Podcast: The Junior School Math Curriculum

In our ongoing “Listen and Learn” podcast series, Director of Admissions and Enrollment Management at Punahou School Maile Uohara spoke with Junior School Principal Todd Chow-Hoy about the math curriculum in kindergarten – grade 8.

Each “Listen and Learn” podcast aims to provide valuable information and insights about Punahou and programs for prospective families. In each episode, we’ll be inviting guests from our school community to share their knowledge and experiences with our listeners. 

You can find Punahou’s Team Up podcast on Apple Podcasts, Spotify, Simplecast and Google Play.

Podcast Transcript

Maile Uohara: My name is Maile Uohara and I’m the director of Enrollment Management and Admissions at Punahou School. I’d like to welcome you to our Listen and Learn podcast, where we aim to provide valuable information and insights about our school and programs. In each episode, we’ll be inviting guests from our school community to share their knowledge and experiences with our listeners. Today I’m delighted to have you meet Dr. Todd Chow-Hoy, our junior school principal. Todd will be talking to us about our math curriculum for our kindergarten through eighth grade students and the philosophy and approach we have towards that curriculum. Todd, welcome to our Listen and Learn podcast. I’d love it if you could share a little bit about yourself to our listeners before we start off with the questions.

Todd Chow-Hoy: Great! Thanks Maile. Thanks for the opportunity. I’m Todd Chow-Hoy junior school principal. This is my 25th year here at Punahou, my third as the principal of the junior school. Prior to that, I had spent all of my time in the middle school as a middle school math teacher as well as a department head and intersecting with all of our young adolescents.

Maile Uohara: And which is why it makes it perfect that you hear talking to us today about the math curriculum. So I’m really excited to dive into that. I think one of the first questions I would love for you to answer is just basically giving our listeners kind of a background of what is our overarching philosophy and approach when it comes to math in our junior school. And so that would be junior school for kindergartners all the way through eighth grade.

Todd Chow-Hoy: I think I can sum it up best by saying that what we want is to develop mathematicians, not students who do math. I think there’s a big difference there. When I started teaching here back in the day, It was very much a very rote kind of learning. The teacher was the sage on the stage pretty much one lesson a day. We showed the students how to do a particular problem by showing them a formula and we just expected that they would be able to plug and play.

Maile Uohara: They can memorize it.

Todd Chow-Hoy: Exactly, but what we found is that they weren’t really understanding the concepts. And what we really want them to be able to do is generate and appreciate math for what it is the beauty of mathematics. And so we started to shift our approach with the advent of technology, which is kind of hard to say now, but it has been a while, in different software and different programs. And just in our own evolution as educators, we decided that we were going to be very intentional about designing curriculum and using curriculum, designing lessons, creating assessments that really helped us to get to know a student and their abilities in mathematics, not just whether or not they could plug and play, but rather do you really grasp this concept?

Maile Uohara: I think about myself as a parent and I think about what I see in my child. And when you say that term to think like a mathematician, what is it that a parent would be able to see or to kind of grasp onto that? I think in theory when I hear that it makes sense, but in practice, what would I see?

Todd Chow-Hoy: Yeah. I think if you are going grocery shopping with your child, your child is talking to them about, well, what does this number mean? Or this number is bigger or this one costs more. As they get older and your teens are buying their own clothes or you’re buying clothes for them, you’re able to ask them, so which is the better buy? Why should I buy this one over this product, over the other one that they’re able to actually use it outside of the classroom.

Maile Uohara: And what does that look like at each division level? We talk in terms of kindergarten, first grade as kind of being a little subdivision and then two to five and then middle school. So how would that perspective look and change over the time of each division?

Todd Chow-Hoy: When students enter in kindergarten and first grade, we never quite know what skills they bring with us, but in true style up in Omidyar we want students to investigate. We want them to take numbers, kind of play around with them. We want them to understand the meaning behind them. We want them to know that there are different ways in which they can put numbers together. We want them to kind of begin their mathematical journey. That way as they move into Kosasa, things become a little bit more about skills and we want to provide them with a really solid skills-based foundation so that as they progress through their time in their elementary school, that when they move into middle school, they have that background with them. Because once sixth grade rolls around, we begin moving into a little bit more of the abstract and the theory behind algebra. And in order for them to grasp that, they should have a very solid foundation in just the basics.

