What’s the right way to teach kids math?

0:00Hi, this is Brook to Vard from Naked Beauty. I am always looking for ways to elevate our daily rituals, and the colder smart toilet is proof that design changes everything. It's this stunning sculptural piece that feels like quiet luxury for your bathroom. It totally transforms your daily ritual into something elevated, with customizable cleansing and touch screen controls. It's functional art that makes your space feel cleaner and more intentional. A modern home deserves a modern toilet. Find the difference of Kohler Smart Toilets. Find more at Kohler.com. Hi, I'm Rebecca Zanberghan, and you're listening to the current podcast. It is October now, and millions of children from across this country have settled back into their school routines. Still there is concern students aren't learning what they need to, especially when it comes to math. OECD standardized test scores out last month show basic math skills have fallen to the

1:03lowest level they've ever been in Canada. New Brunswick is experiencing the sharpest decline. The CBC's Julia Poggle went to one school in Gimli, Manitoba, where staff say big changes have meant big results for kids on their math tests. But along the way, she unearthed a deeper controversy about the best way to teach math. Here is her documentary, Are Your Kids Learning Math The Right Way. Twenty divided by four is what Jackson? Five. Five. Twelve divided by four is what, Beta? Three, you got it. I'm inside Dr. George Johnson Public School in Gimli, Manitoba. Great four students are sitting quietly in rows, calling out the answers to a timed test they've just completed. It's something that happens most days in math class here. I like it. I like it. I like it. I like it. I like it. I like it. I like it. I like it. Fourteen divided by seven is what, Karina?

2:07Two. Two. That's what it is. Focus kids in individual desks, reciting answers to math questions. For some of you out there, you might be thinking, yeah, that's math class. So at a time when math scores across the country and globally have been on the decline, turns out how you teach young people math is a hotly contested topic. You don't compromise between good instruction and bad instruction. Why would anyone do that? As we get a bit exhausted with this conversation about a being that I caught maybe because that way of thinking about it is both divisive. It's also false. But in Gimli, Manitoba, they've started to use something called direct instruction. And according to Jessica Warden who works for this Manitoba school board, since they've started, they feel like they've cracked the code to math success. Yeah, like we want to do the best we can for kids and we think that we figured out how.

3:21Morning, Ellie. How are you? I had one round of change in math, mostly high school math about eight years ago. Scott Hill is the superintendent of Gimli schools. We found a quiet place to talk in the principal's office. Field trips, we have a track and field day. We've got, oh, man. I have a team of Evergreen school staff sitting with me, eager to tell me about the changes they've made. When the provincial government began publishing the results of the grade 12 provincial standards tests, we found ourselves at the bottom of the list in the province on at least one of those grade 12 provincial standards tests in math. We wanted to make sure that we tried to make a course correction around our math results. In high school, cell phones were no longer allowed in class. We talked to students about that was that they would describe classrooms as being spaces where they could kind of take it or leave it. Scott also says there's a change in expectations. Kids had to show up on time and really participate in order to get a good grade and in younger

4:26grades, no more split classes, only a single grade per class. That class from then becomes a grade one expert. And then there's the style of teaching. We're just beginning now really, I think, a change is in math, particularly the elementary level to make sure we're incorporating direct explicit instruction. Direct or explicit instruction. Scott and his team also came across a podcast called Chalk and Talk, created by a math professor at the University of Winnipeg, a podcast with a battle cry. That explicit instruction is the best way to teach novice learners. This is Anna Stalky. And according to her, years of not primarily using direct or explicit instruction has done real damage. Okay, explicit or direct instruction. This is what we saw before clearly teaching essential math content with lots of practice. Again, some of you are like, yeah, that's math class, but I'll tell you what it's in comparison

5:30to in a minute. For now, what you need to know is we have more students who are struggling and fewer students who are excelling in math. And that's a big problem. Why would we want to be doing so much worse than we were 15, 20 years ago? Yeah, so I am a math professor. So I have a PhD in math. I'm in Professor Stalky's office, also her podcast studio. I had like other sound panels over here at the University of Winnipeg. Well, let's see. Okay, so up here we have, there's an oil painting covered in numbers leaning against the wall. That's an oiler's number E and a framed poster. So this is my math genealogy. I got my PhD at the University of Alberta and my supervisor was Gerald Cliff and his supervisor was Ernie. All connected in a family tree of sorts. And you can see, so yeah, math is a massive part of her life. And she believes it plays a big role in all of our lives.

