Dusty Jones: Hello and thank you for listening to the Teaching Math Teaching Podcast. The Teaching Math Teaching Podcast is sponsored by the Association of Mathematics Teacher Educators. The hosts are Eva Thanheiser, me, Dusty Jones, and Joel Amidon. Today we're talking with Keith Nabb. Keith is an associate professor of mathematics at Piedmont Virginia Community College. We're talking with him today for several reasons, one of which is to hear about his role in teaching mathematics at a two year college.

Welcome, Keith. Can you tell us a bit about yourself and your background?

Keith Nabb: Yeah, I sure can. So I'm beginning my 20th year in higher ed. It's kind of hard to believe that.And I've spent about 15 of those years at the two year college level. So at the community college, and I've spent four years at the university level. So I've kind of been around a little bit. I just love helping students kind of make sense of mathematics and just kind of see the joy in the subject that we teach. And part of what I really love is the blurry line between mathematics teaching and also scholarship of teaching and learning. So I like to do a lot of those mini studies with my students about mathematical thinking. Lately I've been actually involving them in the process of research as coauthors, which is has been a very enjoyable part of my job. So I see I really see that as the reflection component of my teaching. So I teach. And then I think about instruction and then sometimes we do classroom research and it's really been fun in the last four years or so to involve my students in that process.

Dusty Jones: Cool. Can you give us an example of one of the questions, or one of the studies that you've done?

Keith Nabb: I sure could. Actually there's a paper that I just worked on with Jackie Murawska. It's in the new NCTM journal, the Mathematics Teacher, that PK through 12. This was about cultural responsiveness and just making sure that we're doing the correct things pedagogically. So there is this problem that I give in my math for elementary school teachers every year that deals with fraction and ratio.
And so the problem is something like, I don't know if I can state it. It's called the condo problem where two-thirds of the men in a condo community are married two three-fifths of the women in the condo community. And then the question is, what fraction of the condo community is married? And the interesting thing about this is I used this problem for many years, and then I started to get some grumbles from my students. And the grumbles weren't about the mathematics, because the math is really very rich in this problem. It's beautiful math. And that's why I can't drop it from my curriculum, but it was really more about, kind of, the the hetero-normative implications of the problem. I had on the student one year say, "Give me a break. I mean someone in that community is gay." And so over many years what ended up happening is I reflected about the problem and you know is this appropriate is this responsible for me to be doing this? And so what happened, what evolved, is we talked about rewriting the problem right to make it more responsible in this day and age, and this is something that I did with my students. And we have a feature article in the in the Math Teacher about it because it's a very, very difficult sort of uncomfortable space to bring yourself into. But I really wanted to do it with the teachers because I feel like they're going to have to confront this very question when they're teaching say K through five. Like, they may encounter the same situations. And it helped them realize that, you know, being a math teacher doesn't mean that you're not going to have to deal with social issues. So that is really the takeaway that I got from that. And I really enjoyed like working with my students because they were they were excited about the project and they were really involved in it.

Dusty Jones: Cool. So what's the best advice you received when you started teaching at a two year college?

Keith Nabb: The best advice that's that's a great question. It's kind of funny because the best advice I received. I probably can't repeat here.

Dusty Jones: Okay.

Keith Nabb: But I can translate it, um, let me see basically give yourself permission to make mistakes, right. In other words, your first year is not going to be your best year. And that was advice I got from Dick Fritz, who was my first mentor, and I think he could tell in my first year that I was sort of terrified. I think everyone is right when you first walk into a classroom. Like, am I going to do this right, or my students going to know more than me. Right. So you just have these fears, right, like what what's class going to be like, and he told me it's going to get much better. And the first year might be rough. And he was right. Because every year. I feel like I get a little bit closer to what I ultimately want to be as a mathematics teacher.

Dusty Jones: Cool. What advice, turning this around. What advice would you give someone who was starting out in this role?

Keith Nabb: So just starting out teaching?

Dusty Jones: Let's say teaching at a two year college.

