How can we break through misconceptions about math and create space for students and educators alike to engage with the fun, creativity, and joy of math?
Today we are passing things over to Kent Haines. Kent is a Heinemann Fellow Alum and middle school math educator based in Alabama. He is joined by Howie Hua, a math instructor at Fresno State University. Howie teaches future math educators and helps people get more comfortable with math.
Kent and Howie talk about teaching math from a place where the humanity of the students is put first, and how memes can level up your math instruction.
Below is a transcript of this episode.
Kent: A few years ago, I got the uncommon opportunity to move from the K-12 teaching world into higher education, teaching a hybrid math and math pedagogy class for future elementary school teachers, along with some 100-level and developmental math courses for the math department.
As soon as I got the position, I knew exactly whom to call: my guest, Howie Hua. Howie is a math instructor at Fresno State in California, and I already knew from Twitter that he is an incredibly kind and giving person, so I figured he'd be willing to talk me through some of my questions and concerns. And boy, did he.
I got so much great advice from him that I decided I wanted to recreate that conversation here on this podcast. I'm particularly interested because Howie seems to really focus a lot of attention and effort on building a classroom community, and I found that the higher education world is a world that's perhaps a little bit, not actively hostile to creating classroom communities, but there's a lot of students who are themselves adults sitting in classrooms, and kind of about their own business, and so getting students to talk and work together and that sort of thing is a big interest of Howie's and a big interest of mine. So, welcome, Howie. Thank you so much for being here.
Howie: Awesome. Thank you so much for inviting me, Kent.
Kent: Just to get started, how about you let us know what classes you teach at Fresno State and to whom?
Howie: Yeah, so I teach five classes. Well, five sections. I teach math for future elementary school teachers, so they major in liberal studies and they need to take three math courses for their undergrad, math content courses. I used to teach all three, but now I specialize in teaching the first and the last one that they take. So, math content rather than math pedagogy. Their math pedagogy classes come in their credential program after they graduate from their undergrad.
Kent: What are the sort of topics that you're teaching in that math content for elementary teachers?
Howie: Well, the topics range from kindergarten all the way to algebra two, so the four operations, like adding, subtracting, multiplying, dividing, all the way to things like completing the square or zero product property, and the reason for that is because we need to hit the topics that are covered in the CSET. The CSET for those that are not in California were the tests that elementary school teachers need to take in order to be an elementary school teacher.
Kent: So when I taught math in college for the two years that I was at the University of Alabama at Birmingham, I found the environment to be more sterile than the middle school teaching that I had been from, not because necessarily that the students were less willing to work together, because, well, middle school students were also not very willing to work together initially, but just, if I'm in a classroom with 20 or 25 kids in a room, I can circulate and chat easily, check in with the four or five or six groups that I have, but when I was in a lecture hall, everyone was all spread out. I had more students, I had a harder time getting everyone to feel comfortable sharing their thinking, particularly if there was a chance that they might share it in front of this entire austere lecture hall.
So, do you teach in a big open classroom environment, that sort of thing, and just generally, how do you structure your courses so that students get over that tentative feeling of, "Oh, I don't know if I'm willing to share what I'm thinking," right?
Howie: Yeah. So I teach in a classroom of nine groups of four, generally, so 36 to 38 is generally my max size. 38 was the max that I've taught before. And community is very important to me, so before the semester starts I give students the option to start on their student autobiographies. I do a lot of work on collaborative Google Slides, so everyone can edit. Before the semester starts, they just grab a slide. They can post a picture of themselves if they want, and they just say a little bit about themselves. Like, "Hi, my name's Howie. I'm blah, blah, blah major, and I want to be a teacher because blah, blah, blah." And then they comment on each other's posts, and it's really cool to go in on the first day and some of them sit next to each other. They're like, "Oh, you were a cheerleader in high school? I was a cheerleader in high school. I saw that on the student autobiographies," and then they just sit next to each other for the entire semester.
