Episode 176: Using Curiosity to Engage Students With Abstract Concepts – An Interview With Elana Reiser

Apr 11, 2022 | Podcast | 0 comments



Today we speak with University Professor, author and former Making Math Moments That Matter Online Workshop participant, Elana Reise. Elana joins us today to chat about how we can leverage curiosity to engage students in solving abstract mathematics – in particular, mathematical proofs! 

Join us for a great conversation with Elana where we discuss her initial hesitation to get into mathematics education and where it has taken her to advocate for the inclusion of a course on mathematical proofs which has now grown to be a compulsory credit for all math students!

You’ll Learn

  • How to modify abstract math topics (like proofs) to become more curious and engaging; 
  • What you can do to teach your students about productive struggle; and, 
  • How to build and use a problem solving framework to help your students become more resilient. 
Start your school year off right by downloading the guide that you can save and print to share with colleagues during your next staff meeting, professional learning community meeting or just for your own reference!


Elen Reiser: The way that I wrote the book is to make it like a journal so they can write in it because, same for you guys, I know you think reflections are very important and that's, I think, a big part of my course, as well, is I want them always reflecting on where they're at, what they know, what they need to know and all that. So they can kind of journal as we're going through that beginning stuff and I think that really gets them in the right mindset and it prepares them so that when we do get to the proofs

Kyle Pearce: Hey, hey, hey, Math Moment Makers, today, we speak with university professor, author and former Making Math Moments That Matter online workshop participant, Elana Reiser. Elana joins us today to chat about how we can leverage curiosity to engage students in solving abstract mathematics and, in particular, mathematical proofs.

Jon Orr: Yeah. Join us for a great conversation with Elana, where we discuss her initial hesitation to get into mathematics education and where it has taken her to advocate for the inclusion of a course on mathematical proofs, which has now grown to be a compulsory credit for all math students.

Kyle Pearce: All right my friends. Hang out with us for a little bit. Here we go. Welcome to the Making Math Moments That Matter podcast. I'm Kyle Pearce.

Jon Orr: And I'm Jon Orr. We are from makingmathmoments.com and together-

Kyle Pearce: ... with you, the community of Math Moment Makers worldwide who want to build and deliver math lessons that spark curiosity, fuel-

Jon Orr: ... sense making-

Kyle Pearce: ... and ignite your teacher moves. Friends we are so excited to bring in a former, we're going to call her former colleague, who joined us in an online workshop. Actually, it was our first online workshop that we had run, and it was a pleasure to learn alongside Elana. And today we're really excited to be able to bring her into the podcast community to share her voice and her learning around teaching at the post-secondary level.

Jon Orr: We're recording this after the interview, but we did chat with Elana, our very first interview ever on video, Kyle. It was before our podcast. 2018 was when we first ran our first iteration, first cohort of the online workshop, way back then. Since then, I think we've run, I don't know, six?

Kyle Pearce: It's got to be six. Yeah.

Jon Orr: Six to seven cohorts of that course. We've had, I think, 1,500 students, teachers through that program. Anyway, Elana was one of the first and it is great to re-chat with her three years later on where she is on her journey. And she's been putting so much of that learning into place and helping students along the way. So let's get to it. Here we go.

Kyle Pearce: Yep. Here we go. Hey, hey there, Elana, thanks for joining us here on the Making Math Moments That Matter podcast. It feels like just yesterday, the last time-

Jon Orr: It does.

Kyle Pearce: ... Jon and I hopped on a Zoom call just like this. But when we actually looked back at our records, it was actually over three years ago when we were chatting with you.

Jon Orr: Actually-

Kyle Pearce: How long, Jon?

Jon Orr: I think it was in December of 2018. I'm pretty sure, because we're stealing her thunder right now, but Elana joined us for one of the first cohorts of the Making Math Moments workshop. We chatted with her after, where that session was, to get feedback, to help it improve for the next run through. And that was three years ago and we would've ended that course in December 2018. Well, Elana, welcome to the Making Math Moments That Matter podcast. It's been three years in the making. How are you doing?