Keith Nabb: Sure. I think I'd say a couple of things on number one would be to get involved professionally, because there are some amazing organizations, as you well know, on the podcast right AMTE is pretty awesome. I want to get more involved with AMTE. So right now I do an awful lot with AMATYC and also NCTM. But I really like what AMTE is doing. I've done a little bit of work with Michael Steele. And MAA is just amazing how much education, right, math education they have there. So number one, I'd say just just go for it. You have to go to a conference, even if it's a local or an affiliate one just go to one of those conferences meet like-minded people and just share ideas. And the second thing I would say is to, if you're not assigned a mentor, is definitely to get a mentor. So my, my first mentor was the man I mentioned before, Dick Fritz, and he would just invite me over his house on a Friday night to write a college algebra test. And that sounds kind of crazy, but we would sit there and share ideas we would laugh, we would write questions, we would have pizza. And I just, I built a great relationship with him and I can't say enough what that does for your first year of teaching. And this can also turn into like research relationships because then years later when the roles were switched. There was a new faculty member. And I could tell. I said, you know, I need to work with him. I need to sit down with him, and we need to write some questions and do that. So I did the same thing with him. I invited him over my house. I said, Let's get some Chinese food and let's write a calculus test. And it turns out, like we were such good friends that we collaborated on a few projects for four or five years. So I think that's very important to to build those relationships and not to just, you know, I know you've heard it before. But don't just teach your classes and go home. Hang out with your colleagues and get to know them.

Joel Amidon: Love that advice, Keith. And I just you know i'm gonna i'm going to basically set you up for a shameless plug for this article in Connections, because it seemed talking about being involved professionally and the the article that's in the Connections newsletter the Call to Action: Expanding Mathematical Knowledge for Teaching in Early College Mathematics. So you can talk about you know what you put in that that piece, but also too just there's you know you talking about some professional relationships that are involved, like maybe how did this product, this article or this, you know, call to action that's in Connections. How did that emerge? You know, like maybe even taking some of the advice that you just put out there with the professional relationships and mentorship. How did this thing emerge?

Keith Nabb: Yes, so it boy. I've been working with Jackie Murawska for many years. So we had conversations, I think, dating back to 2015 about the very idea that's in the Connections piece. And it's funny because we were thinking on the exact same wavelength, because I was digesting all the MKT research and also Pat Thompson's work. Anyone who studies math teaching, I was reading all that stuff probably from 2002 to 2008 or so, and I couldn't believe like this stuff is amazing right just learning how students think and how to transform that into meaningful instruction. But there I was teaching in a community college and I'm saying to myself, I understand why this research is so important and how much it has added to the field. And I was saying, Wow, I see that when I walk into my calculus class, but I don't see this at all as fitting in when I walk into, say, a developmental intermediate algebra class. That's what I'm that's really what that connections piece is all about. Because if you read it basically all the research on MKT. I mean, I know it's oversimplifying it, but the research assumes really that the starting point for instruction is what do your students know, right? So you kind of have to figure out what it is that they know and then you work from that point to, you know, to add on whatever new knowledge, whatever concept, it is that you want them to know, right? So it's mostly cognitive right it's really about content. In the second thing is when you read most of that research, because it's so beautiful. You're assuming that they don't know the content that you're about to teach them right that it's going to be new.

Joel Amidon: Right, yeah. 

Keith Nabb: So if I go, yeah, say, I'm going to teach the chain rule. I mean all of my assumptions are okay. They need to know about functions. They need to know about composition, but I'm going to teach them this beautiful thing about patterns. I'm going to teach them about the chain rule. So naturally, when you go in and do that, you assume they don't know the chain rule. So what we did in that Connections piece, we said, are there any situations where those two assumptions may or may not apply or or they might apply in a weaker sense? And the place would be Developmental Ed. So I spent many years at the community college, and what happens there is, for the first assumption, it's not just about what students know in terms of content or cognitively. But, for lack of a better word, students bring a lot of baggage sometimes to that situation where they have seen the material before and they've actually had traumatic experiences. So it becomes more socio-emotional.

Joel Amidon: Yeah.

