Ep 65. Science of Math: The movement everyone's talking about with Sarah Powell
This transcript was created with speech-to-text software. It was reviewed before posting but may contain errors. Credit to Canadian Podcasting Productions.
In this episode, Anna is joined once again by Dr. Sarah Powell, a professor at the University of Texas at Austin whose research focusses on supporting students with math difficulties. They respond to a recent NCSM statement criticizing the Science of Math movement.
Anna and Sarah unpack what the Science of Math is and why high-quality evidence matters. They address misconceptions about explicit instruction and “one-size-fits-all” teaching and explore why math instruction deserves the same scientific scrutiny as reading instruction. This episode is a must-listen for educators, school leaders, policymakers, and parents navigating the current math education landscape.
This episode is also available in video at www.youtube.com/@chalktalk-stokke
SHORT COURSE
La Trobe Short Course: Evidence-informed Mathematics Teaching – An Introduction https://shortcourses.latrobe.edu.au/evidence-informed-mathematics-teaching
TIMESTAMPS
[00:00:22] Introduction and an overview of the NCSM statement [00:10:25] What is the Science of Math? [00:12:07] Is this only about special education? [00:14:24] Math learning through the general lens of learning science [00:17:19] Is the Science of Math equivalent to the Science of Reading? [00:20:01] The instructional hierarchy applies to learning anything [00:24:07] The same groups tried to discredit What Works Clearinghouse [00:26:30] Responding to claims about research citations [00:29:49] Addressing the NCSM’s claims about quantitative research [00:31:21] Why quantitative research and data matter [00:38:24] Why alignment with IES and What Works Clearinghouse is a strength, not a flaw [00:40:18] Importance of measuring learning [00:42:59] Strange statements about an impoverished pedagogical approach [00:47:30] Misconceptions about explicit instruction [00:51:25] Is there quantitative data that supports mixed approaches or inquiry? [00:55:20] Does explicit instruction fundamentally minimize learners' autonomy? [00:56:32] Final Claim: The one-size-fits-all teaching method [00:58:04] Problems with the phrase “math wars” [00:59:59] Why is there such strong resistance to The Science of Math? [01:02:51] Final Thoughts
[00:00:00] Anna Stokke: Welcome to Chalk & Talk, a podcast about education and math. I'm Anna Stokke, a math professor and your host. Welcome back to another episode of Chalk & Talk.
Today's episode is really important. It gets to the heart of a debate about how math is taught in schools and ultimately how well students learn. Recently, a movement called the Science of Math has gained a lot of traction.
Researchers, teachers, school leaders, and parents have started asking more pointed questions about math instruction. What does the evidence really say about how students learn math? Which instructional practices reliably improve student outcomes?
And how do we make sure fewer students fall behind in math? The Science of Math is a research-informed way of thinking about math instruction. And by research informed, I mean the high-quality kind of research, not blogs, opinions, case studies or anecdotal evidence, but the kind of research that can legitimately be generalized.
Research with strong statistical foundations that allow us to draw conclusions about what actually works in math instruction, like well-designed, randomized, controlled trials that measure math achievement.
A lot of researchers across different branches of psychology have been speaking publicly about research-based math instruction to help educators understand what research evidence tells us. I've had many of them on this podcast, and I hear from teachers all the time who tell me that these conversations have given them clarity, confidence, and the courage to move away from practices that do not work, and that's helped their students.
In other words, the Science of Math movement has significantly helped a lot of teachers and a lot of students. But not everyone is happy about this shift.
Recently, a math education leadership organization, the NCSM, released a position statement that explicitly criticizes and attempts to discredit the Science of Math.
And I suspect they hope it can be used as reason to dismiss this movement altogether. So, today's episode is a response. To respond to some of the claims, I'm joined by Dr. Sarah Powell, a returning guest and one of the researchers who helped spark the Science of Math conversations in the beginning. Sarah is a former classroom teacher and an award-winning researcher whose work focuses on supporting students who struggle with math. In this conversation, we address the NCSM's claims head-on.
We talk about what the Science of Math movement actually is. We discuss why evidence, quantitative research, and instructional effectiveness matter. We address misconceptions about explicit instruction and so-called one-size-fits-all teaching. And we ask a deeper question.
Why is there such strong resistance to applying the same scientific scrutiny to math instruction that we now expect in reading?
And I want to be clear that this isn't about ‘math wars’, a phrase I frankly find unhelpful, dismissive, and a distraction from what are serious issues about how math is taught. It's about whether we're willing to look honestly at evidence and whether we're willing to change course when students aren't succeeding.
As I've said many times on this podcast, it's great that we're moving toward evidence-based reading instruction, and I support that wholeheartedly. But math is important too and deserves the same attention. And the Science of Math movement is exactly what we need to help us get there.
If you're a teacher, school leader, policymaker, or a parent trying to make sense of these debates, this episode is for you. I hope you find it helpful. Now let's get into it.
I have a fantastic return guest today. I have Dr. Sarah Powell joining me, and she is a professor in the Department of Special Education at the University of Texas at Austin. She has a Ph.D. in special education from Vanderbilt University. She's a former kindergarten teacher. Her research focuses on supporting students who struggle with math. She conducts professional learning for teachers in the U.S. and Canada and has also worked with teachers in Australia. She develops and evaluates interventions for students with mathematics difficulties. She has won several awards for her research, such as the Presidential Early Career Award for Scientists and Engineers in 2019 and the Kirk Award for Outstanding Research Article from the Division for Learning Disabilities' Council for Exceptional Children in 2024. She helped lead a lot of the early efforts around conversations about the science of math, which is a movement focused on using objective evidence about how students learn math to make educational decisions and to inform policy and practice.
And so, we're here to talk about science of math today. And it's great to have you on again, Sarah. Welcome to the podcast.
[00:05:30] Dr. Sarah Powell: Anna, well, thank you so much. It is, I will say, great to be here with you. I wish I wasn't talking to you today, to be honest, about this statement that we're going to dig into.
I think we kind of joked about that last time I was talking to you, but I'm really excited to be here today and have some great math conversations with you.
[00:05:51] Anna Stokke: Me too. And we said we are going to plan a future episode on word problems. We're definitely going to do that.