Maile Uohara: When you say in second through fifth grade, they have to have the skills, what do you mean by that?

Todd Chow-Hoy: I mean, we think about just operations with mathematics. So addition, subtraction, multiplication, division of all kinds of numbers, one digit, two digit, three digit, fractions, decimals. We want them to be able to estimate and kind of know when an answer might not look right as well. They should have skills around geometry, shapes, being able to really see how big is something and be able to talk about it and describe it mathematically as well as how they would go about measuring something.

Maile Uohara: What would we see, if we were to just walk around right now in grade two to five, what would we see in the classroom in terms of what’s happening in math?

Todd Chow-Hoy: I think you’d see a range of things. I think you’d walk into some classrooms where, yeah, they’re at their desks working in a workbook. The materials that we’ve adopted are not the same kinds of materials perhaps that you and I used when we were going through school. Yes, there are going to be some problems that are kind of, “can you do this?”. But the bulk or the problems that they’re going to be solving will be word problems and they’re going to be problems that will ask them to think about the math and it’s not going to be sort of a traditional kind of word problem. They might be worded slightly differently in a way that not to trick a student but to really get at whether or not they understand a particular concept.

Maile Uohara: Oftentimes I’ve heard that it’s about the depth, not the breadth. And so how does that concept play out for you in these different divisions?

Todd Chow-Hoy: A lot of math has become collaborative in nature. I think when we moved into these new buildings, the flexible furniture allows us to put kids together in groups where they can have conversations about what it is that they’re learning. And I think before it used to be that we all sat in rows, we were just staring at the front of the board watching a teacher, but now students can ask one another questions, they can be posed questions to discuss together. And I think being able to do that in those small groups provides opportunities to go deeper because you’ll learn from one another, and something that I might’ve missed might, my classmate who’s sitting next to me as we’re talking about it, might be able to help me understand.

Maile Uohara: Would you say that also allows the teacher to understand and meet the students where they are at, at their level? And so what does that look like in terms of being able to meet the students where they’re at?

Which I think, I don’t want to necessarily confuse that with personalization. I think that also has a much different terminology or can be taken differently by different people. So really meeting the students where they’re at, what does that look like for us?

Todd Chow-Hoy: I think one of the beauties of the different programs that we’ve adopted over the years is that we can collect data on student progress. And it’s not just a matter of how many questions they got right or wrong, but we can actually take a look at what it is that they’re doing wrong or what they got wrong.

And if we find that there are certain students that aren’t picking up on particular concepts, we can group them and work with smaller groups of students to make sure that they understand a particular concept before they move forward. And so in that way, we’re utilizing those tools, the assessment tools that we have to really make sure that students are where they need to be and that we are not, well,l personalizing to a certain extent I would say, but just making sure that we are meeting them where they are.

Maile Uohara: One of the things that I heard you say is being able to assess what they’re doing or how they’re doing it. Would you say that that is a foundational philosophy that we really want to understand the how and not just that final answer of what they’re getting, but is what is that process that you went to and being able to show that work that you did so that we can understand that, oh, maybe that final answer wasn’t exactly right, but you were on that path there.

Todd Chow-Hoy: Yeah, I think one of the things I, as a math educator that I evolved was the right answer was never as important to me as the process. And there were times where I would design assessments where I’d purposely give students the wrong answer to every question and I’d ask them to solve it to find my mistake. And I think designing assessments in that way really helps.

I mean, in the same way to tie in some of the work that we’re doing around literacy, there’s so much reading and writing and mathematics that we want them to be able to explain, articulate how they’re getting an answer. So it might not even be done mathematically with numbers. It could just be that for some students doing that numerically could be challenging, but they can tell me in words how to solve a particular problem. And I think that’s another way where we’re meeting students, I think where they are because it’s an alternative way for them to demonstrate their understanding of what it is that we’re teaching.