Keith Nabb: It's less cognitive and it's more affective. So that got me thinking like, where's the affect in Deborah Ball's egg? You know what I mean? I was just like, why am I not seeing that when when I teach. And then the second thing which is bigger. And I had this discussion with Michael Steele and Jackie. Is that because of curricular overlap. I'm not only is the content familiar to the learner, but they already know it. 

Joel Amidon: Right. 

Keith Nabb: So you walk into a classroom and you ask them, Who is familiar with slope? And remember, you're trying to teach slope. Every single student has seen it. So I feel like when they come with these socio-emotional assets and they've seen the content, then that means quality instruction, in my view, has to look different. Because the assumptions are very different, especially when they already know the content and in some cases, when I say they know the content. They could have taken a class, they could have passed and then they have just forgotten the content, so they just can't remember it, or sometimes in the developmental setting, you have a student who is seeing the content for the fourth or fifth time and I'm not exaggerating there. So, to me there's no paradigm in MKT or the math meanings for teaching, the Pat Thompson work, that fits. Right, because I'm feeling like I need to bring something different to be an effective teacher if those are my students. So I think there's potential here to build more on the side of the egg where its knowledge of content and students. Because I think the students in that environment. And in that setting or a little bit different. So that's really what that Connections piece. I know it's probably more than you want to hear but that's pretty much what it's about.


Joel Amidon: No, no. What's cool is hearing like, hey, 2015 we started having these conversations. And then, you know, with maybe Jackie, then you may be loop in Mike and then like these conversation continued to the point where, "You know what we need to share it." And so it's like having that responsibility for you know what we've benefited from these conversations we probably need to share this with other people. So we can at least get these ideas out there so that you know and we say at the end of every podcast like that we can think about the things that we're talking about and interact with them with other math teacher educators that you can talk about these things. And so I'm glad that one those professional relationships led to this product that then now I've got i'm sure Eva's the same way you got some ideas bouncing off of what you just talked about. And what's in the piece. So that's the whole point. That's great. I'm thankful for you, sharing that. Yeah, thanks.

Dusty Jones: So since it's 2020 and the semester and the college format looks very different, and how how things are going, how your classes are going like actually happening than they were 12 months ago. I'm wondering what in this last, you know, few weeks or month or I don't know how long classes have been back for you. What, what makes a good day in our current situation, as someone in your role.

Keith Nabb: Yeah, that's a great question because I mean the cynical answer is if Zoom works, right? I don't know. The weird thing is the start of our semester was, I think it was August 24 and that's when there was the partial global shutdown of Zoom on the eastern coast of the United States, as well as like the UK and Spain. 

Dusty Jones: Yeah.

Keith Nabb: Zoom just went dead. And I thought to myself, this can't be my semester I can't do this. So the first day was really, really bad at least my first class. But since then, like I can tell you, just the other day, it was Monday, and this was my developmental math class. So I have, I have to give you an idea, I have three sections of precalculus, like in different variations, and then I have a developmental ed class. And it's interesting because so many people I know will say, oh, the developmental ed. You know, it's just something you have to do and you have to get through it. I absolutely love this group. And part of the reason is I don't know how to sum it up but they're just not afraid of being wrong and that is the best thing that you could possibly have in a class.

Joel Amidon: Yeah, it's beautiful.

Keith Nabb: Yeah, I'll have these four problems on the shared screen. And I'll say, Okay, I want you to take control here, you know, pick the annotate option. And I want you to solve one of these problems. Put your name by it. And they're sitting there, they're doing the problems they're interrupting each other and they're sorting through the mechanics themselves and this is like really boring dry mathematics. You know what I mean. Like I have to get through. You have to teach exponent, you have to do a little bit. But then of course you get to the rich stuff, which is awesome. But at some point, you just have to teach them some of the mechanics and they are just a great group and they're always pinning me to the wall with their questions and they're so curious and I come out of that class just, I mean, completely energized and I know that must sound crazy, you know, teaching developmental math energized because they're going to be successful and they try so hard, and that is, that's what makes the best day for me. If you're putting in the effort, you can be completely wrong because I can work with you. So I've seen that very much in this class and I need to tell my Dean to come observe this class because they they bring me great joy.