[00:05:59] Dr. Sarah Powell: Eventually, we will get to what I spend most of my time on. Yes, we'll get there eventually. Absolutely.
[00:06:06] Anna Stokke: But what we're going to talk about today, this is a response episode, really. It's a response to a recent position statement from the National Council of Supervisors of Mathematics, that's the NCSM, which is a math education leadership organization in the U.S. And in the statement, they are criticizing and obviously attempting to discredit the Science of Math Group. And of course, to be transparent, I definitely support the work of the Science of Math Group, and I'm certainly not alone.
I hear from teachers all the time who say they've actually changed how they teach math because of what they learned through Science of Math and their web page or by listening to researchers from that group and many of whom I've had on this podcast. And it's given a lot of teachers hope and the courage to stand up to ineffective practice.
We're going to discuss the NCSM's claims and our hope is that this will help educators and school administrators who might be handed that NCSM statement as a way to discredit the Science of Math Group, which I suspect will happen.
And they could perhaps then pass along this episode or a transcript, or maybe we'll just have an information sheet that would help that could go along with this episode and say a lot of what's in that NCSM statement is unfounded. So that's our plan for the day.
[00:07:30] Dr. Sarah Powell: That sounds like a good one. One of the things, and you talked about it, is there in this statement that just came out from the NCSM kind of trying to discredit the Science of Math Group. And I will say that, as you said, I was part of a group of researchers and educators who got that group started around 2020, 2021.
But I don't think it's just a group. And in fact, I think the group got the conversations going. But to me, it's a movement and talking about what are the research validated practices that we are using to teach math in classrooms in the United States and in Canada and around the world.
And I think the focus is a lot on the group and the website, when really that is a teensy tiny part of it. It's so much more than that. And it's really taken on a life of its own.
There's huge chatter on some Facebook groups about the science of math, and it isn't about the website, and it isn't about the people, but it's about what's the evidence to support this thing or these things that we're doing. And I feel that's where I'd really love the conversations to go is on the movement, not on the group. But I also understand why it's easy to focus on a website that has different statements on the website.
[00:08:48] Anna Stokke: And just to kind of back that up, you're right. The website is one thing. And the people who started it initially, in which you were one of them, that's one thing too.
And we're very grateful to you for starting that. But there are a large group of people across North America and not just North America who back the work that you're doing. It's important to make that point.
[00:09:11] Dr. Sarah Powell: There's a lot of people. I'll see things online and on social media where people doing science of math webinars and science of math conferences, people who I have never met. And I think that's great.
But I would always ask, what is the research that you are talking about to support this idea around the science of math? But I do think it has to go beyond individuals to what is this decades of research that I would say are out there and that we can rely on. And let's use that research to figure out what's the best way to teach math and what's the best way that students learn math.
[00:09:48] Anna Stokke: Exactly. And we'll get to the research fairly soon. I think I want to start with some of the framing language at the beginning of that document.
I really think this needs to be addressed. And they characterize the science of math as, and I quote, ‘a small group of researchers in special education and school psychology’. They're framing this as a small, marginal group coming from the wrong disciplines is what it seems like to me.
And they double down on this quite a bit in the document. So, first of all, is that an accurate description of the science of math and why does it even matter?
[00:10:25] Dr. Sarah Powell: I think a lot of the initial people who were involved in the science of math do come from backgrounds of school psychology and special education. And why that happened is because that's where a lot of the initial conversations around the science of reading also came from. In my view of the science of reading, a lot of those conversations started because we had so many students in the United States who struggled with learning how to read.
And I see the parallels that currently we have so many students in the United States and Canada, as you and I have talked about, who struggle with some of the foundational concepts and procedures related to math. And so where would be a natural place to go for some of the research that supports students who struggle with learning to read or struggle with learning math? I would suggest that school psychology or special education would be a natural place to start.
But then that conversation can very quickly go to a lot of different fields. I know that there's a lot of conversations around the science of math that are coming from educational psychology or cognitive science. There's a lot of conversations coming from school psychology and special education.
And I would say there's also a lot of conversations around the science of math coming from general education and, very importantly, mathematicians like yourself. So, thinking about as adults get to the point where they are focusing on math, what are some of the difficulties that adults might have with mathematics? And where did they pick up some of those difficulties?
Or maybe they have some unfinished learning. Often it comes from those school-based settings.
[00:12:03] Anna Stokke: Why do you think they would frame special education as a weakness?
[00:12:07] Dr. Sarah Powell: I don't know. I don't love it. It's because when we think about special education, and you'll have to correct me for percentages in Canada, but typically we're talking about, in learning disability, probably 5% to 7% of student population, which 5% to 7% is small.
But I think that's just those students there on the bell curve. And we're not worried about that. We're worried about all these other kids on the bell curve.
But I would disagree with that because what we see from national data here in the United States is that at grade four, over 60% of students don't meet a minimum level of math proficiency. By the time we get to grade eight, it's over 70% of students. This is not a special education conversation.
This is a conversation about what is happening in general education settings with general education students, the majority of whom struggle with math. And if I'm thinking about students who struggle with math, the strategies that have been very helpful for students that have an identified disability are also really helpful for students that are struggling with math without that formal disability identification. I would say that the science of math is in many schools focused on 60, 70, 80% of students.
And many times, those practices that are helpful for students who struggle with math are actually helpful for all. But it's easy to just say, oh, that's a special education thing to push it to the side and then not saying, not having any accountability for the majority of students in the United States who are struggling with math. And what are we going to do about those learners who have unfinished learning and who have learning gaps?
And we need to address those right now.
[00:13:51] Anna Stokke: I think I've told you in the past, I find this really interesting because, and as you mentioned, I'm a mathematician and I am essentially advocating for the same things you are. But the pushback that I would always get is exactly the opposite, that I know nothing about students who struggle with math or even the middle students because very few students actually go to university and I'm just advocating for the upper echelon. I mean, it's really interesting.
[00:14:24] Dr. Sarah Powell: We get the same thing. We're at opposite ends of the bell curve. Yeah, I often get the same thing.
So, I am a former general education teacher. All of the research that we are doing right now occurs in general education settings. But I often get pigeonholed as a special education person because I work in a department of special education.