And in terms of how do I get students to collaborate with each other, sometimes it's just natural. I just say, "Hey, work with your groups for five minutes on this problem," and other times I like to say, "Person on the left, can you explain how to do this problem to the person on the right? And person on the right, can you please ask questions to the person on the left?" For those that ask questions that they do not know the answer yet to, I just answer them at the end or we explore it together.
I'm very explicit with my teaching, so I say this basically every week, I say two things. Number one is, "We're on the same team," and number two is, "It's okay if you're wrong, I just want to know what you're thinking." Just making sure that it's not me versus the students. It's not teacher versus the students. We're all here together to help each other out. So just explicitly telling them that, "Hey, we're on the same team," I think it really lowers the anxiety in the classroom.
Kent: I really like that. I am particularly interested by the idea that you're just using explicit instruction, except the explicit instruction you're giving is, "These are the values that I have as a teacher," and then of course, it's not just you saying it, you actually create those structures in your classroom so that students see what you mean by that. When you say, "I don't care if you're wrong, I just want to hear your thinking," you create opportunities where it's clear that that's valued.
Something that I've found interesting about teaching future elementary teachers is all of these students are going to be math teachers. They may not see themselves that way. They might see themselves as first grade teachers, fourth grade teachers, what have you, but they're all going to be math teachers. And the majority of them, I would say, have a negative opinion about math or a negative opinion about themselves related to math, and that's a very concerning thing for ... Anyone who's interested in kids having a great mathematical experience from the beginning, you would want all of their teachers to themselves have great mathematical experiences. Is that something that you have also observed, and how do you help students deal with that reluctance themselves, where they may feel, "I'm learning how to become a math teacher and I don't even myself feel comfortable as a math student"?
Howie: Yeah. I want to share two activities that I do on the first day of school that relates to this. So I tell them to think of someone that they know personally that's good at math, and I want them to share five qualities that that person possesses that make them good at math. And they talk with their group, and then I write the five qualities on the board. I've done this for about four years now, five years now, and every single time, except once, the quality of patience was one of the top five qualities. And not only that, all of the qualities that they mentioned can be practiced. So I'm like, "Okay, great." So no one is just born good at math. All of these things can be practiced. And I tell them to write down one of these qualities. They could write down all five, but I want them to really just focus on one of these qualities for the semester saying, can we practice this quality?
Like I said, one of the ones that pop up all the time is patience, so it's very important to be patient with yourself. It's not a competition. Just because someone else got it before them doesn't mean that they are not a math person.
The second activity that I do with them on the first day is, I call, 20 words or phrases, and I tell them to think of 20 words or phrases associated with their typical math class that they've experienced. Not content words like Pythagorean theorem or number line or shapes, but rather, how was their experience in the classroom? You can throw in some emotional words as well. I would hear things like 1-31 odd, competitive, boring, stressful, all of those things, and I ask them after we come up with the 20 words, "Do you want our class to be like that?" And they said no, so I tell them to exchange words that they don't want to words that they do want to describe their classroom, and we create the environment together. It's just the idea of, once again, building a community that we are all on the same team. It's not just me deciding everything.
Kent: Something that comes through in your answers is how respectful you are that the people in your classroom are full human beings, that they are math students but they are also many other things, and that they are experiencing math education from a deeply human perspective. Do you feel that is one of your core tenets of teaching?
Howie: Oh yes. So the Fresno State's Kremen School of Education and Human Development a couple years ago had this program where students were able to send anonymized or not anonymized messages to their teachers. I got an anonymous one that said, thank you for encouraging your students to put themselves first and realized we can be so much better teachers, friends, and humans if we are happy and healthy inside first. And that is probably one of my top three favorite messages from students, just because it's not just about math, it's about seeing people as people first rather than students. That really meant a lot, and just putting a human centered approach to math is one of my core beliefs.
Kent: Well, I appreciate that also, just as, I suppose, as a colleague in the math education space that, well, frankly, you just check in with me every once in a while and I assume you check in with a bunch of other people just saying, hey, how's it going? How's your year doing? What's been going well? Anything you've been struggling with? And I always really appreciate hearing about how things are going in your classroom and that sort of thing. I appreciate the fact that despite the fact that we've never actually met in person, you're still reaching out and checking in on the full person, if we've ever collaborated on an idea or just worked together in any kind of capacity. So I appreciate that.
