Ep 30. Math fluency matters with Brian Poncy

This transcript was created with speech-to-text software. It was reviewed before posting but may contain errors. Credit to Jazmin Boisclair.

You can listen to the episode here: Chalk & Talk Podcast.

[00:00:00] Anna Stokke: Welcome to Chalk and Talk, a podcast about education and math. I'm Anna Stokke, a math professor, and your host.

You are listening to episode 30 of Chalk and Talk. This is the second of a two-part series featuring Dr. Brian Poncy, a professor of school psychology at Oklahoma State University who specializes in math interventions. In the last episode, we talked about how improving basic fact fluency can improve outcomes across the curriculum.

We also discussed the instructional hierarchy. Keep that in mind as you listen. For example, in this episode, we talk about the importance of using assessment to determine when to transition from accuracy to fluency building within the instructional hierarchy. We begin this episode by discussing five compelling reasons that fluency is crucial. Brian shares his research on dosage, which addresses the frequency and duration of practice for math skills.

I ask Brian to define conceptual understanding, and we examine its relationship with procedural skill. We also discuss explicit timing and address concerns that it may cause anxiety, the necessity of data-driven decision-making, and more.

A key takeaway from these two episodes is that achieving fluency with basic facts requires daily practice. Not once a week, not every other day, but every school day. We cover the specifics in this episode. As Brian emphasizes with basic fact fluency, you will see significant effects with minimal investment in instructional time.

Just a reminder that the resource page for these two episodes contains links to articles mentioned in the episodes, and I've also put a link to the math program Brian co-designed called the MIND. As I mentioned at the beginning of the last episode, I had a blast recording these two episodes, and I was really inspired by Brian's passion.

I hope you like the episode. Now, without further ado, let's get started.

Welcome back, Brian. So, in the last episode, we discussed fluency. So, for the listeners, recall that fluency is a rate. It's a combination of both accuracy and being able to do things quickly. Can you discuss some reasons why fluency is important?

[00:02:42] Brian Poncy: Sure. So, all the talk and all the rage now is cognitive load theory, and so people are like, “Kids need to be fluent so it opens up their working memory,” and that's exactly right. That's one of the reasons. I think there's five big reasons. The first one is practice makes perfect.

Opportunities to respond (OTR) is the straw that stirs the drink, like if you do an explicit timing intervention and you have a kid that's at 25 digits correct per minute and 10, and you have them practice for four minutes, one kid practiced 40 times another kid practiced 100 times. Well, who do you think is going to get better faster, right?

So the faster you can do your basic facts, it's going to increase your rate of responding. So going back to my comment about Dr. Skinner and learning rate and Dr. Snow and her focus on time, you know, what we want to do is have children learn as efficiently as possible.

And so we do that by high rates of responding. So you'll get a lot like I don't care how fast they do things as long as they're right. That's not good thinking, right? Now, they have to be right. I'm not saying do it fast incorrectly. Nobody's ever said that that I know of on the history of the planet, but, you know, that gets thrown out there sometimes. We don't teach and stop teaching an accurate responding, we build fluent responding. One of the reasons is it increases, you know, rates of practice.

And again, from a conceptual understanding point, that allows kids to practice more problems per minute, they could go ahead and juxtapose and look, and if they're using a procedure, they can see, “Oh, this is how this procedure works on this and that and this.” Or if they knew both addition and subtraction, they could say, like, “Oh, this is how this works for addition.”

You could just go boom, boom and look at them and make the connection as compared to another kid that's getting a piece of paper, picking up a pencil, drawing arrays and doing all this stuff. Are they really keeping that stuff swirling in their working memory or, you know, kind of juxtaposing back and forth as the cognitives would say, you know, to kind of build those connections. And so that's the first thing. The faster kids are, the more problems they do for a minute.

[00:04:56] Anna Stokke: This kind of reminds me of something because math is really cumulative, so when you're trying to solve a problem, and say it's an algebra problem. That's usually what I use as my example. So you're trying to solve an algebra problem and now you've got to do some fraction arithmetic within that problem.

If you're really slow at fraction arithmetic and you've got to think about, you know, why I need a common denominator or whatever, that's going to make you more slow at doing that problem. So what you're saying is the more fluent that the students are with these sort of more basic skills, the more problems they can practice when it comes to something that uses that basic skill, which makes them better.

[00:05:41] Brian Poncy: Yes, and it isolates, right? It isolates the procedure because they're not using a procedure to figure out the prerequisite skill.

[00:05:50] Anna Stokke: Exactly. This is an excellent point, and I have seen this a lot. You give students homework to work on for what you've taught them, and then some students can just do so many problems because they're really set up like they're in a position to be able to do those problems because of prerequisite knowledge, where you might have another student who only gets through two or three problems.

And so what's happening is that student isn't getting enough practice on that skill that you're trying to get them good at.

[00:06:20] Brian Poncy: That's right, and I don't know how much, you know, textbooks have changed since I was in school, but guess what? The hardest problems are at the end. And those would be your most complex problems, and so if I'm a kid that's just getting through the most basics, I don't get the very depth that, again, the kind of reformists are pushing for.

And I want everybody to realize, like, I agree with them. That's where we all want to go. We all want to be at the top, but you can't start at the top to get to the top. can I use an analogy with reading? People understand reading, I think intuitively get reading a little better.

But if we think about reading fluency, in high school, kids that were in special education for learning disabilities and reading would generally read about 100 to 120 words per minute. And kids, typically, I think kids would read probably around about double that.