And that just at my university is how I'm organized and that is where my job is. But I have not been to an IEP meeting in a number of years because we're working with students without a disability identification to really think about what are the things that we can do with those students so that they don't have an identification of a disability. So, it's much more on the preventative side of things.
But many times people will look at my job title and they're like, “oh, you're special education”. And I'm like, “no, everything we do is in general education”. We work almost exclusively with general education teachers.
It's just easy to push us to the sides when in reality you and I are focused on the needs of, I would say, the majority of students, but actually all students.
[00:15:32] Anna Stokke: It's an attempt to discredit people instead of actually engaging with the discussion, instead of actually debating. I'm quite familiar with this. With that framing in mind, let's move on to their first claim.
They have several claims in this document, and I think it's important to address them. This is the first one. And I had to laugh at this because this has been coming up a lot for me as well.
Here in my province, there are people that have been advocating really hard for improvement in breeding because Canada is slightly behind the U.S. in that regard. And I was talking to someone and she said, you know, every time we go and talk to these government officials or people who can make changes, they say, “OK, yes, we may have to do this for reading”, but it's really important for everyone to understand that math is not the same every time. So, there's some sort of fear.
[00:16:31] Dr. Sarah Powell: Organizations have done a nice job of really trying to get people to think that the learning of math is different from learning in general.
[00:16:40] Anna Stokke: They're really trying hard. That's their first claim. And I quote, claim one, the science of math is not equivalent to the science of reading as an established body of research with respect to multidisciplinary expertise.
And they also write this, that the science of math has just attracted attention, you know, in part because of a perceived parallel with the science of reading. Very interesting claims. What do you think? Or is the science of math claiming to be equivalent to the science of reading or just arguing that math deserves the same scientific scrutiny?
[00:17:19] Dr. Sarah Powell: I think it's that latter. Well, I do think that to me, as we just talked about, the science of reading really came about for students who were experiencing difficulty with reading and researchers saying, hey, we actually know quite a bit about how to teach reading, and we need to be more reliant on those research validated practices. And so, I would say there's an analog to math.
We do know quite a bit about how to support learners who experience difficulty with math and for the math progression that students are on. And we still need to be thinking about relying on that research base to help those learners there. I would say, I don't know if equivalent is the perfect word, but I would say that they are definitely companion movements.
And if you talk to people that work in the area of writing, they would say that there is a science of writings, the progression of how students learn to write and ways that we can teach students to do well with their writing. I think it's just arguing that math does require the same scientific scrutiny, as you said. But in this document, I think they're trying to set themselves apart to say, no, math is different.
Math research is different. That means math evidence is different. If you can be different, then whatever you say goes.
But I feel that what I'm trying to do and what you're trying to do is just say, no, like high quality research is high quality research. And we need to be focused on outcomes for students in K-12 settings and beyond. And we need to make sure that our practices in the classroom support what the research says is really important to do in terms of the support and of teaching and learning of math.
[00:19:03] Anna Stokke: I agree with you. So, a couple of things on that. Of course, math and reading are not the same, right?
Math is math. Reading is reading. That's obvious.
However, the way that you learn something, the roots are kind of the same. The thing to think about, I think, that helps people to understand this, which I learned about from your group, by the way, is the instructional hierarchy. No matter what you're trying to learn, if you're a novice learner, you go through these four stages.
You start with the acquisition stage, you move to fluency, et cetera. I think in that way, they are the same. And as far as research, look, this isn't that complicated.
You design a good research study to determine whether someone actually learned. I mean, it has to be a well-designed study. It doesn't matter if it's math or if it's reading or if it's science or anything.
[00:20:01] Dr. Sarah Powell: I agree. And I think it also goes outside of academic context as well. Last week, I was in Georgia working with middle school teachers in math, and we talked quite extensively about that instructional hierarchy and had a lot of good conversations about how do you help students with the acquisition of initial skill?
How do you move them to that fluency? How do you help students generalize? What types of practice do you design that helps students know when to do this skill and when to not do that skill?
And then we also talked a lot about adaptation, especially around problem solving. And one of the comments that was made during my training is, I wish all of the middle school teachers were here right now. Not the math teachers, everyone.
Because that's how we all learn to do stuff. That's how we learn to read. It's how we learn to think about learning history.
It's also how we learn to do everything like play sports and just function in life. We're all going through that instructional hierarchy all the time. And it's been around for decades now.
And it's always interesting to me that I'm still saying, OK, let's look at this instructional hierarchy. And not everybody is really, really familiar with it. But it goes back to the science of learning.
And I think that maybe that's where we really need to think about the science of math and science of reading and just extrapolate out a little bit to feel how do people learn? And the learning of content area instruction, while it might have some variation from time to time, is not that different. And how great would it be if we could work with pre-service and in-service teachers on that?
So, if you're teaching reading, there's a lot of similar strategies that you can use for the teaching of math, the teaching of writing, the teaching of science and so on.
[00:21:43] Anna Stokke: And, you know, there are other claims that one of the reasons that science of math has attracted attention is because of the parallels with the science of reading.
[00:21:53] Dr. Sarah Powell: I'm so glad math conversations are going on. And if it took the science of reading movement to get those started, yeah, sure. Let's follow on those coattails.
[00:22:04] Anna Stokke: I think also it's just that the science of math has resonated with people because they know there is a problem. A lot of people know there is a problem with the way math is being taught. When you listen to Emily Hanford's podcast and you hear they didn't get reading right.
Everybody was told that this is how you should teach reading. Why would we trust what the same groups of people are saying about how math should be taught? I think that's a good thing.
It's time to start turning over the rocks and seeing what's really going on here.
[00:22:42]: Dr. Sarah Powell: I think it is time to turn over the rocks. And maybe some of the things that are going on in math classrooms are effective. OK, that's great. Like, let's figure that out. But then let's take some of those less effective practices and replace them with things that have a stronger research base to support their use. So, yeah, I think it's great that we're having all of these conversations.
And I was in New Mexico two weeks ago and they were talking about high quality instructional materials that they were going to adopt in their district and having the same things. OK, but which of these has the strongest evidence base to support their use? And its so grad you're asking that question.
And that, I would say, is a science of math or science of learning question. What is the research that supports this set of materials or this set of strategies and so on? Exactly.