6:31It helps students think logically to think critically. These really worried kids aren't getting the basic math skills they need to function in the world. And she sees it as a crisis. Certainly, Canada has been declining over time. Pisa, a program for international student assessment, which measures student achievement and tests math skill to meet, quote, real life challenges. It says Canada is in the top 10 of all ranked countries in the world. But the concerning factor to Anna is the decline in scores. Most countries have been declining in math. That doesn't mean that we shouldn't pay attention to it though, since 2003 scores have steadily dropped. But worse than that, the percentage of students performing at the lowest levels on Pisa has doubled in many provinces. And the percentage of students performing at the top levels, so our high flares, our STEM ready students, has halved. According to Pisa, these high performing students have gone from 20% of students in

7:362003 to 12% of students in 2023. And on a different educational assessment, TIMS or Trends in International Mathematics and Science study, which is more focused on mathematical knowledge, Canada does much worse. Canada is 34th out of 58 countries, below the US and right behind Albania. So it was probably about grade 2 or grade 3. And as attention to how math is taught in schools, started when she saw what was going on in her own daughter's classroom, about 15 years ago. We noticed that they weren't really doing much math in schools. So it was essentially, you know, there was a problem of the day. In the 80s, a form of math instruction called inquiry or discovery learning was taking root. Kids might be in small groups, grappling together over a math problem, maybe finding different

8:40methods to get to a solution. With the teacher guiding on the side, the process of finding an answer that's struggle, often just as important as what the answer is. The Western and Northern Canadian Protocol from 2006 outlines how to balance traditional explicit instruction with inquiry. By quote, decreasing emphasis on wrote calculation, drilling practice, more time is available for concept development. And how that appeared to Anna in her daughter's class, they were not even learning the standard vertical algorithms for arithmetic. So what I mean by that is like adding in columns with a carry, subtracting with a borough. So you know, when kids aren't even learning basic arithmetic in primary school, we have a serious problem. You need to know your times tables off by heart because it makes later math much easier. We know very well that math is cumulative, that it's like a ladder.

9:41And if you are missing rungs on that ladder, the gaps are going to compound and it's going to be really difficult to learn later math. So Anna had an idea. We started hosting a math club at our house, so my daughter would come over with her friends and we would do math with the kids. But then more people wanted to be in the math club because a lot of parents knew that this is a big problem that kids aren't learning math. And so we started a nonprofit or committee's math schools and we just opened it up. So it just started picking up and my colleagues and I founded an advocacy group called Wise Math to advocate for changes to the math curriculum. And then, so I started doing the podcast in 2023 and many episodes discuss how inquiry learning, according to Anna and other experts, is failing kids when it comes to math. I'm not here to make friends, Julia. I'm not here to make friends.

10:42They have this idea that learning should be, I guess what you'd call student-centered, that the child should be at the center of it, that they should be allowed to sort of dictate to side their own learning, that they should be able to invent strategies and that type of thing, and that this will, in the end, make them better math problem solvers. But it doesn't work that way because when children have nothing to work with, they can't be successful. So you know, people feel quite sensitive about this. It's a stance. Martha Koch, a professor of math education and proponent of inquiry-based learning, takes issue with. We do have to disrupt that idea. The inquiry-based learning is, you know, expecting students to discover math concepts all by themselves. It's anything but that, right? It's teachers really carefully planning very specific mathematics learning experiences so that students can engage in that mathematical thinking, develop a deeper conceptual understanding of math.

11:42Martha says she's been involved in math education research for the past 30 years. She teaches at the other university in Winnipeg called the University of Manitoba. When I talk to her, she just returned from a conference where she met with many other math education professionals from across Canada to discuss how to best teach math. The critique from Anna and her podcast is something she's been pushing back against for a while. Straight memorization. I mean, you would know in your own life. Some people you know have a great memory. Some people don't have such a great memory. So what are we doing for a child who doesn't have such a great memory? We know that in mathematics classrooms where students are encouraged to use manipulatives or objects and various kinds of representations, whether that's physical models or diagrams or other forms of representation, as they're digging into math concepts and engaging in mathematical thinking, reasoning and problem solving are really key parts of inquiry-based

12:45learning in mathematics classrooms. We can say, hey, you walk up to an ice cream counter and there are four different flavors. How many different kinds of two-school ice cream cones can you make? And so right away, a child can begin to figure that out. They may not get to the full total number, but they can start to come up with examples right away. It can look something like this. This is a video Joe Bowler shared with me. She's a professor at Stanford University's Faculty of Education and a big figure in the American inquiry-based learning landscape. The inquiry-based learning, I think for me, is having students use their own ideas and combine their own thinking with standard mathematical methods. It's about giving students opportunity to take methods and adapt them and apply them and use them to solve real problems. In that process, they tend to be able to be a bit more creative and use their own thinking