Whole language people would be like, “I just wish people loved reading, and they would pick up books,” and, you know, all this kind of fluffy stuff. And it's like, you take a book like Harry Potter or something like that, and, you know, it's, hundreds of thousands of words, and you think about a child that at half the rate, they read half the material per minute as the other.

That's half the plot turns, half the information, half the laughs if it's a comedy, half the drama, which leads me to my next point. Fluent responding is also all about rates of reinforcement. And the other thing is the higher our skill level is, the easier the task is. We're more likely to start, engage, and persevere, and finish a task that is highly reinforcing.

When we complete things, it's reinforcing. Like, I'm sure your listeners do to-do lists and they write things they already have done. So they cross it off or they really will break things down because it's reinforcing to complete things. So completing a page, completing a line of problems, reading a paragraph. These things are reinforcing to kids. And so, the faster you are, the higher the rates of the reinforcement.

My colleague, Dr. Duhon, just published something in 2024 where they looked at kids at 30 digits correct per minute and up versus 30 and down. And they looked at the explicit timing, all the kids were accurate, and they looked at rates of on-task behaviour. And the on-task behaviour for the kids above 30 digits correct per minute was like an average of 97%.

If they were below 30 digits correct per minute, it was around 60%. So, fluency is important because it increases your rates of practice. Increases your rates of reinforcement, people want to talk about intrinsic motivation. I don't know what that is exactly, but when I asked teachers what they think it is, it's like, “I want kids to choose to do things.”

So, student choice; we can measure student choice. If kids you know, have fluency in the subskills are more likely to choose to do things. My mentor, Dr. Skinner, he did studies where he would intersperse easy problems with harder math problems. And basically, behaviourally disordered students would go ahead and choose to engage in longer assignments that had the easy problems interspersed.

Why? Because it increased rates of reinforcement in the task.

[00:09:43] Anna Stokke: Success breeds motivation is kind of what you're saying, right?

[00:09:47] Brian Poncy: Yeah. Well, exactly. There's something called, if people really want to nerd out, it's called Herrnstein's matching law, and it's a behavioural thing, any behaviour that somebody can engage in has competing schedules or reinforcement, and we're going to choose to engage in the task that has the least amount of effort with the most reinforcement.

[00:10:07] Anna Stokke: Oh, don't I know it. So, so far we've got two reasons why fluency is important. The first is opportunities to respond. So the more fluent you are, the more problems you can do, so the more practice you get, which makes you better at math. The second thing is fluency increases rates of reinforcement. So, the more fluent you are, the less effort it takes to do the math problem, so you'll enjoy it more, and you'll be more likely to stick with it or want to do the problems.

[00:10:42] Brian Poncy: So then that leads us to the third thing, which is cognitive load. And we've talked about that already and it's so vital to isolate things so that kids can kind of focus on the pertinent instructional variable at that time. And again, the NCTMers and the reformists, they want to see kids do multi-component complex problems.

The way you're going to do that is for kids to have ample prerequisite skills so they can focus on the salient variables to make them, what they would call reason or understand. You know, they can verbally describe why these connections exist, or they could explain what they did, why they did it, et cetera.

I won't go over that because you've had much more qualified people to talk about cognitive load on your podcast than me. So, by all means, go back and listen to those brilliant researchers.

The fourth thing is skill maintenance. If you get kids up to a certain digit correct per minute, you know, they will go ahead and maintain the skill. Now, if you do just blocked practice, right, you'll see a little bit of decay. But what people don't talk about, even with the decay from blocked, if you just test them a minute, a minute, a minute, they relearn it right away.

So if I run a study and in two weeks later, you know, I test them and the kid, let's say drops 25%, the alarmist will be like that, “See, you memorize stuff, you know, you lose it.” And it's like, yeah, but if you just test them again the next day and again the next day, they're going to go right back to where they were. And again, think back to what the cognitive people say. You know, you got to do things every day, you’ve got to try things, but it's there.

They just kind of have to relearn it. So, skill fluency is also important it's going to increase the probability that people are going to maintain not only facts, but procedures.

[00:12:35] Anna Stokke: Okay, got it. So, the third thing is that fluency reduces cognitive load. And the fourth thing is really knowledge maintenance. So, as you said, fluency increases the probability that you're going to maintain facts and procedures which will help you solve problems.

[00:12:54] Brian Poncy: And the fifth and most important one and the one that probably has the least amount of research because it's hard to research, basically high levels of prior knowledge increases the speed with which you will learn new related skills.

And so this is what a behaviourist would refer to as skill generalization. For example, the research that they've kind of been doing lately that caught my eye was they looked at, so, high element interactivity, which would be kind of a complex skill, and they basically said, do we want to use explicit approaches or implicit approaches?

And what they found was, you know, if a child doesn't, is low in prerequisites, you have to be explicit, but if a child has a lot of skills, inquiry-based approaches work pretty well. And so that's interesting to me, right? Because, you know, it's in NCTM pushes for inquiry.

And again, we need to stay out of these dichotomous arguments. Like, this is always good, this is always – when is it good? When's it not good? How can we assess kids as teachers so we know, when this is going to work and when it's not going to work? So problem-based approaches are really effective when you're having a child adapt a skill, not when you're learning how to accurately respond not when you're building fluency.