I think that's what's going on at the core. When in actuality, those are not that different. But if they could convince people that math is totally different from reading, then their organizations could then say whatever they need to say without being held accountable for all of this stuff that's going on in the reading world.
[00:23:52] Anna Stokke: Exactly. And the reading stuff has gained a lot of traction. There are a lot of changes going on, particularly in the U.S. with regards to reading, and they perhaps would like to prevent that happening in math. That's probably what this is about.
[00:24:07] Dr. Sarah Powell: One of the things that I often think about is that these organizations are only organizations that survive because people pay money to those organizations. They pay money to go to their conferences, or they pay money to buy their books or to buy into their professional development. And if people were not paying money, these organizations would not exist at all.
And that's different from the What Works Clearinghouse that has tried to put out research-based recommendations for the teaching of math and reading and so on. That has been funded by the federal government in the past and brought together groups of researchers there. But I think there's something that feels a little bit wrong to me about this payment thing.
And no wonder they're always putting out new stuff because they want people to pay and to come to the conference and hear the latest thing. And the stuff that they've been putting out there, I mean, dare I say it, they've been selling it. And a lot of people have been sold on these theories or these practices.
And then if they are going to do an about face and say, like, actually, what we've been putting out there for the last two decades really doesn't have the strongest research base to support its use, that's going to make those organizations crumble. And I think they're pretty afraid. They're aware of that, of how quickly a lot of the conversations around the science of reading dismantled big organizations in reading.
And I think many of them see it coming in math and that they are afraid.
[00:25:46] Anna Stokke: And very few people will take back something that they've put forward for a long time, especially when they're claiming that it's research-based when their research is often not that great. You said it, I didn't. I did.
And stand by it. It's not that hard oftentimes to look at the research and go, this is really not something you can be drawing conclusions about. That's another story.
Speaking of research, this is their next claim, and this is a big claim. They claim that the science of math has engaged in misleading research educational practice. That's an allegation.
And do you have any thoughts on that allegation?
[00:26:30] Dr. Sarah Powell: In this statement, which I'm sure you will link to with this podcast or this video, it's on page four of the statement. They have an example of it says misleading or inaccurate citations on the science of math website. One of the things I will say is that research citations are ever evolving.
Most of this stuff was written in 2020, 2021. I do know that there's some new research out here that we could add in there, but right now there are no updates to the science of math website, if people were wondering. One of the things they say, oh, there's a claim about time tactics, improved math performance, but that ignores this subgroup about girls.
I think that's fair. Let's focus on the difference between girls and boys. But there's also a real nice study that came out last year that did see that there were no significant differences between student math performance in timed and untimed settings, and untimed settings did not lead to math anxiety.
So that's always a big conversation piece out there in the math world. They talk about explicit instruction, and they focus on students without mathematical difficulty, which I think is interesting. So right there, they're saying, oh, but for the minority of students in the United States, this is not the case.
And as you and I already talked about, I'm always focused on the majority of students in the United States. They talk about none of these sources reported anything on the impact of explicit instruction on creativity. That just comes from nowhere.
I'm always focused on math outcomes. I think you probably are too. But if creativity is so important, I would love for them to write a statement about how creativity leads to improved math outcomes.
And then I'd love to know a little bit more about that. They get into just some of the real language. We talked about that the National Math Panel says that explicit instruction should be used regularly.
And then they say, well, this doesn't mean that all of a student's math instruction should be delivered in an explicit fashion. And I actually don't think the Science of Math website says that everything taught in math should be through explicit instruction. I think a lot of the focus is on foundational skill.
So, students who need foundational skill, whether that's in operations or proportional reasoning or algebra, wherever that is on the math continuum, explicit instruction is real helpful for that acquisition of knowledge. Speaking of that instructional hierarchy, it's just a very nuanced thing. And then there's a whole other thing around productive struggle.
And what I would love for them to see is their extensive research base that supports productive struggle. So maybe instead of saying that this is a misleading claim, why don't you provide the research for the thing that you are saying is more important to do in the math classroom? And that is definitely not in this document.
[00:29:10] Anna Stokke: You know, there's some research that we could add, and I'll put it on the resource page for this episode.
[00:29:18] Dr. Sarah Powell: What do you think when you read this table number one? Did anything stick out to you?
[00:29:22] Anna Stokke: I thought it was a stretch. I thought they were kind of looking for something there.
[00:29:27] Dr. Sarah Powell: Very nitpicky.
[00:29:28] Anna Stokke: Yeah. But in any case, I think the telling part is really the next piece about the type of research. That's really what they seem to have an issue with. So that's claim three.
[00:29:42] Dr. Sarah Powell: And have for decades, to be honest.
[00:29:45] Anna Stokke: And I have a lot of thoughts on that.
[00:29:47] Dr. Sarah Powell: All right. I'm excited to hear them.
[00:29:49] Anna Stokke: Claim three, the science of math does not reflect the education research base with respect to relevant forms of evidence and forwards a narrow view of the goals and possibilities for school mathematics. It's interesting because, and I see it almost contradicting the last claim, because in the last claim, they're arguing that the science of math misrepresented research. And now they're arguing, oh, actually we don't like the kind of research that the science of math cites.
They're arguing for research that in my view is much less rigorous in nature. Yeah. I just think this kind of contradicts the last claim, claim two.
They even write that nearly all of the research cited by the science of math is quantitative in nature. You have to realize as someone coming from a math background, and I'm in a department of math and statistics, so I'm surrounded by statisticians all day. I cannot believe this.
Could you imagine any other field saying something like that? That is literally the power of mathematics and statistics in this way. You can use them if you have a well-designed study and you can use that, use the math and statistics so that you can actually make predictions for larger groups, like for the population.
They don't like quantitative research is actually terrifying. I would run from any such group.
[00:31:21] Dr. Sarah Powell: When you talk to your mathematics colleagues, when you go to your faculty meeting in your department, if you were to tell them that we were not going to rely on quantitative outcomes, would they all just look at you? What are you talking about, Anna? That's crazy.
[00:31:40] Anna Stokke: Yes, of course.
[00:31:42] Dr. Sarah Powell: What would they say? I mean, you probably talk to them about this, right?
[00:31:44] Anna Stokke: We talk about this stuff all the time. It's absolutely bonkers. And look, if someone is saying that, just run the other way. Because really, think about what this means. If you don't care about quantitative research, literally anything goes.