Dusty Jones: That's great. That reminds me of, you know, other classes where some people just really don't. They say, you know, this is a class that you don't want to teach or the students in this class just we just have to get through that. But if you can find joy and you can look for those places where it exists in there. I think that's really great. And we don't have to just write off a whole class, full of students. 

Keith Nabb: I should add to, I don't feel like honestly I give the students credit because I don't feel like it's anything that I did, you know, they just have an incredible personality. And it's just they feed off of one another. And so I feel like I just got lucky. They're, they're a great group.

Dusty Jones: So one of the things we like to do on the podcast is give listeners ideas of where to look online for resources for teaching. So Keith, Where do you go when you need some maybe some ideas or you're like, what am I going to do, where can I find something. What, what are your go to spots.

Keith Nabb: I'll try not to imply like any ranking right.

Dusty Jones: Okay.

Keith Nabb: I must say Dan Meyers three-act tasks are probably the best thing I've seen out there. They are absolutely amazing. They get students thinking. His activities are like magic, because you can give them to the least engaged group of students and they will immediately start talking to one another. So they are. It's like magic math to me. I use Kaplinsky's site as well. The Open Middle has some great stuff. Desmos is wonderful. If I'm looking for more like traditional written problems Illustrative Math just has very rich math tasks. So pretty wonderful stuff. I use the Mars site as well out of Berkeley. And the NRich site I don't know if you know that one. Is it out of the UK or something. It is amazing. The products on that site are mind blowing. 

Joel Amidon: It's good stuff.

Keith Nabb: So I when I need something where it's like, Okay, I need to hook you know and have them really think I'll go to the NRich site. So that's, that's probably where I go. Most often for online but I use a lot of in-print materials as well, like the NCTM's Essential Understandings. I love those books, they just have great great problems and great explanations.

Dusty Jones: Keith, what do you like to do for fun? How do you balance things out from the work side? 

Keith Nabb: Yes. What do I do for fun? Well, I have young children. So they keep me pretty young. I do some acrylic paintings. So this is just something where I started actually in 2000, 2001, the same year I started teaching at the community college. Because they're very careful that first year, not to give you too much to do, like they don't want you joining a committee or anything like that because they really want you focused on teaching. And so I would get home and I'm like, all right, I'm all prepped for tomorrow. What am I going to do, you know, and I didn't care much for like TV or movies or anything. So I started painting. And this has become like a love of mine. So I do a couple of year. It's weird because here I am starting in the middle of a pandemic. I don't have any time to paint. You know what I mean. I have zero time to do anything. But this was 20 years ago. So I do some painting. I'm also a really big fan of origami. So I did a lot as a child growing up, my mother's Japanese so she taught me everything she knew about origami. So I went to the I know I'm saying, what should I do for fun, but this kind of intersects with the professional but I went to the moves conference, the Mathematics of Various Entertaining Subjects, in New York City A couple years ago. And Robert Lang, and Eric Demaine where the keynotes. And they are just origami experts and so I got to meet them and talk to them a little bit about their work and it's just wonderful. The best thing I've ever made an origami, I think, is one of Robert Lang's lobsters, and it was 100, I think it was 180 steps. So it took me five days to make it.

Joel Amidon: Wow.

Eva Thanheiser: Wow.


Keith Nabb: Yeah, because your standard origami paper crane is 13. Here you'll appreciate this being mathematicians, right? I failed the first time I made it because I started with a standard piece of paper, because then the lobster would end up being like no bigger than your finger.

Dusty Jones: Ah, yeah.

Keith Nabb: You just can't deal with that. So I had to go to the UC and I got nine square feet. So it was a three feet by three feet. And the actual lobster ends up about actual size. It's about the size of a tissue box.

Dusty Jones: That's cool.

Keith Nabb: And [inaudible] in it is absolutely stunning.

Dusty Jones: There's a painting or your picture of a painting on your website of Gauss in Andy Warhol style. Is that something that you created yourself?