Even generalization, you're probably going to want a program, but, you know, eventually, you know, I keep talking about fading antecedent, and in consequent procedures, at the end of that is now the kid just sits there and they use what they know in novel situations. And that is the end, that is the end. We don't start at the end, but we want to end there, right?

So, the study that we've done that we're going to hopefully submit here in the fall was done by a colleague of mine named Greg Schutte. And this was one of the best studies, you know, I've been a part of. And what he did was he trained kids up to 40 digits correct per minute, in addition.

And why we did that, we probed or measured subtraction skills, and what we wanted to see is if we get kids really fluent in addition, will that generalize the subtraction? What do you think the answer was?

No. Because again, you haven't taught a procedure yet, and again, this is the funny thing, I talked about declarative and procedural, you know, as components of the instructional hierarchy. To me generalization occurs when you combine declarative with procedural. Now, what people see a lot of times is kids magically generalize, but if you actually assess them, they would have already had the procedure. They didn't have the fact.

And then you put the fact, and then all of a sudden, boom, like, and it looks like magic. It looks like the aha moment that people chase all the time. It's like, no, no, no, no. If we really measure this systematically, there's something that explains this. And so the kids got better on addition fluency. It didn't generalize.

So then we went ahead and we taught fact families and we showed how addition and subtraction were related. Didn't generalize. Then we went ahead and we had them practice closed procedures. And a closed procedure is like blank plus six is thirteen. So, the kid would have to be like right in a seven instead of the answer. Okay, so then we put that in, and so when we basically taught part-part-whole relationships, used fact families, in close, you know, with the conceptual lesson, we saw generalization.

Okay, but not a lot, just a little bit. What was fascinating is we went ahead and we took all the kids above 40 digits correct and we put them in a group. And then we took all the kids below 40, put them in a group, and we looked at their data. The kids below 40 digits correct per minute did not generalize at all.

The kids above 40 digits correct per minute basically went from about eight digits correct per minute to 25 digits correct per minute in subtraction without ever practicing a subtraction problem.

[00:17:10] Anna Stokke: Interesting.

[00:17:13] Brian Poncy: Well, think about subtraction is the hardest skill to teach. It is the one that kids are the lowest in, like, you know, in grades. But to think that we literally tripled a kid's fluency without teaching subtraction. But we taught them, right, an add-up procedure. That's what we did. We taught them fact families. And then we taught them, you know, part-part-whole concept. And then we practiced the close, but we taught them to add up.

Because they sat there and they were fluent with, “Oh, yeah, blank plus nine is 15. Oh, six.” And so it was like, well, just look up. You know, when you look at the subtraction problem, what plus six is 15? 15 minus six, right? And so, boom. But the kids had to be above 40 digits correct. And so, we were like, “Well, that's interesting.” But you know, as scientists, we can find anything one time. And so he replicated it with multiplication and division, found the exact same thing.

[00:18:12] Anna Stokke: Nice.

[00:18:14] Brian Poncy: And again, I'm not saying 40 is definitive. Although, if you look at Dr. VanDerHeyden's work and like people are starting to coalesce around that 40 precision teaching aims, they want kids at 50 to 70, not digits, problems per minute. They're really on the wild end of how automatic kids need to be, but I think probably a threshold is around that 40 digits correct per minute.

[00:18:38] Anna Stokke: And just to close that off, the fifth reason fluency is important is that it leads to skill generalization. So, the more fluent you are with a skill, the easier it will be to learn a related skill. So, that makes a lot of sense, and that's really helpful. So, those are five really good reasons that fluency is important.

[00:19:03] Brian Poncy: And I have research. I'm in the process of writing a paper where, you know, I'm putting the literature to all of these five things. You take any one of those five things like cognitive load, and I mean, that's pretty compelling evidence for why kids need to be fluent with their facts. You take all five of these things together? Come on now.

I mean, we just need to quit with the doesn't matter if they have them memorized. You're hurting kids. And again, I mean, the proof's in the pudding, right? So you take the two-a-day study, you know, look at it, you know, you take Schutte’s stuff, boom. And so, and again, Science of Math, it's like people want to trivialize it because it's been politicized.

I'm not a part of that group, I'm not an affiliate. I'm just a guy that does Science in Math, and these are the questions that go through my mind. And this is the kind of stuff that the movement was made for. That, hopefully, we can push our practices forward and people like me can make things like the MIND.

So I haven't even got into you know, some of the other things that dictate you know, what kids need, especially disabled kids need in order to actually obtain and see the growth you know, that every child deserves to make.

[00:20:16] Anna Stokke: Let's have a bit of a conversation about conceptual understanding, which you brought up a couple of times. And so, do you have a definition for conceptual understanding?

[00:20:27] Brian Poncy: Yes. I've written one, and not that anyone cares, but I figure, heck if people can start talking about conceptual understanding in terms of deep and shallow, why can't I have a have a crack at it?

So my definition is conceptual understanding is demonstrated when students have the necessary declarative facts needed to solve the problem, can accurately and explicitly state the procedures needed to complete the problem, can explain when, how, and why to implement each step required to solve the problem.

That's my definition because every single thing I talked about is an observable behaviour. You know, it's not some mentalistic concept that can never be observed. And think about, if you ask the teacher, like, how do you know if a child has conceptual understanding, what would they say? Well, I talk to them, and again, this is when we get into rubrics and different things. I mean, it is a hard thing to quantify.

And if you can't quantify, you can't measure it. If you can't measure it, you don't know whether children have it or not. And you can't determine whether interventions are resulting in your desired learning effect.