Elen Reiser: I'm doing great. Thanks.

Kyle Pearce: I feel like Jon and I know a lot about you, but the people who are listening at home, in the podcast, or maybe some people watching this on YouTube, you can see all our faces on YouTube right now. Tell us a little bit about yourself. Where are you coming to us from, how long you've been teaching, and give us, I guess, a bit of the backstory. What lands you in this crazy world of math education?

Elen Reiser: Sure. I'm coming from Long Island, New York, and I've been teaching, I want to say about 19 years. So for quite a while, but doesn't feel that long. The way that I actually got started, going into college, I always knew I wanted to be a math major. That was no question. But I was adamant that I was not going to be a teacher. And the main reason is because I'm just a very shy person. I'm such an introvert. And I'm like, I can't handle being in front of a class.
So my junior year, one of my professors said, "Oh, do you want a TA for calculus?" And at first I'm just like, "No," but then I sat and thought about it for a little bit. I talked with some friends and I was like, "You know what? I like to challenge myself. It makes me uncomfortable, but let me give it a shot. I'm interested." Luckily it was still available and I was a TA. They also had us work in the math help center. I just loved the tutoring and being the TA. So at that point I just changed my mind. I'm like, "Yes, I'm going to be a teacher."

Kyle Pearce: I love that. That's fantastic. I was curious about that, because I know that, prior to coming on, you had mentioned that in one of the emails, about how that was not your original plan. I was actually you really curious, and that makes a lot of sense, that you have to actually get yourself up in front of a group of people. You have to be, we use the word vulnerable a lot, you have to be vulnerable. You have to be able to do that.
And even just listening to that story about the TA situation, I feel like that says a lot about who you are as a person in terms of just being a little bit more open to not just shutting and slamming the door. You had shut the door initially, but then you actually did give it some thought and look at where you are now. So that is fantastic to see that you kept that door open for yourself.

Jon Orr: I just became insanely curious when we just started chatting about this, with your pivot to teaching. I know that you are a post-secondary instructor and I'm a high school teacher. And I think I'm a lot like you where I've always been kind of an introvert and ended up being a teacher as well. And I know that my friend, other than Kyle, Kyle's very much an extrovert, but my friends that I teach with, my colleagues, math teachers, I find them also very much introverted, but they are, again, they are teachers. I'm wondering about your journey there, on the sense of what was that kind of pivot? Was that an easy pivot for you to stand in front of everyone? Was that tough? Was there a learning curve there and it just became comfortable? I'm curious to hear just that side of things, just because it's making me curious.

Elen Reiser: Well, I think the opportunity to be a teaching assistant and to tutor, rather than me being the one responsible for a whole class, was very helpful because I didn't obviously have to plan the course. I just did what was told of me, but I did run my own section. So I got just a little taste of what teaching would be like and the same with tutoring. I didn't feel put on this spot because I was just with a single person. So I think it was just like a gentle introduction to teaching that kind of made me interested and then, as I got more comfortable, I was like, "Oh yeah, I can do this. It's not a problem." And then I think the next year I was a teaching assistant for a pre-calc class where I was actually the professor, I ran the whole course.

Kyle Pearce: Awesome. Awesome. So it sounds like it was almost like a little bit of a nice gradual intro into that world, which I think is probably a really helpful piece, right? Because if you didn't have that opportunity, you'd probably be looking at it and thinking about teaching a full section on your own and maybe thinking that's way too far of a leap. So you had a little bit of a bridge to get there. So, before we move on, we're really curious about a lot of things, but we don't want to go too, too deep until you tell a little bit more about what are you doing now? What is your role? Where are you teaching? And give us a little bit more of that backstory before we dive into a few of the details.

Elen Reiser: Sure. So as I said, I'm on Long Island. I teach at a private college called St. Joseph's college, which is in Patchoauge. I'm in the Math Department, but also I run the Master's Program for math education. So I kind of straddle between math and education and I teach both types of courses. I kind of teach basically anything that's thrown at me. Like, next semester I'm teaching calculus, I've taught pre-calc, I've taught linear algebra, I've taught prop stats and then some of the graduate education courses, as well.

