Ep 44. Mailbag: Building Thinking Classrooms & more
with Zach Groshell
This transcript was created with speech-to-text software. It was reviewed before posting but may contain errors.
You can listen to the episode here: Chalk & Talk Podcast.
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Ep 44. Mailbag: Building Thinking Classrooms & more with Zach Groshell
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Timestamps:
[00:00:00] Introduction
[00:02:44] Listener Question: Differentiating Direct Instruction
[00:05:52] Zach's advice on differentiation
[00:10:10] Listener Question: Building Thinking Classrooms
[00:11:20] Are multiple access points effective?
[00:15:14] Critique of Building Thinking Classrooms
[00:19:03] Does research support using BTC?
[00:20:53] Is everyone doing it wrong?
[00:22:17] Observing BTC in action
[00:23:46] Defining thinking and why mimicking is important
[00:27:30] Permanent vs. non-permanent learning surfaces
[00:29:04] The practicality of mini whiteboards
[00:31:34] Advice from Anna & Zach on whether to use BTC
[00:36:20] Listener question: Number talks and math fact fluency
[00:37:53] Critique of number talks
[00:40:09] Using effective methods for building math fact automaticity
[00:42:19] Advice on mental math strategies
[00:44:18] Using instructional time efficiently
[00:46:21] Conclusion and book description
[00:00:05] 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 Chalk & Talk. I get a lot of emails from listeners with questions, so to help answer them, I've decided to record occasional mailbag episodes. These will be released sporadically in addition to my regular guest interviews, so I'll continue to release my regular episodes typically every three weeks, sometimes every two.
If you have a question, you can email me at chalkandtalkpodcast@gmail.com, and your question might be featured on a future Mailbag episode. For this episode, I invited Dr. Zach Groshell, a previous guest, to help answer some of your questions. We'll be discussing how to implement direct instruction when students are at different levels, Building Thinking Classrooms, and Number Talks.
I hope you find this useful. Now, without further ado, let's get started.
I am here today with Dr. Zach Groshell. He is host of the Progressively Incorrect podcast. He's a teacher, a coach, and an education consultant. He's an expert on Direct Instruction, that's what the capital D and a capital I, and explicit instruction, and he is the author of the book Just Tell Them. I just read that last night, Zach. Awesome book. It's short, it's packed full of great tips for implementing explicit instruction techniques, with cognitive load in mind. So I recommend checking it out, picking up that book. It's a great book.
You can find Zach on X, Blue Sky, and LinkedIn. Now, he's been on my podcast before. You're my first repeat guest. I asked him to come back to help me answer some great questions from our listeners. Welcome back, Zach.
[00:02:05] Zach Groshell: Thanks so much and I'm glad you read it. And you know, of course in a night. It was designed to be, I hope, a short and quick read, a resource you could use. So I'm happy you enjoyed it.
[00:02:15] Anna Stokke: Short, but useful. Okay, so are you ready to help me answer some listener questions?
[00:02:20] Zach Groshell: I'd love to, and this is where your podcast shines. You're bringing in the teacher voice and the practical piece. And I hope I can do that justice.
[00:02:30] Anna Stokke: Thank you, Zach. I wouldn't have asked you if I didn't think you could. So I went through my emails and I picked out some of the most common questions I've received. So I think today's episode is going to be really useful for people. So I'm going to get right into it, and I'm going to start with a question from a listener named Jaime.
And it's a bit long and I'm going to read through it, but it's important that you have the context. So, Jamie says that “two years ago, the entire primary school underwent professional development in math, and we all took a course from YouCubed. I was inspired, invigorated, and absolutely fell in love with teaching ‘mathematical mindsets.’
However, some things just haven't been adding up for me, and now I have been listening to your podcast, I see why. My weak students just didn't improve, for starters, and fluency was often holding them back. Now I know some really strong teaching practices that I can immediately start to implement, but I have some questions about how to best implement direct instruction when your students have a large ability range.
I am not sure what to do in my classroom when about 50% are already fluent with math facts, and the other 50% need to work on not simply multiplication facts, but even number bonds up to 20.
I had kids who needed direct instruction in completely different math standards, which was clearly documented by my pre-unit assessments. It took a lot of time to come up with different problem sets for different students, but I did it.”
So this teacher's working really hard.
“But what I really couldn't figure out was how to differentiate direct instruction. The students are at different levels working on different concepts, but they all needed direct instruction first. Otherwise, there was unproductive struggle. If I leave the strong students to simply try to figure out how to solve a problem, I found they couldn't, they still needed me to guide them. Often my colleagues or admin would tell me to implement low entry, high ceiling tasks. But again, this negates direct instruction and the fact that, for example, some kids needed direct instruction on fraction equivalency using models, and other kids started the unit with the knowledge already, and were eager to learn to multiply and divide with fractions. I often find I'm facing groups of learners who need different math instruction for different math concepts from different grade levels.”
So their students are at all different levels when it comes to prior knowledge and. Honestly, Zach, I'm exhausted just reading this.
So they go on––there's another issue with pace.
“The disparity in the pace at which students access the material is really problematic. I can give all kids in the room the same problem to solve on a mini whiteboard. The challenge I have is that there are some kids who take so long to solve the problem while others do it in three seconds. It creates a classroom where I never know if I'm rushing the weak kids to respond faster if I don't let them solve the problem, or making the stronger kids completely bored because they have to sit and wait for all students to come up with the answer.”
So now onto the question.
“How are teachers supposed to realistically differentiate when students are accessing different math concepts, and are above or below grade level?”
So what do you think, Zach?