And so the fact that we don't have really good, simple, reliable, and valid measures for things like conceptual understanding and strategic reasoning, or whatever they call it, should really be alarming to everybody because you cannot do science on things you cannot observe.

[00:21:57] Anna Stokke: That's my biggest problem with the phrase conceptual understanding. It is not clear what it means, and I think, generally, some of the things I've seen, people seem to think it means that you can describe something with pictures, or that you can do something in several different ways, and it's just not really clear what this means.

What was the first part of your definition?

[00:22:23] Brian Poncy: Conceptual understanding is demonstrated when students have the necessary declarative facts.

[00:22:28] Anna Stokke: So I think some people would take issue with that part of your definition.

[00:22:32] Brian Poncy: They're wrong because you cannot think about something you do not have. If you've never seen it before, and you don't know what it is, and you don't have base knowledge, remember, if a concept is about connecting, you have to have a fact or a procedure to connect it to, all right?

And you can't really do a procedure without a fact, and when I try to explain this to people, because I've had people I work with and teachers, you know, they just look at me like I'm an idiot. They'll be like, “You always teach the concept first.” I'm like, really? Three-year-old was in their high chair and they were counting Cheerios, you wanted to talk to them about a concept before just, you know, rotely going “One, two, three, one, two, three.”

I remember teaching my daughters, I would get them out of the tub and we would jump on the bed and we would just go “One, two, three, four, five.” And that was just a verbal chain, that was rote. They didn't know what it meant. You know, if I would have told them about quantity or something like that, it would be the dumbest thing on earth. I mean, literally from a pure learning perspective, teaching a concept, if they don't have a declarative fact, which would be in this case a verbal chain, is absolutely idiotic.

So, you had to teach declarative fact, which was the verbal chain. Then you had to teach one-to-one correspondence, which would be the procedure. Now once they have that, now maybe I could teach them to identify numbers. And they don't know what that means. Those are squiggly lines, right? But that's a one, that's a two, that's a three.

And now I can put arrays next to them, and we can talk about what that means. Now we're starting to define what each number means, and we can talk about more and less, we're building so much declarative knowledge, vocabulary number identification. And now we start to move that over to a number line.

If they don't have verbal chains, they can't identify numbers, they don't have one-to-one correspondence, then using a number line is useless. If you're a second-grade teacher, kids come in with all sorts of prior knowledge. So what they do is they teach the concept first to activate prior knowledge, and that makes perfect sense. But don't conflate that with how human beings learn.

Human beings have to have the declarative fact first. So when you use the concept to activate prior knowledge and you got the bottom 30 percent of the kids that don't have that prior knowledge to activate, guess who's screwed with that lesson? Those kids. I don't know how you could argue it. Letters, you're going to teach the kid the letter? Or you're going to start talking to them about, “Well, in the English language, there's something called letters and they represent sounds and we put those together that spell words that represent things we talk about.”

Come on now, you would just teach the letter, and then you would teach the letter sound, and then you would teach the blending procedure, and so on, and so forth. And again, why in colleges of Ed, they're not teaching good sound learning theory like this I have no idea.

[00:25:31] Anna Stokke: So from your point of view, the definition has to involve a behaviour that you can observe, right? That's the idea behind your definition. So, at what point do you think conceptual understanding comes into things then? Are you sort of the position that fluency building comes first and then conceptual understanding comes after that?

[00:25:55] Brian Poncy: Not necessarily. So, for example, as long as you can accurately do the declarative fact, even if it's slow, and you can accurately but slowly do the procedure using a number line, let's say you're a slow counter or whatever, you can still teach concepts of more or less or, you know, whatever with those.

Fluency helps, but you don't necessarily have to have it. And remember what teachers want to do a lot of times, and this makes sense, you know, they want, they need to teach as many kids as possible. So if I can ensure they can count and identify numbers and I give them a number line, now all of a sudden, they can accurately respond to every addition problem sums to 10.

Then that's what I would tell them to do. I would never say, “Okay, just have them memorize three plus five.” I would never have them do that before. You know, they basically were counting and pairing arrays with numbers. And if you look at the mind, it's all in there. But once a child can, you know, say, “This is a two, this is what it means, this is how I use it, these are how I combine it, here's my vocabulary, I can explain it,” now let's go and let's build fluency and let's automatize this so that we can build.

When do you wait to teach a concept? It's like, well, in kindergarten, if a child can do all the things I just said, you can teach fact family sums to five. And you could talk about reciprocals at that point. And you could say, well, two plus three equals three plus two. And you could be very explicit and show them. Then you could teach them sums to 10. And now you could ask them “You know, four plus three is seven. Do you know any other problems because of that?”

Now you're still cueing the child, but you know, now the child has to kind of come up with it with this commutative property, right? And so then they can do that with sums to 10. Then when you teach sums to 18, now you're going to want to see generalization, right?

You shouldn't have to tell them because you've already practiced doing that. When I talked to my teacher educator friends, they're just like, “Oh, I just hate what you do because there's no aha moment.” And I'm like, "It's not an aha moment to you." But I said, "It's an aha moment to them."

You're like, “Yeah,” I bet you don't know another problem to, you know, how you can use that problem to get the same answer. And then the kids like, “I'll show you, it's four plus three,” or, you know, they say the opposite. And then by the time they learn seven plus five for the first time, now they know, “I know seven plus five, well, I know that five plus seven is another one.” And then you see that generalization.