Jon Orr: Gotcha. Awesome. Awesome. Thanks for that. You know, we wouldn't be doing our job here if we didn't ask you what your math moment is or was, or when you think about math class, usually people are, are kind of stretched back to when they were younger, but it doesn't have to be that. So when we say math class, Elana, what is coming to mind? Share a math moment for us.

Elen Reiser: So I'm going to share when I was in my freshman year of college. So up through high school, I was always really good at math, it came easy to me and, as I realize now, I was a very good memorizer. I followed the rules. Even outside of math, I'm a rule follower, so that was good for me. But I feel like no teacher really explained the concepts, but also nor was I interested in understanding the concept.

Kyle Pearce: Yeah. I can relate.

Jon Orr: Yeah. Yeah.

Elen Reiser: So, come freshman year, second semester, I take an Intro to Proofs course, which is kind of the divide between thinking of math as a computational subject versus a theoretical subject. I just remember sitting in that class having no idea what the professor was talking, about completely lost, and I just felt like such a fraud. I was like, am I supposed to be a math major? This is not making sense. What is going on? I don't even know what math is. So that's my moment.

Kyle Pearce: I love it. I feel like there's so many people that can relate. We've said it a billion times before. Jon and I were both memorizers. We felt safe in that place. Like, nobody really asked us why things worked, so we sort of got away with it, that all we had to do was make sure that we could spit out some answers and we were good, we had the free pass. And I think, when you realize that, after some time, it really does make you think a little differently about how, especially in education, how you want to help more students to see and understand the mathematics.
So we ask this a lot more recently about your math moment. How does that influence what you do in the classroom when you're teaching your students? Does it influence at all what you do or how you plan and deliver your lessons? Or is that something that you've got kind of tucked away and you don't think about a whole lot?

Elen Reiser: No, it definitely influences my teaching. Anytime I think back on that, I remember what it's like to feel, as a student who's lost, not understanding what's going on, and I can kind of put myself in my students' shoes and help them navigate and figure out how to best get them towards understand.

Jon Orr: I would like to keep moving things along here and I know that you've been doing lots of work in this proofs course and that being such an important aspect of your math moment, but I know that when you joined us for our first cohort of the Making Math Moments That Matter online workshop, you joined us, you went through all of the learning there. We chatted with you afterwards. I know, from our communications through email, but also in other places, that you were thinking of taking that proofs course, or so some of the courses you were teaching at a higher level and inserting the elements of the Making Math Moments That Matter three-part framework. I wonder if you could elaborate a little bit on what you've learned from the workshop and how you're using it to kind of push this proofs course and get a university-level course, thinking about math pedagogy, instead of this kind of university "We don't really think about pedagogy."

Elen Reiser: I will answer your question, but I want to back it up a little bit-

Jon Orr: Sure, no problem.

Elen Reiser: ... and give a little bit of background about the development of the course first.

Jon Orr: Yeah, for sure.

Elen Reiser: So when I came to my school, we actually didn't have an Intro to Proofs course, which I thought was insane. So I kind of had to push for that. First, I was like, "Oh, let me make it a one-credit course." So they're like, "Okay." Then a couple of years later I'm like, "Can we just change it to two credits?" And they're like, "Okay." Eventually, I got it to three credits, which is what our courses typically are. And then a few years later, eventually I got it as a required course for all of our majors.

Jon Orr: Oh nice.

Elen Reiser: So that was a slow process.

Jon Orr: Nice. I love it.

Elen Reiser: So now we have this course and what I was noticing is just, I didn't have the term at that point, but the lack of productive struggle. That students would look at proof, maybe give one shot, it didn't work, and they'd be like, "Oh, I don't know how to do it," and give up. So I've been struggling for a long time. How do I get them to go through that struggle? And then one summer I took Joe Bowler's online workshop and that just totally clicked. I was like, "Yes, they need to have a growth mindset. That's what I'm missing."