So, I want to dive a little bit into the content that you are teaching to these students. Like you said, you're going all the way from kindergarten through algebra two. There's a lot of material to cover there. There's certainly the risk that you could cover it in such a way that it just feels like a cram course, like their worst nightmare all over again. But there is also the opportunity, that I found myself in the same classes, where you can have students really truly understand something that they already know they learned at some point, figured it out procedurally, regurgitated on a test and forgot the understanding of right. And I think that is a very powerful experience. And I've seen that happen, well, frankly, with visual patterns and the knowledge of functions that students get from them that I actually talked about on an earlier episode with Fawn Nguyen.
Do you see any particular topics or content where you see those students, the light bulb going off like, oh, I never realized this is why it works this way? Where students can start to establish a more positive identity as I understand something about math here, and I can help my students understand math in this same deep way.
Howie: Yeah. So I really like talking about the connections between topics. So I say like, hey, remember when we did this a couple weeks ago, it's literally the same thing. So for example, the power of rectangles, whenever we multiply, so in the first couple weeks we multiply with just whole numbers and then in a couple weeks we do multiplication with fractions and then couple weeks later we do multiplication with polynomials. So it's like, hey, we're doing the same thing, it's just the same rectangles. So every time we think of multiplying two numbers we just think of the rectangle, and same thing with division as well. Division of whole numbers think about rectangles, division of fractions, decimals, polynomials, think of rectangles. So it's just the connections of like, oh, we already did this, it's just variables instead of numbers.
Kent: That's a really great example because I always try to make an opportunity of telling elementary school teachers how valuable rectangles are and how important it is that students understand arrays, because we are really going to lean on that. I do think that the world of math education is increasingly moving in that direction where more and more middle and high school teachers are leveraging that understanding of arrays to help with the distributive property and all sorts of other things like that. That's a really good one because it spans so many different areas.
One that I found, I taught one class, it was particularly for middle school teachers, they were going to be teaching middle school math and so I wanted to find some stuff that might help them think about algebra in a different way. Actually, we spent a few sessions, probably three weeks of class working through the Exploding Dots curriculum. I don't know if you have had personal experience with that. But just quickly, it's essentially a system created by James Tanton where students relearn arithmetic with all sorts of different base systems. So if we start over at 10 and we say one group of 10 and zero left over, but this might get you to regroup at two or five or eight, or what have you. And it is so fascinating to watch adults struggle with double digit addition. Because they're adding double digits in a different base system, because they have to regroup it 8 instead of regrouping at 10. And at the end of that, you realize that in some ways you can think of a polynomial as a multi-digit number in an unknown base where it's like you regroup it X.
So there's some really fascinating stuff that happens. But the big idea is that if you make a lot of mistakes when you're learning a brand new base system, which is precisely what all of the kids are doing. That's what a second grader is doing is learning a brand new base system, it's brand new to them. And so I think it engenders a sense of respect for the challenge that students are going through the very first time they learn about multi digit numbers or decimals or what have you. I don't know if you've ever had an opportunity to work with base systems at all, or if it's just, like I said, there's just so much curriculum to get the students to encounter.
Howie: That is actually one of the first things that we talk about in the first course of just doing the four operations in different bases just to really understand place value and all of that. So, yes, I totally agree.
Kent: One other thing that I think is particularly interesting about your course, you have a very interesting technique for giving tests in your classes. Can you share what you do?
Howie: Yeah. So the first five minutes of class I tell them to put their writing utensils on the ground. I give them the tests and they hold the tests and they can talk about the tests with their group for five minutes. And then the rest of the class period is just individuals. But just giving them the first five minutes just to chat with each other and walking around, you hear some of the best conversations. That is, I think one of the best parts of this. I call it test talk, and students have mentioned that it just really lowers their testing anxiety. Just because it's so stressful sharing everything that within those 50 minutes or that hour, 15. So it's nice to just chat with each other because we chat all the time. I think maybe 60% of each of my class sessions are group work of just having them work together. So, it's nice to just do five minutes of that and then the rest is individual time. The reason why I have the writing utensils on the ground is so students can really focus on the conversation rather than just writing down the answers.