[00:28:35] Anna Stokke: I understand that you've done a lot of research on dosage. So, in other words, you've studied how much practice students need and how frequently they need practice to develop automaticity with math facts. So, can you tell us about, that a bit? Is there a sweet spot?

[00:28:55] Brian Poncy: Yes, and so dose is a really important concept that's rarely talked about in the literature. The big move in the past, I'd say 25 years, has been empirically validated interventions. And that makes sense, right? But if you want to build up her body strength, pushups is an empirically validated intervention to do that.

But if I only do one pushup a day, It's not going to build upper body strength. It's just insufficient. Same thing if I take ibuprofen and I just have a pile of ibuprofen dust in front of me, and they're like, well, ibuprofen will help pain. And I take a pinch, and it's 20 milligrams, it's not going to matter.

And the same thing with the ibuprofen, if I take over 800, right, it's probably not going to confer any additional benefit. And so when we do interventions, there should be what we refer to as a therapeutic range. And so there's a minimal amount of dose that kids need in order to learn. But then you begin to get diminishing returns, and we're wasting our instructional time after that.

And think about it. If we were scientists and we made education like medicine, which I know will trigger people, we could predict this kind of stuff. And with facts, we can do that. Like, that's what we're doing right now. Gary Duhon, a partner, we've conducted dose research across pretty much all the major fact-building interventions. We haven't done it with flashcards. I talked about the instructional hierarchy and how these align, but there's really four classes of interventions.

You got flashcard drill, you got cover, copy, compare, you got paste problems or taped problems, and then you have explicit timing, and so we basically looked at all of those. And what we've done is we've had kids do two minutes once a week, two minutes twice a week, two minutes every day, twice a day, four times a day, eight times a day, 12 times a day, 16 times a day, just trying to find, you know, what this kind of curve looks like.

And anyway, what we have found across interventions is that, you know, we talked about learning rate. Because remember effect and rate are different things. You'll learn more if you do it longer, but you may learn more efficiently doing less. And what we find every time is that one to two minutes a day will give you the most bang for your buck. So the first time you practice a set of items you're going to learn the most.

The second time you do it, you're still going to learn, but not quite as much. When we think about like the Facts on Fire. The reason we did this at four minutes a day is because if you do it every day from the day they set foot in school, you're going to get the most bang for your buck.

Now, if I get a child and I have to remediate in order to get more growth, I'm going to have to probably do things longer. I'm going to sacrifice a little bit of the rate, but I'm going to get the effect. Does that make sense?

[00:32:00] Anna Stokke: Yes, two minutes a day, but it has to be every day. That's likely just the right amount for most students. But if you have to remediate, you likely want to do more than two minutes.

[00:32:12] Brian Poncy: And so, it's interesting on a lot of levels. So one of the levels is if you don't do it every day, this suggests you're wasting your time. And so if you're one of those people, it's like, well, “I'm going to do facts on Friday. So we're going to have Friday fact day.” You might as well do nothing, it's probably wasting time, and if you do every other day, we've shown small effects with that, but not statistically significantly different from control.

We don't find the statistical difference from control until you do it at least every day. And so what's that say? It's like, well, if you want to build facts, you need to do it daily, and you don't need to do it for very long. The third thing that we've played around with is set size and set size to me is the Holy Grail of fact practice because, for example, people will say use flashcards with your kids.

But if a parent goes home and doesn't know any better, and they have their math fact flashcards, and they go through all hundred addition flashcards, it's going to take them a long time, and the child's going to get one repetition, and they just wasted that instructional time. Now, if I take 10 items, and instead of doing 100 items with one repetition, I do 10 items with 10 repetitions, the child's going to learn those 10 problems better.

So what we find is if I'm working with a child with intellectual disability, if I have 100 repetitions, I may do five problems with 25 repetitions. That's a bit extreme, but you get my point. Kids generally will respond pretty good to set sizes around 12.

If a child doesn't, you have two options, three options actually. You could reinforce them because sometimes they're just not engaged, and so reinforcement, you get more meaningful practice. And then the second thing is you could increase the dose. Taped problems, we have it set up to where with 12 items, you pace them at five seconds, so you're basically doing 12 problems every minute.

And so, we did basically one versus four versus eight in the OTR. Match the time. Okay, so for every minute we're doing a repetition. But if you think about it like, you could sit there and if a child was a non-responder. Think back to when I was talking about Harlan, and I'm working with Susie, and even though the group research says this, it doesn't mean anything for Susie.

I need to go ahead and assess Susie and work with her, and determine what works best for her. And so I go ahead and I use time series design and, you know, and she doesn't respond to, we'll say four repetitions. And so I can go ahead and do eight repetitions. And oftentimes, I've found that more than not, we'll find it to work, Duhon did an intensity study way back in 2009, where he did two minutes with students with explicit timing for a class, and three kids didn't respond. So, with all three of those kids, then he did five two-minute timings, two of them responded, one didn't. Then he did ten two minutes, and then that child responded.

So the intervention was correct for all the kids because of course, we assessed them beforehand and we placed them in the right instructional level material. So it literally was matter of finding. you know, what dose worked for that child. So with our dose research, what we're trying to find is that kind of group sweet spot.

And if we have that group sweet spot, teachers will know where to begin. The skill remediation of the mind, like Facts on Fire, they just practice all the facts. The remediation starts to break the facts into sets of 12. So if a kid's not responding to the Tier I, now you'll go in and you'll supplement that with the Tier II, they'll get additional time, they'll get a smaller set, and, you know, we should begin to see that student’s response to intervention.