13:48and their own ideas, which is usually much more interesting for them. Our story also expresses how heated this battle of the methods can get. A new math curriculum was adopted in California in 2023. One Joe Bowler and many other math education experts were advisors on. Critics called into question the validity of some of Bowler's research. Attacks which Bowler characterizes as part of an anti-DEI movement. Answer is when all these match the criteria and they're like one remaining left. In this video, kids are gathered around what math education people call manipulatives. In this case, small blocks, which kids are using to come up with their own way of solving a math problem. Their teacher talks about why she loves this style of teaching. I mean, there were kids today that when they figured something out, they were so excited. I think I found the answer.

14:48Oh my god. Just like all of this, I think I read for the answer. Let's. Martha says a reliance on direct instruction with memorization and time to tests. We actually end up doing is pushing a lot of students out of mathematical work at all. And so we again have learning theory research and mathematics education research that shows us that if I just have a procedure, I may not know when to apply it. Or I might know for long enough to write the tests at the end of the month, but a couple of months or years later, if I don't have a conceptual underpinning for that procedure, I really won't know when to apply it. Which is pretty much the opposite of what Anna thinks. She points to research to back her up. She says you can't understand the bigger concept if you don't have basic procedures down first. So it's like, you know, when you first learn to skate, you're kind of wobbly on the skates.

15:48You don't want to go into a hockey game. I mean, you could, but then if there's kids in the hockey game who can skate really quickly, they're going to skate circles around you. It's going to be a humiliating experience, right? Anna says we sell kids short. If we don't believe they can find mastering a complex subject. Interesting. She's seen at work. And so has the grade seven teacher at Gimli High School. By shooting them equally, then I teach them the same way. My name is Abel. Lugumire. The competition for two years. Abel teaches grade seven at Gimli High School. And he thinks what makes direct construction very cool is, I don't waste time on a thousand things. Yes, we're going to learn a different pace, but we don't have to have a thousand ways of doing one thing. And once I did that, then kids,

16:49engagement sky rocks. I'm watching Abel teach using direct instruction. The students have these mini whiteboards. Abel calls out a question, and every student is expected to respond with their answer written on the board. Times up, and they hold up their whiteboard in front of them. You see? Abel walks around checking the answers. And if one kid doesn't have it right, he pauses to help him out. I mean, I know a reporter's watching, but these kids are dialed in. I chat with a few of Abel's grade seven students, two girls who are checking their answers together during the lesson. Yeah, we're pretty focused during math, because lots of kids in that class I'm pretty sure like math. I personally love math. I feel like I'm pretty good at math. I mean, there's some things I could definitely work on, but I'm pretty good at it. Yeah, um, like tests don't usually stress me out in math, because I'm pretty good at them.

17:49But I don't get stressed because during class, he does most of the answers just with different numbers. So, and the test will be prepared and know what we're going to, like know what we're going to expect. According to some inquiry education advocates, testing can create test anxiety and eventually push certain kids away from math. But Anna says there actually is no evidence by the way that time testing causes math anxiety. It highlights a point in all of this that can be a bit confusing for us non-academic math and math education people. It's something you've heard a few times already. Research shows supported by research. Good research. Decades of research. Research that both sides say, prove their style of teaching is the right way to go. Now, Anna says there's a big difference in the kind of research she's talking about. When people in education say, research shows you have to be very careful about it.

18:49It could mean anything. It could mean a blog piece. It could mean an opinion piece. I mean, these papers get published in education journals. You know, look at the Institute for Education Sciences. Look at the National Math Advisory Panel final report. They synthesized good research. You know, and by that I mean the kind of research that's actually generalizable. Martha Koch disagrees wholeheartedly. She points to stacks of high caliber peer-reviewed journals filling her shelves. Many of which celebrate the outcomes of inquiry learning. Outcomes that aren't always connected to high grades. According to her and many other education advocates, high grades aren't the only thing students should be getting from school. I think there's no doubt that report card grades are enormously valuable for students. One thing that's really important to think about for report card grades is that it's much

19:50more than adding up points on tests or quizzes. You know, broad agreement that all of the curriculum documents in Canada ask students to develop many many things beyond what we might call basic skills. So it's not just content knowledge. It's engaging in problem solving in sustained ways and you know, keeping going when it gets tough. Being able to work collaboratively with other students in some of the problem solving and other things that are going on. Still waiting in line? Again? That's time you'll never get back. Save time and money with stamps.com. Over four million businesses have skipped the line with stamps.com. Join them to save up to 90% off-career rates from your computer or phone right now. Print postage for Certify Mail, Register Mail, and packages in seconds. Then schedule a pickup right from your home or office. For a limited time, go to stamps.com and use code podcast for a free welcome gift. Taxes and fees apply.