After the test I do test revisions as well. I have the sentence frame, at first I thought, but now I think, and then they do the problem again that they missed.
Kent: What would you say to, I guess, what people would say would be the common objection to this, which is that at the end of a unit or what have you, a test is meant to be an understanding of what this student on their own can can produce. We do lots of group work in class and that sort of thing, but at the end of the unit, fundamentally, I want to know what she can do and what he can do and that sort of thing, if I just hand this to them and all they have is, well, the knowledge that they've gained throughout the unit. What would you say to that?
Howie: Yeah, I think that in a lot of jobs you are able to talk to and consult with people and the work is your own at the end, but it's nice to just consult for a couple minutes and then work by yourself after that. So, I would just allude to what happens outside of school.
Kent: And I also think it's an interesting thing for me to consider. This is not a policy that I've implemented in my classroom, but it certainly makes me think about how would my test writing change if I knew that students were going to get those five minutes to talk. I think one thing that I would have to do is I'd probably have to strip away anything that I felt like could be so quickly answered by just one kid pointing and saying, oh, it's B, that sort of thing. Any sort of lower depth of knowledge stuff and what would be left would be a lot of deeper and more challenging questions. And then I wonder, "Well, would my students be able to talk through the answers to a whole test worth of challenging, higher depth of knowledge questions?" And the answer is probably not. They'd probably have to spend some time really talking about a couple of things and I don't know, it sort of, it makes me think about the possible benefits of it, although it's certainly something that also I feel tentative about as I think many teachers would. So what do you think, how do you think it impacts your test writing?
Howie: Yeah, so I definitely don't do this for multiple choice just because I don't want them to memorize. It's like B, A, D, D, C, whatever. So it really definitely impacts my question writing. For example, it could be scenarios. Is this a misconception or not? Write a word problem that describes two and a quarter divided by half, or so having them make up questions, scenarios, what's a visual, what are three ways that we can multiply 16 times 24 and all of that. I try my best to do test questions like that. Multiple ways, how do we visualize this, think of a word problem, a scenario, what would you say to this student?
Kent: Think of a word problem is such a great question type. And it's one that I've used in class, but I've never used it on an assessment. And now I'm thinking, "Oh, that's a really interesting idea." Certainly I've learned so much about what my students know about operations just by seeing what they decide how to set up a problem that could be modeled certainly by fraction, division. My goodness, that's like throwing them in the deep end. But it's a great question for somebody who's going to be teaching fraction, division to sixth graders or what have you.
In addition to teaching these math classes for future teachers, your other pastime is as an ambassador of mathematics on social media. You make a ton of math based memes that you post on Twitter. You also have a very lively account on TikTok where you share all sorts of things. You share quick math lessons, really interesting patterns that appear, sometimes you're dealing with things that are topical, teaching conditional probability to talk about vaccination rates and things like that. What drew you to TikTok initially as a platform to communicate about math?
Howie: I think it was two things. One, I'm very sentimental with things ending. I only see students for one semester, two if I'm lucky if they take my first course and my last course. And I have a little LISTSERV for my past students that want to still hear from me. I sent them a message saying like, "Hey, if you still want to learn math from me, I made a TikTok account. So feel free to follow me if you want to." Half of it was that just so I can still teach my past students. And the other half is that maybe students don't want to watch a 20 minute YouTube video on multiplying fractions or why we flip the second and multiply when dividing fractions. Maybe they just want a one minute explainer. I just wanted to do my part in just helping in that sense of just doing one minute quick explainer videos.
Kent: I'd love to focus in on one that I found to be great, especially because I saw a lot of really positive reaction to it, which is the idea that percentages are commutative. Could you share, well, I guess I'm asking you to sort of reenact your TikTok, but can you just share with the audience what you were sharing this interesting property of multiplication?