Jon Orr: Right.

Elen Reiser: So since then, I've been gradually trying to introduce different things, to get them have the growth mindset. And that was what kind of led me to taking your workshop. I'm always trying to learn, always trying to get better. So I'm always taking workshops, going to conferences, stuff like that. So from your workshop, in our conversation that we had after that, one of the questions I asked was, because I was teaching the proof course that next semester, and I was like, I want to use a lot of these ideas, but I don't feel like they were for theoretical type courses. What can I do?
And I actually remember in that conversation, I believe it was Jon, you said, "You just want to spark their curiosity, just make them curious." That stuck with me and that was kind of the driving force for, how do I start to make these changes, is I just wanted to get that curiosity in there.
So the way that I kind of structure the course now, and I wrote a textbook that follows this format as well. The course, in the beginning, we don't even talk about proofs until a third of the way into the semester. First, I teach them about a growth mindset, what it is, and we go through exercises. I teach them why it's important to struggle. We do a little bit of the math background, which is logic and problem solving and stuff like that.
But the way that I wrote the book is to make it like a journal so they can write in it because, same for you guys, I know you think reflections are very important and that's, I think, a big part of my course, as well, is I want them always reflecting on where they're at, what they know, what they need to know and all that. So they can kind of journal as we're going through that beginning stuff. And I think that really gets them in the right mindset and it prepares them so that, when we do get to the proofs, they are much more able to sit there and struggle through it. And I've seen it, because I've been teaching it every semester. The last couple of semesters I've seen them. They don't give up.

Jon Orr: I love that.

Elen Reiser: It's just been amazing. Yeah.

Jon Orr: Great.

Kyle Pearce: That's awesome. It's funny because, when you describe these are university or college students who are taking this course, giving it, we'll call it, maybe a weak go. Initially they give it this like "I'll try," and then they give up and I feel like everyone listening, regardless of the grade level they're teaching, sees that. Whether it's a student in grade two who gives up on a word problem or a student in grade seven who gives up on a problem that feels like it might be a little bit too difficult, all the way into now you're in post-secondary where students still have this same, I don't want to say ability because it's like, everybody has the ability to struggle, but it's almost like this, I would say, reluctance to struggle, reluctance to put themselves in a situation where they don't know the answer.
And to me that just rings the alarm bells that it's likely that these students have sort of been going through, much like we all in through school, where things sort of came easy to us. We either picked up on the pattern very quickly or we memorized it or whatever it was that got them to that point. And it's almost like they just don't know how to handle this struggle. So I really like this idea that you're setting them up, getting them prepared, thinking about what is a growth mindset, getting them to almost get comfortable with the struggle and then leading into a concept that I'm going to be honest and say, proofs aren't always the most exciting math concept. That's not where people are typically starting. Right, Jon?

Jon Orr: I completely agree. Even though I always loved the proof side of mathematics, even in high school, that was one of my loves of mathematics. And maybe that's what drew me to that subject, other than, say, the computational. Because I agree with Elana when she said most of us view math as computational until you see proofs. And it's kind of like all of a sudden it's like, whoa, this is mathematics.
I want to jump back to what you were talking about with your sparking curiosity or bringing in curiosity into your proof course. I know that you've learned a lot along the way about how to do that, but I know a lot of teachers listening right now to this podcast are dabbling in that area. Like we've got people who are like, I'm all in, I'm just getting started, I've started, but I'm trying to work out the bugs and the details.
Elana, I wonder if you have any kind of tips or suggestion, if you've implemented this in something that's so abstract? Maybe you can give us an example of how did you do that with, say, some proofs course? I know you might even talk about some proofs, if that helps you kind of give examples, but also maybe what's an important aspect of bringing curiosity when you're designing lessons.