21:16Subscribe to BecauseNews now on Spotify, Apple Podcasts, or anywhere you download podcasts for free. Martha says the creators of these larger international assessments like PISA and TIMS. They are actually very upfront about the limitations of these assessments. They aren't a particularly good measure of how well we're doing teaching the curriculum in our province. There's so much mathematical thinking and this is well documented that really cannot be effectively assessed on a one-time large scale assessment like that. So one way we might interpret lower scores is that teachers are maybe focused on other aspects of mathematical thinking that aren't on the assessment. And maybe that's not so bad. I just think that those assessments provide one useful point of information, but should not be interpreted as a full sum picture of how mathematics education is happening in any province or in the country overall. But after many years of promoting discovery and inquiry learning, in some places, the pendulum

22:20might be swinging to direct instruction. This fall, Ontario is rolling out a quote back to basics, kindergarten curriculum, and in Australia some districts have integrated direct instruction into their curriculum expectations. And it knows all about it. She just joined a team that lethrobe university in Australia as part of their science of mathematics education lab. It's the end of the year as I walk around Gimli's schools. Some students are out on field days and others are laughing as they exit the hallways into the sunny afternoon. Teachers tell me they love the vibe at these schools. They like teaching here. Scott Hill, superintendent of Gimli's schools, thinks part of why direct instruction is working in his district is because he's giving teachers training and resources to follow. And Scott and Jessica show me they're very happy with the results of the changes they've made. Oh yeah, so he's got a pre-calmed student.

23:22In 2017, we are at 39.1% and in 2024, we're at 81.5%. This is like an average score on our grade 12 pre-calculus provincial math test. Out of 100. Yeah. From 39% to 81%, scores basically double. Scott reminds me this style of teaching is just one of the many changes they've implemented. But still. Is a massive change, yeah? You can just see and feel the difference because even on a quick visit, you're hearing the voices of basically all 20 kids in the room. It's about trying to make sure that every kid will have the tools to participate, you know, say things out loud when those things need to be said. So we think that the pathway to get there is more likely through you know, our version of direct and explicit instruction that it is through other iterations of that we've tried, you know, that we've tried pretty enthusiastically that are built around the idea

24:24of inquiry or discovery learning or emergent learning. I feel like I don't know, really grateful in, you know, that what are probably my last five to 10 years in my career, I'm going to feel like I was part of something that was really making a significant, noticeable, measurable, and observable difference in the lives of kids. For Anna, a good indicator of the need to address the challenges of teaching math right now are the number of teachers who are reaching out. Many of them feeling lost as to how to actually do their job. It's overwhelming. I need an assistant because I get so many emails and I can't respond to all of them. Like think about the fact that you have all these teachers around the world. They're writing to a math professor with a podcast about math for help. You know, that shouldn't be

25:24happening. This whole debate has been framed as a math war. I don't like the phrase math wars. I think it's distracting. I think the phrase math wars characterizes this as some sort of silly argument that people are having and it isn't silly. It's actually rather serious. I also don't agree with let's just try to come up with a common ground and a compromise. It isn't about compromise. It isn't about balance. You don't compromise between good instruction and bad instruction. Why would anyone do that? You have to take good instruction. Right? So we have to teach in a way that is going to give us the best math outcomes for students. That way of thinking about it is both divisive. So it tends to pit people one against another, which is not helpful and not constructive. But it's also false in the sense that it's not supported by research. So we know that there's no one

26:25single strategy that's going to be effective for all learners. Learners are diverse, complex, individuals. So is mathematics. Right? There's no one single recipe for effective teaching. It is never going to be all explicit or direct instruction or all inquiry based. Right? Education belongs to kids. Right? I don't know why I'm doing this. Don't get me crying on there. I'm very tough. It doesn't belong to adults. Right? It's the children that are in there every day and it's their future that we have to look out for. That documentary was produced by Julia Poggle with the CBC's audio documentary unit. For more CBC podcasts, go to CBC.ca-podcasts.