Keith Nabb: Yes, that is something I think from one of the only sketches of Gauss. I know he's appeared on stamps, on postage stamps. So yes, that's one of the ones that I did. That was right before I think my qualifying examination for my dissertation. So I was very stressed. So I said to myself, I need to do something to release the stress. And so that when I cranked out in about three days.

Dusty Jones: Cool. 

Keith Nabb: Yeah, that's an example of the type of art I do. Absolutely nothing original. I'll take something like, Oh, I'll take this Gauss picture and maybe just put a Warhol spin on it. I'll just blend two things that I think are cool and make something new out of it. 

Joel Amidon: That's awesome. I think you wrote a piece in one of the NCTM journals, right, that had to do with origami?

Keith Nabb: Well, I presented a couple of times. So I did a couple of sessions on origami for engineering. 

Joel Amidon: Yeah, yeah, that's what I saw.

Keith Nabb: The Miura-ori fold is a pretty awesome example of collapsible origami. So yeah, I did a couple of workshops based on that, so that's that's the thing. I can't help but it seems like even when I do something for fun. It always comes back to math and it always comes back to teaching. I don't know, even if I try to stay away and say, you know, keep this recreational and don't involve the math. I just always come back to the math.

Joel Amidon: Well, I have one more question.

Dusty Jones: Go ahead. 

Joel Amidon: I have another question for you Keith about, because a lot of our candidates that are coming at the University of Mississippi, though they might be coming from a community college experience where they're taking the first two years, they're getting the associates degree, but then they're transferring into our programs straight into from whatever community college they're a part of in Mississippi. And just curious, like, what advice might you have for either folks that are working with community colleges that are you're working at community colleges sending teacher candidates into for your universities to finish up their degrees or those in in four year institutions that are receiving community college transfers. Like, do you have any ideas or any advice or perspectives to share with regards to that transition?

Keith Nabb: So are you asking this from the point of view of like a faculty member and you're saying like you have like a community college student in your classes?

Joel Amidon: Yeah, someone who's teaching math teachers and there are people that are transferring in, there are teacher candidates that are transferring in from a community college, like what advice might you have for them just to help those students, you know, be as successful as possible in their transition. 

Keith Nabb: Yeah. Well, I can't remember what the current research says, but I know a few things I have read have indicated that the Community College transfers tend to, I think complete at a higher rate. Right. So they actually when they transfer, they do very, very well in the four year setting. Obviously it has to be the right fit. Right, and they make the correct school because I have heard some horror stories where a student, for example, will go to the University of Illinois Urbana Champaign and they feel like we're in the world am I? And I think that has something to do with the size of the school. Yeah. So the great thing about community colleges or or maybe something that you could share with those students is that, I guess sometimes faculty at four year, I don't know, they might have other obligations on teaching may or may not be their primary focus. That's something I noticed, even when I was at the university level. So I do think they get a lot of one on one attention at the two year.

Joel Amidon: Yeah.

Keith Nabb: And they get a lot of that focus working with their classmates and working with the teacher so that might be something where it might be a shock to them. Sometimes when their teacher is not as available as they're accustomed to seeing but I found that you know the the students that I've talked to, when they come back and they complete their degree. It's wonderful to talk to them and to hear about their experience, at the four year. And yeah, I don't know if you want to hear this, what I'm about to say. But in my 15 years at Moraine Valley, in Illinois. You know, we'd have students go to U or I or UIC in Chicago and they would come back and they would say, honestly, my, my best years of instruction, the best teaching I ever saw, was at a two year college. And that's because the faculty there are there for that reason, and for that reason only. So many rock star teachers that are really focused on on just student learning and student success. And that's not to say that that's you know that's not a blanket thing, you get some incredible teachers of the four year, but I think sometimes you do have, you'll have the occasional teacher that is really focused on research or grants and they don't give that classroom teaching quite as much of a focus or quite as much time.

Joel Amidon: Well, maybe that's a suggestion for those from four year institutions to have better relationships with those community colleges and seeing like what has been successful and working with students there and, like, how can we learn a little bit more about teaching a little bit better. And so no, that's that's that's good encouragement for that we should be, you know, interacting with our colleagues beyond our own institution.