[00:32:03] Dr. Sarah Powell: Yeah. I mean, this goes back to when you talked to Brian Poncy, I think it was last year. He was talking about how students learn the facts. But he's like, if you can't measure it, you can't say that it's working.
And I think that goes back to that bigger idea that out there. It's like, yeah, if you can't measure it, you can't manage it. And I think about that often, because I think what they're saying is that, well, we're not always going to measure it quantitatively.
And if you're not going to measure it quantitatively, then as you said, anything goes. I could say, oh, this or that, and it's fine. But what quantitative data allows us to do is it allows us to draw comparisons across students, across schools, across states, across countries.
And I think it also, it holds us accountable. And I almost think that they're trying to say, we're not going to always be held accountable for what students are doing in the math classroom. And from a group of math educators, okay, they can say that.
But if you talk to a parent or a caregiver, or better yet, talk to a teacher and say, “oh, we're not that worried on math outcomes anymore”. Teachers would be like, “that's not what my school's telling me”. And especially if you talk to principals or superintendents, every principal or superintendent knows exactly the percentage of students in their school that are not meeting a minimum level of math proficiency.
And that is quantitative data. And if you said, “oh, we're not going to rely on that quantitative data anymore”, they would be like, “well, no”, but the state is expecting me to do that. It's just almost a ridiculous thing to put out there.
But it also then allows them to put stuff out there in the world that doesn't have a strong research base to support its use and is also not replicable. And I think that the replication conversation around some of the research that they are saying that, oh, we should be doing this as well, it really brings a lot of, I would say, flaws to that style of research because it isn't always replicable from one research team to the other or from one school to the other.
[00:34:12] Anna Stokke: I think the qualitative, maybe observational type research, I think it's maybe good to get ideas for what you can do more quantitative research on, but it can't stop there. And I should have also mentioned earlier, because you mentioned about how they were saying that none of these studies measured creativity. Well, of course they don't, because you can't measure it because it's not, what is it?
[00:34:38] Dr. Sarah Powell: Well, and also what is the correlation between creativity and math performance? I'd like to see that first to understand how important creativity is to improve your math outcomes, but all of that would have to be quantitatively measured, Anna, and they're not going to do that.
[0:34:55] Anna Stokke: Creativity is a hard thing to define. I had a conversation with Jared Cooney Horvath about that, and he explained it really well. And he said, he's talked to all the creativity researchers and creativity is really just problem solving.
It's taking knowledge that you have and applying it. That's it.
[00:35:14] Dr. Sarah Powell: Well, and if that's the case, then I'm thinking about that adaptation in the instructional hierarchy, which is really where you're getting into that. And I would suggest that having strong foundational skill in whatever you're working on is going to be absolutely essential for that creativity.
[00:35:30] Anna Stokke: It is. You can't be creative with things that you don't have, like with knowledge you don't have. He kind of described it as, and you've had these moments where you were working on something for a long time.
You couldn't figure it out. You're in the shower and all of a sudden it comes to you and that happens, but things can't come to you if you have nothing to think about. So that's really creativity.
[00:35:54] Dr. Sarah Powell: So many of those quantitative criticisms have been around for at least in the United States the last two decades, especially when the IES, the Institute for Education Sciences in the United States created the What Works Clearinghouse (WWC) about 20 years ago or so, there was a real big focus on the quote, gold standard of educational research as being randomized control trials that are relying on outcomes that are measured quantitatively. And from Newish to the research game, I've only been doing this for about 15 years or so, but from what I understand when that came out, that caused a big hubbub of like, people were like, “oh, but we can also do research qualitatively”. And I think that a governmental organization saying, no, this is the thing that we're the most focused on.
You can do that other stuff, but we're most focused on this. And a lot of that came from ‘No Child Left Behind United States’. So, it said, we are going to be measuring students’ math and reading performance every year.
And we are going to do something about schools that are not meeting certain thresholds in terms of reading and math performance. This is a decades old thing where it's like, well, but there's also the qualitative research. Well, yeah, but sometimes you have to make decisions as to what's the most important.
And I think what you're saying and definitely what I'm saying is that I see that in the United States and Canada, it is important to measure students’ math performance in a quantitative way so that we can understand where students are and which students need additional support. And I think that trying to discount that approach is then trying to separate math and saying, oh, but we're this different thing over here and we do different stuff. In reality, that is not the case.
[00:37:34] Anna Stokke: No, it's not the case. And also, I would just caution listeners when someone says their program is research-based, you do want to find out exactly what that means because it can mean that the author themselves did some strange study that tested engagement.
[00:37:55] Dr. Sarah Powell: Or often you see that the curriculum uses strategies that have an evidence base, but the actual program itself has not been tested for its application.
[00:38:04] Anna Stokke: I agree. That is quite common, actually. So, you do have to be quite careful.
What do you think about them criticizing science of math for their alignment with the longstanding agenda of the Institute of Education Sciences and the What Works Clearinghouse?
[00:38:24] Dr. Sarah Powell: I'd say every school district, probably in the United States and Canada. Going back to that thing is we assess what students know in math through assessments. And I know some people probably don't like that, but that is in 2026.
Those are the parameters that are in play. And it's not going to change anytime soon. If I'm a person that's trying to help schools and teachers improve the math proficiency rates of students, you do have to look at that quantitative data and you have to understand it.
You have to know which students are doing well with their current instructional program and which students need additional support. And when we provide additional support to students, is that paying off for those students? And to me, all of that occurs through the collection of quantitative data.
And going back to my earlier comment, I don't think you could talk to a principal or superintendent or teacher who would tell you quantitative data isn't important. I think these are almost like these heady math ed conversations that are occurring well, well outside of the confines of a classroom without any understanding of the day-to-day practical considerations of what teachers and principals are focused on. And maybe one day this changes and we assess students in a very different way, or we don't assess students at all, but that's not in the cards right now.
And so we need to figure out what's going on. And it's actually helpful for schools to know how many of their students are on track to meet end-of-year standards and which students aren't so that they can provide the appropriate services and support at that time. And quantitative data is a very quick way to understand which students are doing well and which students need that additional support.