Howie: Yeah. If I ask you to find 4% of 75, but you don't feel comfortable with that, you could just switch the numbers. You can find 75% of four, which is three. So three is 4% of 75. It's nice to just know that multiplication is commutative, that you could just switch things around to make it an easier problem if you don't feel comfortable with the original problem.
Kent: What I love about this is, well, it's a really cool trick. So it's going to hook somebody who's not in a math context. I can imagine you're just flipping through watching videos on TikTok and you see something like, "Oh, that's actually kind of useful." And so, but then as a teacher, maybe this could be the prompt for a lesson about this because although we are talking about the commutative property here, it is actually to me, I'm thinking about it, "Okay, 4% and 75 are actually different numbers than 75% and four." Where's the underlying use of the commutative and I think a associative properties probably in here? And so you could go deeper. And you could say, "Well, let's say, well, what does 4% mean?" Four groups of one out of a hundred.
And then we're multiplying that by 75. Well, let's just take the one out of a hundred and multiply that with the 75. And now you've got 75%, that sort of thing. But it makes me as a teacher think, "Okay, how do I find a hook into this?" Because I can't think of a topic that's taught worse probably than the properties of arithmetic. So many teachers are like, "Well, here's the commutative property. Here's the associative property. Here's the distributive property. Here's an example of each." And every student who sees it that way just says, "Okay, I have no idea why I'm being asked to prove that two plus three equals three plus two." They have no reason to figure out which one is which, and seeing that as a hook, a hook into this is like, "No, you can use the property as a mental math trick." Well, it just helps me think about how to take something that seems kind of boring and find a way into it.
Howie: Yeah, making these TikTok videos is definitely an exercise in itself of what you mentioned of how do I hook them in because with TikTok, you need to hook them in three seconds or else they're just going to swipe. They're just going to keep going. It's definitely an exercise for me. One of my proudest ones is showing how cool A times zero equals zero is, and how A times zero equals zero can show why a negative times a negative equals a positive.
Kent: Say more about that.
Howie: Yeah. So A times zero equals zero. So you can replace A with any negative number, say like negative three and replace zero with any zero pair, like negative five plus five, and then distribute. So you get negative three times negative five plus negative three times five equals zero. So you can kind of switch it up and say, "Okay, well, five groups of negative three, that's negative 15, well, something plus negative 15 equals zero, forcing that negative three times negative five to be positive 15." And you could replace those threes and negative fives and positive fives with Xs and Ys to show that negative X times negative Y equals X times Y. I know that's really hard to imagine without visual.
Kent: Yeah, if you haven't checked it out, Howie's always got a whiteboard right there. So don't worry, I am very much somebody who likes to see the numbers and variables on the screen too. So having done a bunch of these videos and you've seen some of them take off more so than others, just the nature of social media is that some things go viral. What do you think your most popular videos have in common?
Howie: I think it's the videos that show how creative math is. The most popular one on TikTok was how do you do 17 plus 18? I got over like 30,000 comments on it of students, or not students, but just the general public saying, "Oh, I did 17 times two plus one," or "I did 10 plus 10 plus seven plus 8" or "I know 15 plus 15 so I did that plus two plus three." Things like that. So just having them share how creative math is, I think those are the ones that are the most popular, and that is really cool to see just because you would think that people think that math is just one way, let's just do the traditional algorithm. It really makes me happy to see how the general public sees how flexible math can be.
Kent: I agree with that. And I think that frankly, anything that can spur a valuable mathematical discussion in a non mathematical space like social media, that's just great. I think that's just got to be a win. I remember a couple years ago there was a girl who I think it was in high school who posted a video that was basically just like, "Who invented math?" Is this stuff like, well, essentially it was coming down to this idea of like at what point does the truth lie in mathematics? Is this stuff still true? If mathematicians invented the operation of multiplication, like where does the truth of that come from and all this sort of stuff. And there was an initial wave of sort of people kind of making fun of her because it's like a girl who's like, kind of talking like this and sort of saying like, "Where does math come from?" And it sort of like played into, I guess, the stereotype that might come from that. Really, if you listen to her, she's asking one of the most fundamental questions about the nature of mathematics and the nature of truth, frankly. And it led to such a deep, very swift backlash on the part of myself and you and the members of the math education community saying, "No, this is real stuff right here that she's talking about." Do you recall that video by any chance?