Elen Reiser: I think the main part I bring the curiosity in is when we go over definitions. I use number theory as the way to teach proofs just because I feel like it has stuff that people are familiar with, even in odd numbers, rational numbers. They've at least heard of that stuff before. So when we get definitions for each of those, I use a lot of the structures that high school and middle school teachers are using.
Before we get to the proof section, one thing we do is, I took this from Sara VanDerWerf. She has an activity about thinking like a mathematician, on her blog. So I go through that and that's with pattern recognition, but I kind of show them the steps of "This is how mathematicians think." I'll give you an example with even and odd numbers. I don't just give them a definition. So for even numbers, I would just put up a list of even numbers and I would say, "What do you notice? What pattern do you see? How can you generalize that pattern?"
Maybe they won't have it in the perfect form so I'll take their idea. Eventually, they'll say, "Oh, it's two times an integer." And then I'll just write the definition a little bit more formally, but using their idea. Then, and for odd numbers, I will have the even list and then I'll put the odd numbers right under. And I'll say, "What do you notice between these two lists?" Eventually they'll notice, "Oh, if I just add one to an even number, I get to an odd number." And then we can use our definition for even numbers, which was two times an integer plus one. That'll give us our definition for odd numbers. So just things like that, with the definitions, I feel like it's helpful, where they're sort of coming up with the definitions rather than me giving it to them. Another example, like with rational numbers, I'll do a "Which one doesn't belong?" And I'll put up different forms of rational numbers or irrational, and they'll have to discuss that.

Kyle Pearce: I like it because a couple of things. You're bringing in the student voice again, which I think is a theme that we're constantly talking about. When you're sharing your own thoughts and you're seeing those thoughts being respected and leveraged, you know where you want to go. Elana, you've got it all worked out and here's the path we're going to go down. But it's like, that hook, when students are sharing their thinking and you're showing that you value their thinking and bringing it to the forefront, it's like a natural hook. It hooks you in and it wants you to keep going deeper with that.
I think that's so key. And the other theme I'm hearing here, which again, links back to curiosity at all grade levels, whether it's more abstract concepts like in proofs, or whether it's something like very early on in elementary math, is the idea that asking good questions, asking people to think. And when I go back and I think about the struggle you had highlighted where students would start a problem and not finish it. Jon and I are constantly talking about, how do we get students to start problems and stick with them?
Well, by asking more questions more often. If we're just constantly asking our students to do the thinking, it becomes a habit without them realizing it, and I'm sort of seeing this theme emerge for you. So I'm wondering, when you get into the actual proofs, are you feeling like all of this lead up with mindset with, you had mentioned about problem solving and helping students sort of build this productive struggle mentality, are you feeling like all that groundwork sort of makes it just easier to introduce the proofs? Or are you introducing the idea of proofs in some other way as well? Or is there an aspect there that you're doing now differently than when you had done previously, when you first started teaching?

Elen Reiser: Yeah, definitely. I also developed just like a framework for them to follow. So it says, what do you know? What's given? So they have to put it in a... I call it a usable form. Meaning, apply a definition if you need to. Then, what are you trying to prove? Again, put it in a usable form. What proof method could you use? And then do some examples with numbers plugged in. Just because usually that helps you understand the proof a little bit better, when you're looking at examples. And then I have, like on the bottom, a little place for them to doodle where they could just try things out.
They probably hear me say this almost every class. "It's okay if you don't get it right the first time, just keep trying. Try again. You'll get it." So they just kind of share anything they want. And then there's a box for where they write their final proof. So I feel like at least they can get the beginning steps, so at least they're not sitting there just thinking, "I have no idea how to get started."
So I feel like that framework has helped a little bit. One thing I really like that I found on the YouTube site. There's an interview with Steve Strogatz and, in that video, he talks about a time when he didn't understand a math problem. And he's like, "Oh, I felt so embarrassed." And he's a world-class mathematician, so to hear him talk about how he couldn't do something, I just feel like it helped me when I heard it. But I think it helps the students, too, just to hear. I just really try to get across that nobody is born a proofs person.
I didn't just pop out and be like, "Oh, I know how to do proofs." It's the same in younger years. They say, "You're not a math person," or here I say, "You're not just a proofs person." I think what also is kind of hurtful is if they have seen proofs in an earlier course, the person who's presenting the proof already knows how the proof works, has already seen it done, probably memorized it, and they just present it. And students begin to think, "Oh, this is how a proof should be. I should look at it, automatically know what methods to use, know how to do it and it should just pop out."