[00:40:12] Anna Stokke: You have to measure learning. You can't know if someone learned if you don't actually measure it.
[00:40:18] Dr. Sarah Powell: Well, if you're not measuring it, then you're not held accountable. There's these little things out there that you're saying that they're doing that is really trying to take some of the accountability piece off of them and off of the practices that they have been suggesting over the last few decades are helpful because I think we're seeing that those are not helpful strategies and helpful practices.
[00:40:41] Anna Stokke: Absolutely. And if you are promoting instructional practices or programs that don't work and perhaps you're making a lot of money off those programs through professional development, selling books, et cetera, and if they really don't work and you kind of know that, which I think in a lot of cases they do, you really don't want testing.
[00:41:02] Dr. Sarah Powell: No, you don't want that outcome data out there. Or you provide evidence that is more about things outside of math outcomes. Oh, are the students engaged?
You know, that's a pretty popular program that's out there has engagement data, but not math outcome data. And I would just move the other way away from that if it has no data to support improvement on math outcomes.
[00:41:24] Anna Stokke: My personal opinion is I don't think governments or divisions, that's taxpayer money. I actually don't think it should be going towards programs that haven't actually shown that they can improve math achievement. That's part of the problem.
Have to say one more thing about this section. I found it bizarre. So, this one's really, really crazy. They criticize research grounded solely in considerations of efficacy. Like if not efficacy.
[00:41:55] Dr. Sarah Powell : Whether something works or not.
[00:41:57] Anna Stokke: What would you want? Something that doesn't work?
[00:41:59] Dr. Sarah Powell: I think that's the thing so much in this is they throw this stuff out there and then it's what is the alternative? If you're not going to focus on math outcomes, what are you going to focus on?
If you're not going to focus on efficacy, what are you going to focus on? If you're not going to look at quantitative data, what are you going to do? And there's little hints and throughout, but it would be really nice instead of having this criticism paper, why don't you put together a position statement of here's what we would suggest to do and then here's the research that supports that.
I would love to see that, but I don't think it's going to come because I think it would be really hard to put that paper together.
[00:42:41] Anna Stokke: Let's go to the next claim. Claim four, the science of math elevates an impoverished pedagogical approach to the exclusion of all other forms of teaching. What do they mean by an impoverished pedagogical approach?
[00:42:59] Dr. Sarah Powell: This is where there's some language about explicit instruction. I've not only seen this in math, but this is out there in general is that explicit instruction is a pedagogy of poverty. So that's where they are pulling that.
That comes from an article that came out about 40 years ago or so. I think that they're saying that explicit instruction as they are envisioning explicit instruction, I mean, the criticism there is that we're just always teaching students to be regurgitators or mimickers of knowledge. I think this is where explicit instruction really gets a bad rap.
First of all, they do not operationally define explicit instruction and give an example of what explicit instruction is. If they were to, I would guess that it's very, a very, very narrow definition of explicit instruction. When actually explicit instruction is very student focused, very dialoguing with students.
It focuses on both conceptual and procedural learning. Many times people will say explicit instruction is just a procedural thing. And that is not true at all.
I mean, if you look at any of the intervention work that I do and a lot of colleagues that I work on, we teach students a lot about word problems. It's all about these concepts that are in the word problems. We're explicitly teaching those concepts, but it's focused on that conceptual knowledge.
We also have an example from a fractions intervention we're working on right now that really digs into these different models of fractions. It's all based on conceptual understanding of a fraction, not just procedural understanding. I think there's a bad rap for explicit instruction.
Then if we think that their definition of explicit instruction, maybe just putting some words into their mouth, it's just this mimicry. They're saying that's a pedagogy of poverty, that then we're not teaching students to really deeply understand this content or be able to adapt this content to other settings. I think that language is pretty harsh.
And my thing, this kind of goes back to the reading thing. If you're going to say that explicit instruction in math is a pedagogy of poverty, then are you pulling that criticism for, I will say, most of the entirety of the science of reading movement there? And I would love for you to say that to some reading people that are explicitly teaching letter sounds or explicitly teaching word reading or sentence reading and reading comprehension and so on.
I think that's where it's coming from, but I would love for you to comment on this whole thing about this quote, impoverished pedagogical approach.
[00:45:28] Anna Stokke: I also agree with what you said about conceptual understanding, which in itself is not a well-defined term, but I will say that people conflate it with inquiry-based learning. And I've seen a lot of people conflate.
[00:45:45] Dr. Sarah Powell: It's like they go hand in hand, explicit procedures go hand in hand, inquiry, conceptual go hand in hand.
[00:45:51] Anna Stokke: And it's absolutely incorrect. If you want to teach someone why procedure works, if you want to teach basically where that comes from and et cetera, you can teach it explicitly. In fact, I would argue that you should teach it explicitly.
That's just not correct. The other thing is there's always these caricatures and by the way, they would say the same thing. When I talk about inquiry and discovery-based learning, just to be fair, they'll say that I'm not defining it correctly and that I'm conflating it, et cetera.
So, we can go back and forth on this type of thing, but we should be clear about what we mean by explicit instruction. And we mean that you explicitly model for students that it's really the I do, we do, you do approach. There's a lot of interaction in the class.
There's a lot of opportunities to respond. There's a lot of feedback and it's fading instruction so that you get to a point where students can do it on their own. So that's what we mean by explicit instruction.
I do want to comment on something they wrote there. They wrote that over-emphasizing knowledge of facts and procedures and failing to honour the richness of what it means to do, use and benefit from mathematics in one's life.
I hear that language all the time. And just to be clear, I'm a mathematician. I'm pretty sure I have benefited a lot from the richness of what it means to do and use and benefit from math in one's life.
I know this very well. It's what I do for a living. When you look at this closely, what are they claiming here?
[00:47:30] Dr. Sarah Powell: Well, I think that shows their definition of explicit instruction is like, you're just teaching facts and you're just teaching procedures. I can read through to be like, okay, that's their definition of explicit instruction. Mine is much different and much broader and much more interactive.
But I would also say without the factual knowledge and procedural knowledge, that's really foundational to so many things that we're going to do in math at every grade level. And without that, then it's going to be really hard to do mathematics and use mathematics and benefit from mathematics. It really isn't an either or, it's actually both.
But I think that they are couching it as an either or.