Howie: Yeah, I do. I don't remember any other details the ones that you mentioned, but yeah, I totally ... Yeah, the math community was definitely on her side saying like, "These are great questions."
Kent: And god, wouldn't it be great to have a student in your classroom asking that level of question. And frankly, the fact that it was in social media space meant we could spend as much time as we wanted to discussing it because you don't often get to say, "All right, hold up class. Instead of going over transformations on the coordinate plane, today we're going to talk about the nature of truth." But social media gave us a venue to have that conversation. I should also say that in addition to these TikToks, Howie is a purveyor of memes. He seems to have a gift for coming up with mathematical themed memes.
And I promised myself that I wasn't going to sit here and read a bunch of memes over an audio format like I used to do, like forcing my parents to listen to this Calvin and Hobbes comic strip when I was a kid. And they would be like, "Yeah. Okay. So what did he say in the second panel?" So I'm not going to do that. I'm just going to say Howie Hua on Twitter, you can go back through and if you click on the media tab, you can see a link back to a ton of his TikTok videos and also a bunch of memes. I guess I would say, how did you realize that you were pretty good at writing these things?
Howie: I don't know. I'm just very grateful that people have the same type of humor as me, because these are the ones that make me laugh, but I think that I have a weird sense of humor. So I definitely don't take for granted that people have the same type of humor as me, because I'm like, why do people like this? This is so niche. This is so random. This is so different. Besides going through my media tab, you can just go to HowieHua.com. I organized all of my memes by category, so like K to eight, high school, general teaching memes, and all of that, so you can definitely just look at that. I like sharing my memes. We have a meme of the day at the end of my class sessions, just so we can all end in a smile or end with a laugh and stuff.
Kent: That's funny, you just anticipated my last question. Do you incorporate the TikTok videos and the memes into your classroom and clearly you do, at least with the memes. What about the videos? Do you have any opportunities to incorporate your videos into your classroom?
Howie: Yeah. Talking about the memes, I've only incorporated meme of the day during virtual teaching. And this is my first semester since the pandemic started that I'm teaching in person and I was contemplating whether or not I should keep them just because people don't really laugh at memes out loud, so I would just hate if I end with a meme that I think was funny and no one laughs. I'm like, it's just really demotivating to just end with that every single class period. I still do it anyway. Sometimes they're a miss. Sometimes students audibly laugh. So, I'm grateful for those times.
For my TikTok videos, maybe half of my videos are topics that we talk about in class. So I'm like, "Hey, I made a TikTok video on this. If you want a refresher or if you were absent, here's a quick explainer about what we learned today." So we don't really watch them in class, but it's more of a supplemental like, "Hey, if you want to, feel free to watch them." And actually had a student as we were preparing for a test, she mentioned that to study for the test, she was just looking through my TikToks just because it's nice to just hear me talk about math. I thought that that was really cool.
Kent: Well, thank you so much for coming on and sharing your passion for creating these communities and, frankly, reaching out and getting people to talk and think about math in whatever avenue possible. You can check out all of Howie's videos and memes at his website, HowieHua.com or on Twitter at Twitter.com/Howie_Hua. Howie, thank you so much.
Howie: Thank you so much, Kent.
Kent Haines is a National Board Certified middle school math teacher in Birmingham, Alabama. He has spent 10 years in the classroom, as well as two years as a visiting instructor at the University of Alabama at Birmingham. Kent is a 2016 Heinemann Fellow and has helped develop curriculum for The College Board's Advanced Placement program, A+ College Ready and Citizen Math. He writes about math games for parents and kids at Games for Young Minds.
Howie Hua is a math instructor at Fresno State where he teaches math to future elementary school teachers. He loves teaching and he loves learning. Outside of the classroom, Howie enjoys playing the piano, watching gymnastics, spinning rifle/sabre, and watching Parks and Recreation.
Howie shares his teaching tips, memes, and TikTok math explainer videos on this website and Twitter.