Kyle Pearce: True.

Elen Reiser: So I always try to share. And even with other things, I always try to be transparent. Like, "Here is whatever teaching method I'm using," so I try to say, "This is the reason why I'm using it." So anytime I do this, we have a discussion about the homework, we have a discussion about the quizzes, anything I do in class, I'm like, "There's a research-based reason behind what I'm going to share it with you."

Jon Orr: Right, right.

Elen Reiser: I feel like that is also helpful because they know I'm on their side, I'm doing this for them. So they don't feel like, "Oh, this is just work to do work.

Jon Orr: Right. How are your students responding to these changes? I'm imagining proofs can't be the most fun course to ever take in class, especially now, even though you think it is and I think it is, and now it's a requirement for all of your students. We deal with this in our high school classes all the time. It's a requirement to take math. We constantly are teaching. That's primarily our job is to teach math to kids who do not want to take math. And that's partly why we've implemented the three-part framework, is to kind of get kids to enjoy math so that they can learn with it and learn from it. How are you seeing the kids, the students, respond to these changes? Are you seeing some of that change to the concept of proofs or the class? I don't know if you want to comment on that.

Elen Reiser: Yeah. I'm definitely seeing changes. See, my students are a little different because, for the most part, they're all math majors. They have chosen math, right. So it's not like high school where you're kind of stuck with it. But I do feel like I don't hear "I hate proofs" or "I can't do proofs." I don't hear that anymore, which is really nice.

Kyle Pearce: I love it. I love it. Sometimes, too, we've mentioned it before. It's like one of the greatest compliments I feel, as a math teacher, is when the bell goes and students say, "Wow, that went by fast," or something. It's not like them turning to you and being like, "This was the best class I've ever been to." Just this general enjoyment. There's just a general positivity or a positive vibe in the air, which is huge.
You've shared a lot there, Elana, with your journey coming from your experience of feeling introverted and not wanting to be a teacher and then sort of landing in this place and realizing this is exactly where you want to be. And you've gone from teaching, essentially, can I say almost begging to teach this course, and maybe once that happened, you were probably like, "Oh geez, what have I gotten myself into? It's proofs and students aren't really enjoying this process a whole lot."
And then yet, now you're in this place where you're actually making a difference for those students in really building the confidence that they can work through hard problems, and it has led you to actually writing a book. And we want to dive in a little bit with this book. I think we have a little bit of the backstory as to why you wanted to write this book. I'm wondering if we were to dive in here, if someone was thinking and they're going, "Wow, I can relate to this experience that Elana's sharing." Maybe it's with proofs, maybe it's with some other math concept. What are people going to get? Who did you write the book for and what are you hoping that the reader is going to walk away with when they pick up that book and they take a deep dive in there with you?

Elen Reiser: Essentially, it's really just written to be a textbook for anyone who's teaching an Intro to Proofs course out of college. So that would be the main audience. I suppose maybe if a high school student or somebody who just wanted to self-study, they could also pick it up as well, but it kind of mirrors the way that I teach the course. Now, unfortunately, every time I teach the course, I teach it differently because I'm always learning new things. So by the time the book came out, I was already teaching things differently.

Kyle Pearce: Yeah. That's how it goes.

Elen Reiser: But it kind of puts in a lot of the things that I do. It gives you a lot of information. It has the homework problems to do, and all of that. So it's really meant to be like a textbook.

Kyle Pearce: Awesome. And it sounds, too, what you're advocating for is, if someone picks this up and they're using it either to self-study, like you had mentioned, which might be more of, we'll say, a more rare case, to someone who's teaching a proofs course, and they're looking at it as a guide. It sounds like what you're saying is it's not meant to necessarily meant to be like, "This is the way to do it," but more or less "Here's a structure. Here's what it might look and sound like," and then obviously educators are left to their own devices to sort of add, subtract, rearrange and maybe implement it, how they see fit.