[00:48:09] Anna Stokke: Actually, I personally would not want a teacher who thinks that facts and procedures are not rich, that they're boring. A good teacher should be able to sell, for instance, the standard algorithm for multiplication. These are absolutely wonderful procedures.
They're efficient. They were developed by mathematicians over many years. I think it's really sad that whoever wrote this has such a negative view of, I would say a very narrow view themselves of what math is.
And you're not going to benefit or honour the richness of mathematics if you can't do it. Like being able to do math is what makes people appreciate math.
[00:48:59] Dr. Sarah Powell: Oh, yeah. It's all going to influence, yes. I'd love to know their definition of explicit instruction and their example of that, because I think this entire paper, while criticizing the science of math, is really a criticism of explicit instruction. And while there's a lot more that goes into teaching, that's the thing that people just love to hang on to.
But then they say, we really need to use this guided inquiry approach. Okay, great. This is where I'm like, tell me not what to not do, but tell me what to do.
I would like to see what's their definition of guided inquiry. What does this look like? Provide some examples.
My hunch, and I've said this probably with you and some other places as well, I think that looks a lot more like explicit instruction than people are willing to admit. And then what is the data that supports guided inquiry? I want to see some quantitative data.
I know you don't want to give it to me, but I'm going to need some focus on student math outcomes. But it's like, you can't say, well, this is what we should be doing without defining that and then providing data that supports it. And I don't want one study, and I don't want five studies, but I want some meta-analytic data from dozens of, or if not hundreds of studies.
Seems that like they indicate that there's a whole world of research out there that's not being talked about in the science of math but really provide the data and focus on student math outcomes. I want to see some examples of guided inquiry because that's where I think if you paired someone's example of guided inquiry and my example of explicit instruction from some of our word problem interventions, I think that they would almost look the same.
[00:50:39] Anna Stokke: You don't think they're trying to sell, you know, we could take a bit of what you say and a bit of what we say and we'll meet in the middle, and we've got balanced math.
[00:50:50] Dr. Sarah Powell: But I think when they talk about this quote, mix of approaches, I would ask, and I know the question is kind of silly, but they show me the data that that's important. But if I've already said, “hey, we're not always relying on data”, then I don't have to show you the data that supports that mix of approaches.
It's just this like ever evolving conversation that's just so cyclical where we never actually centre on anything.
[00:51:14] Anna Stokke: Do you think, is there any quantitative research that would support anything they're saying about the mix of approaches or inquiry?
[00:51:25] Dr. Sarah Powell: Not terribly. You know, the one study that always gets cited is that Alfieri et al 2011 article about saying guided inquiry is better than explicit instruction. But if you read that paper closely, oh man, it's so tricky.
But actually, in that comparison, they compared guided inquiry, which had a different name in the Alfieri article, versus all other instructional approaches, which included explicit instruction and unassisted discovery. There's actually, there's no conclusion there. You cannot conclude that guided inquiry is better than explicit instruction from that one article.
And that's the thing is, show me some other stuff and just show me some examples where teachers implemented this guided inquiry and it helped lead to improved student outcomes over students who did not participate in that approach. But if the data is not there, that's going to be pretty hard to come to that conclusion.
[00:52:18] Anna Stokke: But there are quite a few studies that do support the use of explicit instruction.
[00:52:24] Dr. Sarah Powell: Oh yeah, I'd say hundreds, if not thousands at this point. And there's a lot of meta-analyses in the area of math, meta-analyses, those studies of studies, that say like, oh, across these 50 studies, all of which used explicit instruction, we saw that on average, outcomes improved this standard deviation over students who didn't receive that explicit instruction. There's a lot of it out there.
And some of it's in special education. A lot of it is with general education students. Some of it's coming from cognitive psychology.
We see that also in school psychology. When they were talking about, oh, this is not coming from a variety of fields, I think that that is a falsehood because there's a lot of research out there that does use explicit instruction.
[00:53:07] Anna Stokke: Within that claim, and you had mentioned, they said this thing about mimicking, and I'd actually like to address that myself too, because they write that explicit instruction fundamentally minimizes learners' autonomy, relegating them to primarily following and mimicking their teacher. I think when someone's first learning something, they mimic their teacher. That is what you should do.
We always talk about hockey here. So, if you want to become a good hockey player, you mimic someone else who knows how to do it. That's how you learn how to do stuff.
This mimicking stuff, it's meant to be a pejorative here, but it's, you should mimic when you first learn something.
[00:53:51] Dr. Sarah Powell: I think that's where I'd love to see their definition of explicit instruction, because there is this idea of old school direct instruction, where it was, I would say something, and there was some snapping involved, and then the student would say four or whatever. And I feel that that's what a lot of people think explicit instruction still is. Whereas I see explicit instruction as much more dynamic, much more interactive, and isn't always this mimicry.
But I do agree with you, Anna. There's a lot of things in math. So, if I'm going to count these fingers, there's something that I've learned through mimicry, and that is one, two, three, four, five, six, seven.
And I've only learned that through mimicking. But that word of mimicking really sticks out to me because it comes from popular book that's out there that says we're not trying to teach students to be mimickers in math. We're trying to get them to be problem solvers in math.
But there's still no data that actually supports that approach. And I think they're just picking up on that language as it's used in popular culture.
[00:54:55] Anna Stokke: And by the way, that's why I'm bringing it up. But I'm actually going to mention the program. It's Building Thinking Classrooms, which is quite popular.
And that language is commonly used with that program. And that program actually has no valid research supporting its effectiveness in terms of learning. What do you think about this claim that explicit instruction undermines autonomy?
What does that mean?
[00:55:20] Dr. Sarah Powell: I don't know. To me, I see it in a different way. I see that when students receive explicit instruction and learn how to add or learn how to solve a word problem or learn how to place a fraction on a number line, that actually opens up a world of math to them.
And there are some just facts and skills and foundational content that everyone needs to learn in order to be successful and move to that generalization and move to that adaptation in math. And I don't see that it would undermine students' autonomy at all. Instead, I think it could benefit students and help them go on to the next more complex thing in math.
What do you think?
[00:55{58] Anna Stokke: I think you're exactly correct. You actually give people more power and more independence if you give them the skills to do things on their own. And then you build their confidence.