[00:36:05] Anna Stokke: When you talk about two minutes a day, are you mixing skills or is this two minutes on a specific skill?

[00:36:13] Brian Poncy: No. And I would worry about mixing skills, right? Because in essence, what you're doing is you're doubling the set size and you're running learning interference. So, when we think about interleaved practice, it's after you have things mastered. So, when you're building fluency, you do not want to mix skills.

And this is a real problem with Facts on Fire because you may have some listeners and they're like, “Man, we want that kid to get that in our school.” Well, then what happens is they're like, “Well, we're teaching multiplication here in third grade. And these kids are all on addition, what do we do?”

And the answer is, well, you have a systems problem. You need to start back at first grade, and you need to roll it out. And in the meantime, I would say, practice multiplication if you're teaching multiplication because again, there's interference, it's doubling the set, and so, again, it gets difficult to you know, to kind of incorporate and roll this out.

[00:37:09] Anna Stokke: Just to clarify something, with the Facts on Fire, the school that you worked with you were doing four minutes a day. And then you mentioned, though, that your research shows that on a specific skill, the most efficient is actually one to two minutes a day.

Why were you doing four minutes a day?

[00:37:29] Brian Poncy: Well, we didn't have the research then. We’re from the special ed part of the world, and RCTs (randomized controlled trials) are great for the averages, but we have tails too. And so, we would rather err a little bit extra because some kids need the extra repetition, and we want to ensure that 80 percent of our kids respond to Tier I intervention.

And so even knowing what I know today, I would still do four minutes. Probably what I would tell them to do if I had my druthers, Iwould say, do four minutes in the morning and four minutes in the evening. Greg Schutte, that guy I talked about that did the generalization research, he also did some distributed practice research. And he had four groups and one group, they did a four-minute timing.

Another group was two two-minute timings and another group was four one-minute timings through the day. And so they all got the same amount of time. And what he found is when you got away from the block, and you distributed the practice, you got about 25 percent more learning with the same amount of instructional time.

Now, obviously, it's more for teachers, right? Because they got to pass things out and take them in. And so that was kind of what we were looking at, is the bang for the buck there? To me it’s fascinating stuff. I've devoted my life and my research career to how to teach math facts.

[00:38:51] Anna Stokke: Yeah, it turns out it's actually not that simple when you think about set size, dosage, and maximizing instructional time.

[00:38:58] Brian Poncy: And here's something that will blow your mind. Duhon and I did a study because if you want to do good fact practice, you need to do goal setting, you need to do explicit timing and you need to provide performance feedback. And so, we went ahead and we did explicit timing with goal setting and reward.

And what that looked like is it was two minutes a day, and we looked at how many problems they got right with two minutes. This was subtraction. We would score them at the end of each day and the next day we would say, “You scored, we'll just say 21 digits correct per minute. If you go ahead and beat your score today, tomorrow when we give you your score, you'll get to choose from the prize box,” or whatever, right?

Or at the end of the day or whatever it was. We had three groups. We had a control group and then two groups that got exactly what we just said, and this was a computer program. And here's the fascinating part. The only thing that discriminated the two groups that got goal setting with reward was every time, every single problem, it went, “Bing!” and a green check mark came up.

Every single problem. And then the other one, they just did it, went to the next problem. The other one, it was “Ding!”, if they did it right. The “ding” doubled their growth. Us old behaviourists, we got some settled science that works pretty well. But if you think about it, right, the kids didn't get the feedback on their performance till the next day. You want to give feedback immediately, that took a fraction of a second as far as, when we talk about instructional time.

And so again, and this is why you have to do learning rate. You do learning per instructional minute. Like cover, copy, compare, for example, the kid writes it, boom, gets feedback on whether they were right or not. If they work at doing worksheets at their desk, they hand it in, the teacher scores it, they get it the next day.

I mean, it's just not very good instruction, right? And so the instructional quality of some of these interventions is really a big deal, but literally, it's drill and practice with reinforcement. Goal setting is good. And with a lot of the students we work with that are struggling, for the first time in their life, we assess them, we get them right in the sweet spot of instructional material, we control the set size to have a high probability of success, the child does better.

They grab it and we begin to have conversations. Why do you think you got better? Because at first, they totally like attribute their success not to themselves. They see themselves as stupid. They see themselves in a lot of different ways. But you can literally, as a teacher, begin to cultivate. People want to call it growth mindset - it's like, no, graph. And let's have conversations about effort and behaviour and outcomes.

And if you don't time your practice, you cannot have standardized outcomes to communicate with the children about.

[00:41:50] Anna Stokke: I'm just going to really stress this, that you can get the MIND, you can grab it for free, you can use it, but no matter what, let's try to aim for basic facts for four minutes a day. It's got to be every day. It can't be every other day. It's important, it's like how we're supposed to exercise, you know, you should do it consistently, daily. Same with basic facts in the classroom. Four minutes a day, every day.

[00:42:18] Brian Poncy: That's right, and again, it is a Tier I thing. Everybody needs to do it. And the other thing is, you have to assess and you have to place people correctly.

[00:42:29] Anna Stokke: You've mentioned explicit timing a few times. Can you say a bit about explicit timing or timed practice? Can you also say something about the idea that timing causes math anxiety?