Elen Reiser: Yeah, definitely. And in the introduction, I do actually mention, basically, exactly what you just said. I share some of the teaching ideas. I say, "This is what I do in my course, but feel free to pick and choose what you like or add the way that you want to teach it." I think one problem also with math textbooks in college level is students can't really understand them so well. They're written at a very high level. So this book, I think, is very understandable. It has a lot of examples infused in it. It's really meant for the students. You could say, "Read chapter one," and in the chapter there's exercises. So at the professor could choose to do those exercises in class, which I sometimes do. Or you could say, "Read this chapter and just write in the exercises for the homework," or something like that.

Jon Orr: Elana, you've done a ton of learning along the way to be able to write a book. I'm in awe of people who could write a book, because you've done so much learning. You've done so much practice to kind of bring that expertise out into the public, into the public domain. That is amazing. I'm wondering, with all of that learning that you've been doing from your teaching practice, to your writing the book and all the other things that you've done, if there was a piece of learning that you felt is the most valuable? Well, maybe like a big tip for teacher.
So it's like a teacher for proofs, but it could be a teacher for any math subject, from high school all the way to elementary school. I think teaching is, in general, lots of great practices. So I would say, what's your biggest takeaway for the listener right now? What would you want them to go, "Hey, this is the most important thing I've learned along the way and I want to make sure that you know it"?

Elen Reiser: Well, I think right now I would say read the Thinking Classroom, because that is the best book on math I've ever read. It's well written and it completely changed the way I wanted to teach. I hadn't mentioned, but I do use some of those techniques in this course as well. We do use the visible nonpermanent surfaces. I have the students stand up at the end when they're working on proofs on their own and I do the visibly random grouping just to build a classroom culture. So I do use some of those aspects. I don't do it fully, just because I don't feel like it fully fits with this type of course, but I do it as much as I can. That was where I learned a lot by reading that book.

Kyle Pearce: I love it. I love it. And we must agree. We reference Peter's work so much and it is so applicable to so many different grade levels, so many different we'll say concepts or levels of mathematics and obviously well into post-secondary as well. I would argue, the more adult-like you are, the better those strategies work to get people up and collaborating and working together and thinking, which I know is happening in your classroom with proofs.
Elana, you have shared so much awesomeness with us tonight and, as well, you have an amazing resource which we will share in the show notes, the Science of Learning Mathematical Proofs. We will share that for those who are interested in checking it out. I'm wondering, any last words, any places people can find you, get in contact with you, before we sign off for the night?

Elen Reiser: I think, for last words, I would say to just always keep challenging yourself, always keep growing as a teacher, don't be afraid to try new things and just be honest with your students. Share when you have struggled. Don't pretend to be perfect. They'll be better off if they know that you had trouble doing something. In terms of getting in contact, I know everybody is using Twitter, but I am not really on Twitter. But I am on Facebook so I am in your group, I'm in a few other math groups and I did also put together a website to kind of go along with the books. That's scienceofproof.com. I put a lot of information. I put like some teaching ideas that I do that weren't in the book, I added there, and a few other pieces of information.

Jon Orr: Awesome.

Elen Reiser: And it has my email address on that site, if you want to email.

Jon Orr: Awesome stuff. We'll toss that in the show notes with all the other resources that you've mentioned, and we've mentioned along the way in this discussion. So, Elana, we want to think you so much for joining us here. I know the listeners get so much value from hearing you speak and also the other guests, but thanks so much and we'll catch you soon.

Elen Reiser: Thanks.

Kyle Pearce: Have a great night. We'll see you soon. Hey, Hey, Math Moment Makers, as always, I hope that you gained a whole lot from this episode. It was great, not only for Jon and I to get to reconnect with Elana, to see all the great work that she's doing and really to see the growth. I don't know about you, Jon, but I can see it's like the confidence in taking the work that you love. And this is the challenge as math educators. You love the mathematics. That's why you're teaching it in the first place.
But when you go and bring that to students, sometimes it's not as received as well as you might like for students. And to see all of the growth that Elana has done since three years ago, when we were working with her inside the workshop and she was doing all of her learning around the growth mindset and around the curiosity path and what that might look like in post secondary, I'm super, super geeked and super excited for her to see how things are coming along and how she continues to grow along her own teaching journey.