So many things are related to that. Otherwise, they're dependent on calculators. Their last claim, which we've kind of addressed a bit throughout this conversation, is that the science of math ignores the full complexity of learning environments and learners faced by teachers and school leaders, providing a one-size-fits-all answer. So what are your thoughts on that?
[00:56:32] Dr. Sarah Powell: That's an interesting comment there. But I think that when we're thinking about the complex learning environments and the learners that teachers are working with in those complex learning environments, I would say that we have more than half of students in the United States who do not meet a minimum level of math proficiency.
And as I said before, a minimum level of math proficiency is a very low benchmark. And that's really complex. And we have to think about what is the best way that we can support that majority of students in those U.S. classrooms. And I would say that when I'm considering these different pedagogical approaches, explicit instruction, as I, Sarah, define explicit instruction, has a strong research base to support its use to help students with that acquisition and that fluency and that generalization and adaptation of knowledge. And I don't think it's a one-size-fits-all approach. I see that it's going to help our learners that need the most assistance in math.
And if we don't do something about that now, we're going to send them on to the next grade level with even more unfinished learning. And then that's just going to cause a lot of difficulties as students move down the road in math. But I would say, well, how do you address the complexity of these complex learning environments?
Guided inquiry. Show me the data. Show me that information.
[00:57:56] Anna Stokke: What do you think about the media or some other researchers framing this as a ‘war’, a ‘math war’?
[00:58:04] Dr. Sarah Powell: I don't really love it. It's an easy way to talk about this. And many times, people talk about these different camps. I think that's a false dichotomy.
And this is where I'm going back to my idea of my version of explicit instruction is probably a little bit more similar to guided inquiry than anybody wants to admit. But it's always on this pendulum. And I'm thinking I would love to see some of these other examples to really understand where we are on the pendulum.
But yeah, I mean, the math wars is something that has been talked about for decades. And it's like, oh, the math wars are back. I think what's maybe not back, but what the thing is right now is just having some conversations about what is the evidence that supports this practice or this series of practices that you're putting out there.
And so, it's not a ‘war’, but people might see it as war-like because we are questioning. That thing that you've been saying for the last two decades actually doesn't have a research base to support its use, either a strong research base or any research base at all. And then people feel like they're under attack.
And then that war analogy seems like a natural one to pick up on.
[00:59:17] Anna Stokke: I’m not a fan of it either. It makes it into something that's a silly argument among children.
And it's not serious when it actually is really serious.
[00:59:27] Dr. Sarah Powell: It is very serious because there's thousands, if not tens of thousands, or hundreds of thousands of students that are being impacted today by this idea. I do also think that then it's like, oh, let's focus on the war instead of, well, what should we do? And how can we look at evidence and think about what are some of the best ways that we can support all these learners in our classrooms?
[00:59:51] Anna Stokke: Why do you think there's so much strong resistance to science of math from organizations like NCTM and CSM?
[00:59:59] Dr. Sarah Powell: I think that as a whole, they see how fast some very popular programs and some very popular strategies in reading got dismantled by the story and a lot of other efforts that were happening at the same time. And they are looking at some of the stuff that they've been talking about and they're like, oh, yeah, that's coming for us. And so, I think they're worried.
And going back to that idea that they only exist because people pay to go to their conferences and people pay to buy their books. And if people stopped doing that, those organizations would be more limited. Some people would lose their jobs.
And I think that's probably the biggest concern is more for the bottom line and eating some crow of things that they've said over the last few decades than actually a big worry about what's going on in math classrooms with teachers and students.
[01:00:58] Anna Stokke: What's that phrase? There's a phrase that if you threaten someone's livelihood, they'll fight back really hard. And I think that's what we're dealing with.
But I think people are threatened. They've been in control of math education for a long time. They've had a lot of influence over math education, and they don't want to give up that power.
And there are careers at stake, you know, not even just NCTM. But I mean, I don't know who wrote this document, but there's a lot of education researchers out there that they're publishing papers and they've held this view and those papers may not be quantitative in nature. This is a big threat. If teachers find out about that, that actually they should be looking more at this quantitative type data. And if they're looking for effectiveness, ask questions, et cetera, those are big threats to them. So that would be my guess.
[01:01:55] Dr. Sarah Powell: Well, at least we're here talking about it. You're doing such a good job with this podcast of getting so many people to think about these conversations and to ask what we're buying as a school district. Does that have a research basis to put it to use?
And then those materials are not everything. How are we using those materials? Our instructional strategies that we're using, our instructional approaches, do those also have an evidence base to support their use?
And just getting those conversations going is awesome. And I'm glad they're going and I'm okay to be in the middle of it. And I'm just grateful to people like you and many others who are really helping get a lot of those conversations going all over the world.
It's really exciting.
[01:02:38] Anna Stokke: Yeah. And we're not going to let them beat us down.
[01:02:41] Dr. Sarah Powell: We are not. Yes. Feels a little tiring sometimes, but you're exactly right.
[01:02:46] Anna Stokke: No, not happening. And because there's too much at stake.
[01:02:50] Dr. Sarah Powell: Too much at stake.
[01:02:51] Anna Stokke: So, no, we're not. And you should be really proud of your work. I absolutely am so grateful all the time for the work that you and others in your group have done. So be proud of it.
[01:03:02] Dr. Sarah Powell: Oh, thanks. It's gotten the conversations going and it's fun to see there's a Facebook group about the science of math that has well over 35,000 people and just the daily conversations that are going on there about what's the evidence for this or what's the evidence for that. And it's just so cool to see that hive mind come and talk about research and evidence.
And they're not really paying much attention to this statement here. It's more, I've got this student who's experiencing difficulty with this. What do I need to do?
What are some of the things I should consider as we choose instructional materials for our state or district? It's taken on a life of its own, which is what it needed to do. And it's really exciting to see so many people talking about evidence-based practices in math and what that means for improvement of, I would say, quantitative student math outcomes.
[01:03:58] Anna Stokke: Well, thank you so much for coming on. And it's been a pleasure to talk to you and we'll get this out there.
[01:04:03] Dr. Sarah Powell: All right. So nice to talk to you again. And I hope you have a wonderful day.
[01:04:08] Anna Stokke: You too. Take care.