[00:42:43] Brian Poncy: I have a study done with Fontenelle and we did a skill-by-treatment interaction. So we looked, we compared explicit timing with taped problems. And what we found was that if a child was below 10 digits correct per minute, explicit timing did not work.

It was the same as control. And so if you're putting kids that are below 10 digits correct per minute in explicit timing, it's probably not going to work. Now, taped problems did work. And then if it was above, tape problems and explicit timing both worked. But again, I mean, there is so much science to this and timed tests, I call it timed practice because we time tests to do things like screen and, you know, so forth.

But timed practice really gets a bad rap. I don't want to look down or belittle people that have had negative experiences, but realize that timing isn't the cause. And when I say that, like, nobody's born afraid of a stopwatch, I mean, it's like people are put and timed inappropriately, and they're punished. And it doesn't mean that the teacher yells at them; a child knows when they can't do things very well. When we do have kids do round-robin reading and a poor kid has trouble, it's a very public display.

And the same thing is if you have a kid and they're on an island doing a timed test and you have them in a skill that's too difficult, then it's real. And it's frustrating. But that's not a timing issue, that's a placement issue. And the other thing I'll say about that is antecedent timing procedures can come in a lot of different ways.

Deadlines at work, for example, how many people work best with a deadline? Almost all of us, right? Our rate of responding increases as we get to that deadline. That's an antecedent timing procedure. And when we sit there and we're like, “You don't want to cause anxiety because of timing kids.”

Well, you better get used to it because it's coming. And the other thing is, you know, anxiety is likely conditioned from negative experiences, like I just said, and if somebody has had that experience, the gold standard for treatment of anxiety is exposure therapy. But what you have to do is have very low-pressure situations.

Like, for example, if I time a kid with cover, copy, compare, the problem and answer is right there. Do you get my point? Like, it's not a difficult thing. And you could begin to reinforce the kid, they will forget about the timing. Because you know, they're going to get used to this format, and you're just practicing, and you're doing it every day, and then you move to explicit timing, and you got a small set, and so now you're timing, and the kid's self-graphing, and now the child's getting better, and now the timing becomes reinforcing.

You know, Robin Codding, again, brilliant researcher, I think her latest study showed that kids like to know if - they like being timed. It was the not timing. It was the unknown that freaked them out. If you have a consistent intervention that they do each day, and so people really misunderstand the timing piece.

[00:45:53] Anna Stokke: Okay, so you're saying that it's important to time, but it has to be used appropriately. So in other words, you need to assess where students are at before determining whether or not to time. This matches with something Robin Codding said when I interviewed her, that her research showed that it's best to start engaging in timed activities when the student is around 90 percent accurate.

So again, the assessment piece is really important for determining when to move from accuracy to fluency building on the instructional hierarchy.

[00:46:29] Brian Poncy: It's not all good or all bad. We need to use the science to know when to use things the right way, okay? And so there's a time to time. There's a time not the time, right? There's a time to use inquiry. There's a time to use explicit. And the thing that ties everything together, and this is why behaviourism is so vitally important to all of this, you have to assess it.

If you can't assess and know prior knowledge, you don't know where to start, you don't know where to place, and you can't measure whether they got better because remember cognitive load theory, they put out like a formula, prior knowledge is at the bottom. So, if you don't sit there and assess observable measurable terms that all this falls apart. It's why you know, I'm against these kind of fuzzy terms like reasoning and conceptual understanding because if you can't measure it, you can't guide instruction.

But think about the whole push and pull, right? They're just like, “This isn't medicine. Don't make us medicine.” Maybe that's why we've stagnated as a profession for a lot of years because it's difficult when we have to start doing the stuff like element interactivity, and we start to have to do complex task analysis to begin to look at the functioning of procedural fluency versus declarative fluency versus conceptual or prior knowledge.

It gets very difficult to isolate variables.

[00:47:54] Anna Stokke: You advocate for collecting more data and making data-based decisions, right?

[00:48:01] Brian Poncy: I'm a school psychologist. And as a behaviourist, even, and I think most psychologists would admit this, the great thing about behaviourism is its proof system. We don't assume anything, but what we do do that's so important for education is we don't know what's going to work or not.

We're going to put in a hypothesis, right? We're going to measure behaviour. We're going to come up with a hypothesis. We're going to test the hypothesis on the individual or group, but we're going to use time series design, so basically measurement each day, and we're going to look at student growth. And the only way we know if we taught correctly is when the child learns. So if a teacher teaches and a kid doesn't learn, did the teacher teach?

[00:48:47] Anna Stokke: Well, they taught, it just maybe wasn't effective.

[00:48:51] Brian Poncy: That's right. With the cognitive people, they'll say learning is a permanent change in long-term memory, and a behaviourist is like, learning is a permanent change in behaviour.

Now that being said, I'm cool with the cognitive people. I can learn something and never tell somebody. But as a teacher, and this is where behaviourism and being pragmatic comes in, as a teacher, the only way I'm going to know if you have learned something if you've committed it to long-term storage, is if you behave.

You have to behave. I have to see it. That's the only thing that gives me the feedback. And behaviour can be pointing, it can be talking, it can be writing. There's a lot of different things kids can do that are verbal, non-verbal, you know, that basically demonstrate the acquisition of a skill. And of course, fluency would be the frequency of pointing, of talking.

People hate the mechanistic approach of it, but the science is wonderful. And so why don't we take some of the more higher inference mentalistic approaches, but always keep that behavioural short-run empiricism, you know, with our students. So they used to say, right, the rat's always right.