Jon Orr: And I think it's another amazing thing to see her, not only share her learning with her students at a university, but also her teaching program at her private college there, but it is amazing to see that she's not alone in this, where people who have taken the workshop, especially after a couple years of implementing some of, or a year after implementing some of the teaching, have not only helped kids, but that are now helping teachers help other kids. Elana's doing that.
She wrote a whole book on how to take her learning over the last little bit and put into place for proofs at, say, post-secondary, but she's not alone there. We've got lots of people who have reached back to us to say they're now in coaching roles. And it's due to a lot of the learning that they've been doing through our course and our other courses. It's just amazing to see the community growing and then re-helping the rest of the community. It was good to see that here.

Kyle Pearce: And I think the common theme is, we say it all the time, we're constantly learning. You and I are learning through the doing of this podcast, through leading the online workshops and working with the academy members and just having this ongoing conversation around teaching. The different perspectives just make you think a little bit differently. So what are you going to do in order to kind of push yourself further?
First off, I would say you already have a huge feather in your cap. You listen to this episode, you're taking the time to kind of think about different perspectives. You're hearing other educators. You're trying to think of, even if you're a grade-three teacher and you're listening and you're saying, "How does Elana's story affect me?" Well, you certainly can take pieces from every single educator story and try to weave it into your own situation, your own context.
So make sure you're having those conversations as well. Go talk to a colleague, write it down, share it on Twitter, on your blog, whatever it is that you're going to do. Or maybe you want to connect with some other Math Moment Makers over on Facebook, by checking out our Math Moment Makers K-12 group on Facebook, or maybe on social media, Twitter or Instagram at Make Math Moments. But whatever you do, make sure you're doing something just so that this doesn't kind of fade away like footprints in the sand.

Jon Orr: For sure. Thanks, Kyle, for that. In order to ensure you don't miss out on the next episode, as we release them every Monday morning, and we've been doing that for a number of years straight. Every Monday morning, we've got an episode for you and we are going to be doing this forever.

Kyle Pearce: You're making that commitment right now.

Jon Orr: I don't know. We definitely don't see an end so we're going to keep them coming to you so you can help your students as well. But hey, hit the subscribe button, why don't you? If this is your first episode, welcome. We hope this was a good one for you. Hit that subscribe button so you get the next one. And if you've already hit that subscribe button and you're listening to us some more, welcome back.

Kyle Pearce: Awesome Stuff.

Jon Orr: And thanks so much for that.

Kyle Pearce: Absolutely. And I've got a couple links to share. We've got show notes, transcripts, all of that good stuff. All the resources that we've shared in this episode can be found at makemathmoments.com/episode176. That's makemathmoments.com/episode176. And I do want to take a moment just to let you know that if you're listening and you would love to come on for maybe a Math Mentoring Moment episode, we are going to be sending out another batch of emails to those who have put in that pebble in their shoe. So go and share. What's your pebble in your shoe? Head over to makemathmoments.com/mentor. That's, makemathmoments.com/mentor, and you can share a common math class struggle, and we'll bring you on. We'll have a chat about it. I'm even going to invite some of you that maybe you have an idea you want to share.
You know what? Use the same link. Just let us know in there. Maybe it's not a pebble. Maybe it's something that's worked for you and you just want to share it with the world. You just want to be able to have a way to share it with at least one other educator out there in the universe. Go over and head to makemathmoments.com/mentor. We'd love to have you on. And like I said, we'll be sending another batch of invites out very shortly so that we can have a chat with you real soon. Well, until next time, my Math Moment Maker friends, I'm Kyle Pearce.

Jon Orr: And I'm Jon Orr.

Kyle Pearce: High fives for us and a high five for you.

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