Keith Nabb: I agree. I wish, I wish there was more collaboration and we, I had this discussion with Jackie, Jackie Murawska and Mike Steele. And I know that's one of AMTE's, I think it's a strategic priority right to engage with a broader constituency for AMTE. Like we need to involve the you know the high schools, the Community College, four years, and R1 schools that you know we all have the same goals, we're trying to accomplish the same things.

Joel Amidon: Right 

Keith Nabb: And teaching at a community college, I have felt sometimes the community college is just somewhat forgotten right, that there are some amazing research that goes on at that level and they're amazing people doing amazing work for community colleges. I think there's a lot we can learn from community colleges. And of course, vice versa. Two years can learn an awful lot from the awesome research that's going on at universities.

Joel Amidon: Yeah, excellent.

Dusty Jones: Eva, what are you hearing what questions do you have?

Eva Thanheiser: I am hearing a lot that I resonate with. If I could choose who and what to teach. I would teach remedial math over anything else. I love teaching the pre service elementary teachers and trying to make sense of mathematics in general. And I think that's something that is the sad fact that often those classes are kind of not wanted. Rather than seeing for their potential. So I resonate with a lot of the things that were shared.

Keith Nabb: I think, Eva, you and I would really get along, because that I totally believe in that. I interviewed some two year college teachers, I think it was three years ago, about, and this was specific to developmental math. So if you wanted to frame it, these would be the weakest students who had a lot of trouble with mathematics and they brought some negative dispositions. And when we spoke to these teachers, they really they had an entirely different definition of how they described quality mathematics teaching. And it was all about just building a bond with their students. So the funny thing that Jackie and I found is when they were describing what makes a great math teacher because they were all teaching developmental ed. They were saying it's really just showing that you care for your students and you know, giving them positive feedback and helping them when they need it. So I found it shocking when I was first reading the transcripts, because they weren't mentioning anything about math. They were just mentioning everything about connecting on a human to human level. And that's something that I think the reason that I like the developmental so much. I mean, not that I don't connect on that level with my calculus students. Of course I do. Right. But with these students that is almost a necessary condition, like you cannot talk about the mathematics unless you sort of express on that care with with your students that I'm here for you. I'm going to teach you some math. And if you've had some past traumatic experiences. I'm going to help you work through it. So that was an amazing, that was a mainstay and all of our findings is that all of these teachers were saying that same thing. That's how they connected.

Dusty Jones: Well, Keith. Thanks so much. I have a class where I'm teaching people who want to become two year college professors and I think I'm going to make them listen to this podcast as a part of their recommended classwork just because I think you're giving us a lot of insight as you talked about AMTE's strategic priority of expanding the membership to a broader constituencies and I really want to know more about the folks in the in the two year world because I'm not aware of what goes on there. So this has been really helpful. Thanks so much. 

Keith Nabb: That's awesome. Now do you have a program for Community College teaching? Is it that specific?

Dusty Jones: Not specifically for community college teaching, but it's a Master of Arts program and it is for, it's in mathematics and we focus on teaching. And so the primary students to enroll for this are either high school teachers who wants to teach dual credit courses and so they need enough mathematics graduate credits to do so, or people that wants to teach at a community college. It's also a stepping stone for a PhD in mathematics, but the, or Mathematics Education, I'm sorry. But the the primary audience are people who want to teach at, for example, Lonestar Community College in our area.

Keith Nabb: I know some people there at Lonestar. 

Dusty Jones: Cool. 

Keith Nabb: Yep, that's, that's an awesome thing. I now you're making me think too. I guess that's the point of a podcast. I think there should be programs for community college mathematics teaching because it's a very specific domain.

Dusty Jones: Sure. 

Keith Nabb: And so that would be wonderful to think where that could go.

Thanks again for listening to the Teaching Math Teaching podcast, be sure to subscribe to the podcast and we hope that you're able to implement something you just heard and take an opportunity to interact with other math teacher educators.