That's what behaviourists would say, Skinner would say, right, the rat's always right. And I've always viewed it as the kid's always right. If the child doesn't learn, it's my fault. And so, it's really bothersome to me, as a school psychologist, we do a lot of assessment, and we talk about processing disorders, and all that is, is a scapegoat to blame children for poor teaching. Because again, every child can learn.

It's about rate of learning and rate of forgetting. And we can measure those things. You know, what's interesting in that Duhon study, the kid that had the dose of 10 didn't maintain it. So the child learned it, and then they assessed it. The child didn't maintain. Well, what does that mean? Does that mean that explicit timed practice is horrible? No, it means that that individual child's needs are great.

And we know that even if we get them to fluency, they're going to probably need more and more practice to ensure that they don't forget. And we're never going to know that if we don't objectively measure that child using a rate measure every time.

So, you know, one of the things I was hoping I could get through in this podcast is, you know, all the interventions in the world and all the theory in the world and all this stuff's all fine and dandy and great and help shape practice. At the end of the day, if we're not training teachers to be data people that literally measure and make decisions based off of data, because remember, you only can evaluate data against comparative standards, so it's even more than just collecting the kids data, we have to know how much should kids learn, under what conditions if we're going to make sense of any of this.

Well, how do we do that? Well, we do that through science, just like medicine. Dose, set, very controlled things. And so I know that I'm not going to be popular with the educational crowd on this. But again, you know, if we want to refine practices, we have to bring science into this

[00:52:08] Anna Stokke: Well, I'm going to call you the basic facts guy because you know more about basic facts than anybody. You've got the research to back up your statements. So what are some main points or is there anything that you'd really like to leave teachers or administrators with about how to improve outcomes for students?

[00:52:30] Brian Poncy: Yes. So the most important thing that schools are failing to do, in my opinion, is they need to operationally define a scope and sequence of critical skills. This isn't the hundred standards a teacher has to get through. I'm not talking about that. I'm talking about every grade needs to sit down and say, “What are the three to six big ideas, big skills that just have tentacles through everything we're going to do.”

And once they identify those. They need to go to the grade above them and say, “This is what we think are most important. Is this important to you?” And so you got to have vertical alignment on critical skill fluency, and you have to have daily, short, high-intensity practice to build those. That could be letter sounds, that could be math facts, you know, whatever it may be.

But basically, you have to align your district assessments with this critical scope and sequence. And you have to have comparative criteria. So, what do you want these children to know? And because it's a critical skill that has to be mastery. And so, for example, like letter sounds, you probably need one a second, right?

With math facts, you probably need at least 40 digits correct per minute. And I get it, for kindergarten and first and second grade, especially with writing issues, you know, you're going to change those a little bit, but align your district-wide assessment, identify a critical scope and sequence, have students engaged in that on a daily basis.

Make sure all your teachers are on board that this is important and meaningful, and then obviously administration need to build the infrastructure to support that this happens and it needs to be tied to a multi-tiered systems of support. And so, in kindergarten, when kids fall behind, you get on it right then and there.

You're not waiting. This type of approach is to assure all kids have access to the general education curriculum. I'm sick and tired of seeing us implement curricula and pedagogies that help the top half. Everybody deserves to learn. Everybody has a right to learn. And we, as teachers, need to be accountable and responsible to ensure we have the assessments to make sure that all kids are responding effectively to intervention.

And if we begin to see that they're not, then we need to have conversations with the administration about what types of practices we need to do to build those. And so again, none of this happens without good, solid curriculum-based measurement and assessment. And I know it's become sexy lately to spend lots of money on computer programs that are spitting out standard scores.

But I hope that teachers will realize the importance of the curriculum-based stuff. You listen to that child read, you watch them do math facts, you talk to them about it. We need to empower teachers with the database tools so they can have control over, you know, what they're doing in classrooms. And as teachers are probably rolling their eyes at me as we speak, they're saying, “Well, we got to get through This curriculum, that's our job.”

Yes, by doing what I'm saying, you're going to get more kids up to that level to where you can do your job more efficiently. And you won't have the heterogeneity in your populations that make it difficult to do your job. And so, believe me, my heart goes out to teachers. They got the hardest job in the world and God bless them and everything they do for kids, but let's help teachers be effective.

The way to do that is through basic skill fluency, whether that's writing, whether that's reading, whether that's math. And if you don't have it right now in your curriculum, get it in. You will see large effects with very little investment in your instructional time.

Thank you so much for having me on, I appreciate it.

[00:56:31] Anna Stokke: Awesome. So, some powerful statements there and some really great advice. Thank you so much for coming on today and sharing your expertise. I think it's going to be really helpful to a lot of people and to kids too. So thank you so much.

[00:56:49] Brian Poncy: All right, thank you.

[00:56:49] Anna Stokke: As always, we've included a resource page for this episode that has links to articles and books mentioned in the episode.

If you enjoy this podcast, please consider showing your support by leaving a five-star review on Spotify or Apple Podcasts. Chalk and Talk is produced by me, Anna Stokke, transcript and resource page by Jazmin Boisclair, social media images by Nicole Maylem Gutierrez.

Subscribe on your favourite podcast app to get new episodes delivered as they become available. You can follow me on X for notifications or check out my website, annastokke.com, for more information. This podcast received funding through a University of Winnipeg Knowledge Mobilization and Community Impact grant funded through the Anthony Swaity Knowledge Impact Fund.