapted your instructional approach during COVID-19 and teaching remotely?

Matt: That is a great question. And one of the things that helped was that this online stats lab that we’ve put together over the years really made it so that these labs were kind of ready to go. So, in that respect, the materials had been developed as had many that people had put together at the end of the spring 2020 semester. Those were just in the bank and ready to be used in the fall and are even stronger now. There are lots of models being used throughout the country, for dealing with COVID-19 and instruction. So maybe I’ll just drag the one that we’re using so that listeners can get a better sense of how it all fits together. We’re using a modification of the HyFlex system, which is called NAUFlex. And we started using that really in the fall of 2020. As is the case, I think, for many, after spring break of 2020, people went into mostly completely online mode. And so the NAUFlex system starts off with teaching being done completely online. And that allows students to get on campus and be tested and all of the things that build that strong safe infrastructure. And then somewhat later, students are able to opt in if they choose to participate in in-person classes. Now, the online classes that are held are synchronous, so there’s an expectation that students will be there for those. And then we also have COVID adjusted room capacities. And so what that means for some classes, is that they have two groups or three groups of students who can come in, so that we can maintain that distancing. My experience has been that most students have opted to stay online, which means that they show up for the lectures or the labs in either Zoom, or what I use is BB Collaborate, which is built into our learning management system BB Learn. And so that’s how it works for us. And kind of the unsung heroes in this whole evolution have been the instructional designers who helped make this work, and also the folks from Information Technology Services who found hardware that works, that allows us to both interact with our students in the classroom and push it out there to students who may be in places that have varying degrees of connectivity. What I’ve done to modify my instruction, somewhat based on feedback I’ve gotten from students from the spring and fall semesters: what they liked, what they didn’t, how it worked for them, and try to really bring to the lab, this sense of organization and consistency and safety. One of the things, as educators, we’re used to doing is walking into a classroom and being able to gauge energy levels and look around the room and be able to tell who’s got that faraway look, and maybe we need to go back and regroup and cover some material. And some of those cues aren’t there anymore. And so what I’ve found is that I’m much more elaborate in my explanations so that I don’t leave anybody behind. And I tried to foster an environment which makes everybody feel comfortable asking questions when they want. And it’s very rewarding for me when they do. And I know that, in a class of 30, if a student asks a question, there are several others who probably have the same one. So the other thing that I think, and I know that this is something shared by your listeners too, is just that the notion of teaching with compassion, these students are really out of their academic element, if you will, of the in-person classes and going from one place to another. That sequencing is no longer there. And so it’s a much different world in which they need to learn. And some of them learn very well in an online environment and some don’t, but they’re forced into that anyway. And so I tried to have lots of compassion for what the students are going through and try to extend that in my syllabi for late assignments and things like that. And I think I’m a little more careful with humor, because I don’t know the backgrounds of all the students. I have not had that experience with them in the classroom. And so I’m really careful about how I express things so that everybody can get it, and it’ll be something that everybody can accept and understand. The nice thing about the labs is that we have all of these resources that we can use. And so it’s designed to be delivered in an online environment completely. And so students have interactive tutorials they can go to that help them master the content, complete the assignments. As an aside, one of the things that I found helpful in this communication, is that I wear a clear face mask when I’m teaching. Part of it is because I appreciate that myself. I’ve got some hearing loss. And so I’m a little bit reliant on reading lips. And in the classroom, students need cues that “this is important,” or “I’m trying to be funny here.” And I think that it helps the students understand the content and my commitment to their success when they can see my face better. That’s a little thing, but I thought I’d put it out there. I’ve gotten feedback from students that they found that helpful. And the other thing is that having taught this lab so many times, you mentioned pinch points before, I’ve got an idea of where those are going to occur. And so when we’re coming up on one of those, I can be more explanatory, give them a much better foundation for getting past those. So those are the things that I’ve changed.

John: One nice thing that may come out of this whole difficult teaching experience this past fall, is that I think all faculty have learned to be much more inclusive in their teaching approaches for all the reasons that you mentioned. And I’m hoping that that’s something that will continue as we move past the pandemic.