Maile Uohara: How does this philosophy then progress? I think you touched upon it a little bit going on into middle school and the skills that we’re trying to demonstrate in middle school, but how does that trajectory look for them and ultimately because we’re trying to set them up for what they’re going to do in the academy too. So what does that look like?

Todd Chow-Hoy: As I mentioned, the shift from arithmetic to algebra happens right around sixth grade. I would say the first quarter of sixth grade might still be continuing to review the work that was done in fourth and fifth grades, but it quickly shifts to higher level skills, but also higher level thinking and the algebraic skills that are going to be needed moving forward. And I think the kinds of – the way that teachers design their lessons, allows for students to again, learn in a way that helps them process the information, helps teachers kind of know where they are, and then that information then can get passed along to the next grade level and it scaffolds over the years. There’s always that neat thing of there are topics that are covered in sixth grade and seventh grade and eighth grade that are expected, but you’re always doing the recursive learning throughout because there are just some skills that, again, no matter how many times you hear it, you just want to make sure that you have those before you can move forward.

Maile Uohara: What was one of the most inspirational things that you saw as a teacher in teaching math – whether it’s a project that you did with your students or an outcome that one of your students had, what do you remember most or that brings you the most joy or brings a smile to your face?

Todd Chow-Hoy: Oh gosh, there’s so many to choose from. There’s the student who walked into my class on the very first day who said, ’I hate math,’ or ’I can’t do math’. And we end the year with math being something that they feel better about or that simply they don’t hate anymore. There’s the student who just struggles with a particular concept no matter how many different ways you try to explain it, no matter how often you meet with that child, and then you see the light bulb click. I think about my own experience. I mean, not to make this about me, but as I think about my own experience in math, I think it was never an easy subject for me, and it took a teacher, and it took someone who worked with me, helped me understand and waited patiently for that light bulb to finally go on before my own journey took off. And that wasn’t until high school. And I remember those lessons and I remember what that felt like to be the student in the class who sits there and you’re watching and you just don’t get it. And just kind of how you feel and what it does to your own psyche around your ability to do mathematics and wanting to make sure that no child in my class ever felt that way. And that as a department head wanting to make sure that the faculty knew and understood that there should be no child who leaves math class feeling unsure or that kind of negativity because everybody can do math

Maile Uohara: And it’s building confidence in them and trying to find the ways to build their confidence. I mean, I think when I go into so many of our different math classes, that’s one of the things, especially in the middle school, the enthusiasm that I see from the teachers and the excitement they get in numbers, which I’m the same way … I was never that numbers person, but I’m just like, had I been in that class, I would’ve just been so excited because, and what I love about it is what I see is that it’s not, there’s just one way to solve a problem, which I think is the way that I was taught was like, this is the way you solve the problem. This is how you get to the answer. But really seeing teachers taking the time to say, let’s look at it from different angles, different varieties, and that’s how it’s going to do. How would you tie that into, because Dr. Latham often talks about the application of skills to life skills, how would you say that we are able to take this idea of mathematics, but then really connect that to these, our foundational to life skills? Is it through projects that we do with them? Is it through works or challenges that we give them at the different stages within the junior school?

Todd Chow-Hoy: I think the beauty of the junior school, even starting with kindergarten through fourth grade where we’re self-contained to fifth grade, where there’s a math, science and a humanities teacher, and then the teaming structure in the middle school really provides those opportunities for the integration, and students being able to see that math isn’t a standalone and that it’s connected to everything. It’s what we hope that all teachers are doing. So yes, there’s some things that you just need to teach, but if you’re able then to show how it connects, there’s so many great children’s stories that you could read to kids about that use numbers. There’s writing that can be done around math. I mean, you can ask students to write a haiku, you could ask them to write about a concept. And then of course, there’s the science connections and there’s sort of the different kind of challenges, inquiry kind of challenges that we can give to our students that push them in that direction. And then there’s applications, hopefully, that teachers are bringing into their classrooms like economics and the social sciences. So it’s not always seen as something just math and science – that beyond STEM there are other social sciences that play a very important role that math contributes to.

Maile Uohara: Figuring out your discount on something.

Todd Chow-Hoy: Absolutely. Or supply and demand. And I think as I think about some of the projects that we have students do as they go through the junior school, there are just opportunities galore. And I think the more we’re able to do that and involve students, I think the stronger their connections to the subject will be.

Maile Uohara: And their enthusiasm. Because what you’re trying to get to is that enthusiasm towards math. So why don’t you tell us a little bit about how we prepare in eighth grade our students for their trajectory towards the academy. What does that eighth grade math program look like?

Todd Chow-Hoy: Yeah, so a few years ago we made a little bit of a shift and we created a guided pace, an accelerated pace, mathematics. They’re not separate courses, but we have guided pace and accelerated pace in eighth grade math, which gives students an opportunity to work at a level at which they are most comfortable. So for example, we know that students at this age in middle school are maturing constantly. And that for some, the development happens early on and for others it takes a little bit of time. And to try to pigeonhole a particular student at such a young age into ’you’re a math person’ and ’you’re not a math person’, essentially is something that kind of ran counter to what we were trying to accomplish. And so by providing these two opportunities within the eighth grade math program for students to find their place and the flexibility at the start of the school year to continue to find their place, what we hope will happen is that students for whom math is their thing, or they’ve come to develop into – the light bulb’s gone on, in other words, – that they can proceed at a pace that will allow them to take accelerated math in the academy. And then for those who still need a little bit of time and maybe for whom that math is just not their thing, and that’s perfectly okay, they have a path as well. We have, fortunately, our eighth grade math teachers are amazing at being able to support students who might be at different places in their mathematical journeys. And we ask them to kind of work with them as they move forward, as they prepare them for eighth grade.

Maile Uohara: And I think what I love about looking at it from a teacher’s lens is that they, or a parent lens is that the teachers really do see them for who the student is, the potential that they have. And it’s not like we’re just going to let everyone just squeak by and you’re like, no, no, no. I can see. See that light bulb or I see it kind of brightening up. Let’s push you and guide you towards that. And I think that’s the beauty of the teachers that we have, but it’s also the program –  that it really allows those avenues for all of them. And I like that we’re not, I think you used the word pigeonholing or just kind of saying that you are this, because I think for so many of us, it’s like if we had that moment at that crucial developmental stage in our life that kind of said, you can do it, let’s just try a little harder, that maybe I’d be a mathematician right now!

Todd Chow-Hoy: That’s right.

Maile Uohara: Is there anything else that you feel that you commonly hear about the math program that you would really, from parents that you’d really like to share with our listeners?

Todd Chow-Hoy: Math is a journey, and I think for a number of families, they want their child to be able to … math is something they want them to find success in, and yet math is not going to be for everybody. And I just want families to know that we will meet your child where they are, that we have created and developed multiple pathways for them to find where they fit mathematically, and that once they find their spot, that’s not the only spot they have to sit in. And that as they progress through their time at Punahou, particularly when they move into the academy, they’ll have additional pathways and options laid out ahead of them. But I think our job is to build the skills to help them see themselves as mathematicians and get them started on their journey. And we just hope that every child who comes through the junior school finds success, feels good about themselves as a mathematician, because again, we don’t want people to have this negative perception about themselves as learners of math.

Maile Uohara: And I would say to always build within them that curiosity and that you have this innate curiosity where you want to learn more about the subject, learn more about math, dive into it, and that if you happen to be that math genius also, that we have avenues that we can also meet that too. So I think it’s that broad spectrum, but I think it’s what Punahou does best – is the possibility of opportunities and pathways for students of all types.

Todd Chow-Hoy: That’s our goal.

Maile Uohara: Fantastic. Well, thank you so much for joining us for this podcast. It was wonderful spending time with you and learning a little bit more about our math program in the junior school. And thank you so much.

Todd Chow-Hoy: You’re welcome.

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