Matt: I agree with that completely. I think that there are really important initiatives to promote that in every classroom. But I do think that the situation which we find ourselves in now does encourage us or motivate us to do a better job with that. And so that’s one of the things that I would throw out as well is this whole idea of universal design for learning, something that I think is really important, and simulations play into that nicely, don’t they? …in that they provide this other way of representing information, content that students can get, particularly those that the students can work on themselves time after time after time until they feel like they really get it. And so I think that this universal design for learning thing is something that we should probably keep in the forefront as well. And some systems really do a nice job with making that easy for us. So for example, there’s an add on to BB learn that takes PDF files, for example, and creates those in alternative formats.

John: Ally.

Matt: And so you’re familiar with that. And for some students, it’s the only way to get that content. For others, it’s a convenient way to listen to content while they might be on the bus or in the car. And so I just think with these simulations, it just feeds nicely into what I think is a mandate to try to make things available in as many ways as possible, so they can really resonate with students.

Rebecca: Do you have any other tips related to simulations that you want to share with folks who might be teaching similar kinds of courses?

Matt: Well, that’s a great question. And while I’ve talked about simulations, one of the things that might be on the border of that, but I think is very useful for incorporating into classes, are some games. And in the face-to-face labs, I used to really enjoy doing like Stats Jeopardy and things like that. It’s a little bit more difficult to do in an online environment. But one of the things that I’ve done in the correlation module is to use a system put together by John Marden. He’s a Professor Emeritus at the Department of Statistics at the University of Illinois in Urbana Champaign. And he’s got this nice little system where he provides students with panels: four scatter plots and four correlation coefficients, and they need to match those. And so what I’ve done in previous semesters, and look forward to doing again, is having a competition across all the sections to see who has the longest sequence of correct panels, the winner of that gets a copy of a book by Tyler Vigan called Spurious Correlations, which if you haven’t seen it, his definitely worth a look. And there’s a website online as well, which is kind of fun. And one of the things that I’ve noticed with this particular gamified module is that students really work hard to get it. And at the end, they do, there are heroic efforts to win that book. And at the end, they really do know how to look at a scatterplot and get an idea of what the correlation coefficient might be.

John: For people who might want to go a little beyond using simulations in class, do you have any suggestions on where they might go to learn how to use, say, Shiny in R in order to create their own simulations? Is there a good reference out there?

Matt: I think there are some good references out there. They’re not, I think, specific to building simulations for teaching psychology. Although I have to say that one of the links that I’ll provide following the podcast will take you to an array of Shiny apps that were built specifically for teaching introductory statistics. And here’s the thing, they were built by undergraduate and graduate students for that express purpose. So this is a beautiful selection that were student built. But I think people who start working in R will look at some of the blogs that are out there and start being able to put these together themselves. But again, I think with all of these things, it would be starting off simple and going from there. Some of the ones that you’ll see out there are incredibly elaborate, and I know that they’re not in my skill set to build at the moment. So I would start with simple and go from there. But in the meantime, take a look at some of the other ones that are out there either to implement directly or try to emulate.

John: We always end by asking what’s next?

Matt: Well, for me, what’s next is a nice organized, gradual wind down of 2020. I think all of us are looking forward to 2021. I mentioned how grateful I am to have the opportunity to talk with you today. In preparation for this, I did lots of looking at things that are out there and I’m just really re-inspired to find simulations to put into my lab wherever I can. And also, as I’ve mentioned, planning on maybe building some assignments into my undergraduate teaching apprentice class about how they can use this. But I think I’m missing the contact with students in the online environment and in the lab, and I’m looking forward to being back in the classroom and using some of these things. But, I think, immediately what’s next, maybe another cup of lemon ginger tea.

Rebecca: Sounds like a good way to spend an afternoon.

John: This has been fascinating, and I’m looking forward to doing more of this during the spring myself. Thank you.

Matt: You’re very welcome. Thanks, John. Thanks, Rebecca. It’s a real pleasure to be here today.

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

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

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