[00:05:52] Zach Groshell: I love that question. It touches a nerve with me because the schools that I've worked in, people will say that the RTI pyramid is upside down. You know, they just mean most of the students are below grade level, but not only that, the span, the spread of their levels is just ridiculous.
We're talking about six, seven grade levels by the time they get to middle school, where some kids are in there learning at kindergarten math, and other kids could be starting algebra, right? And they're all in the same classroom. And what do I do? It seems like explicit instruction is incompatible.
The first thing I will say is that people have recognized this for many decades and what they've done is created solutions that schools don't often choose to use. One of those is homogeneous grouping, and that's where students are given a placement test. And then this is the important part that never happens in schools, is that they are then matched with materials that address the, the gaps that were identified in the placement test. One of the programs that does that very well, but only to K through five , is Direct Instruction. The program’s called Connecting Math Concepts. What that does is it creates a very narrow set of abilities or skills or prior knowledge in a classroom. And it allows teachers to teach on level. And when you do that, every choral response you do, every answer is correct. The pacing of the classroom is more or less similar, but between kids and when kids want to go faster, you keep on mastery testing them and you can accelerate them out of the, the level, or you can drop them down a level.
This has been addressed and people don't like it. Maybe it's too complicated. They think they don't want to subvert the whole, the whole system. So we have the other solution. The other solution is we just move kids up by age and we just sort of deal with it. And that's what this person is dealing with.
Something that was a red flag for me in that question was that I have kids solving things on mini whiteboards in which everyone's waiting for them. I wonder about the scaffolding in that situation because if I was going to introduce just a small step to everyone's repertoire, I would take off a lot of the things like for example, number multiplication facts, and I would put that on the board or we would do a do now just before to review those multiplication facts. So when I introduce this, this small step here, I either have a reference for certain kids or we just practiced it. It's fresh in their mind.
“And I'm going to have you do just a little bit on your mini whiteboards. 3, 2, 1. Show me.” I would never use a mini whiteboard for an extended large, complex problem, and I'm waiting for everyone on the carpet. There's five kids who aren't there. That's not how I would do like a kind of a slow motion type problem where I'm slowly introducing these answers.
They should be fast, they should be rapid. But you know, you've got kids that even there, they're doing the multiplication algorithm. They've gotta know all their multiplication facts. There's multiple steps. Doesn't matter what you do, you can't give them the key 'cause now they have to look through the key.
We have to use MTSS better in schools. MTSS is just multi-tiered systems of support. There are certain students that require an extra dosage of math and honestly, we may need to do something that's akin to homogeneous grouping where we have kids walk to math . Schools are often not sophisticated enough to do this.
People that are MTSS leads don't do anything. They don't plan, they don't use spreadsheets. What you need to do is, as a school, start thinking broader. If you can identify those problems, there's a solution to it. There's a para somewhere who's sitting around twiddling their thumbs. What are they doing?
How do we get them the extra dosage of multiplication facts or number bonds? That would be my kind of broad answer there.
[00:09:49] Anna Stokke: Okay. That's super helpful and I'm glad I brought you on to answer that question, so thank you for that.
So let's move on to the next question and this one might take a while. I will say, I get a lot of questions about this particular program, so you know, it's time to discuss it on the podcast.
So this question is from Jennifer. And Jennifer wrote this:
“One of my colleagues has highly recommended Mathematics Tasks for the Thinking Classroom, believing it provides multiple entry points. However, I've heard much about explicit instruction in literacy, and I wonder if a similar approach should be applied to numeracy.
I recently came across an article from Education HQ that questioned the effectiveness of Building Thinking Classrooms, citing a lack of supporting evidence, and mentioning your perspective.”
By your perspective, she means my perspective, and that's true. I was, quoted in that article.
“Given that many of our students still struggle with foundational numeracy skills, I am concerned that the Thinking Classroom may not be the best approach. I would greatly appreciate your thoughts on whether explicit instruction should be prioritized or if both methods can be integrated.”
So Zach, before we unpack this let's talk about multiple access points. So what are multiple access points?
[00:11:20] Zach Groshell: I mean, it's an idea of a design for a type of you know, a type of problem or so on, in which students can come at it with different strategies. So essentially you could have a child who's at the, you know, drawing pictures, or you could have a child who understands this is more of like a repeated addition type of thing.
Or you could have other kids that are actually applying grade level math or advanced math that they learned at Kumon right? You can have everybody taking kind of a low ceiling type of task. And this was mentioned just earlier. I didn't get a, I didn't get to critique it well enough, but this sort of perfect solution to all of our problems that every kid can use, the math that they know, and that this is a form of differentiation.
That’s my answer to that. There's obvious problems with this, but anyway.
[00:12:09] Anna Stokke: So the multiple access point is, is this an idea for dealing with this differentiation problem where you have students that are at all different levels in the class?
[00:12:20] Zach Groshell: I think in one and on one level it is on the other. It's sort of just like an empathy piece, a misguided empathy thing. What it ultimately does is it doesn't hold us accountable to bringing kids up to grade level.
It says whatever your prior knowledge is, that it's sort of a postmodern, modernist, maybe idea that everybody has a different way, a different way of thinking. And so we don't need to hold ourselves to account to teaching them the most efficient way. What happens? You can already imagine.
You got the kids who come into this multi multiple access point type of open-ended thing. And they know the grade level math great. They get to practice it, they get to play with it. They get to perhaps build on, build blocks on their own. Then you get kids who are doing very unsophisticated, sort of childlike type of invented procedures.
I always say, it's like if I had a plumbing problem and I decided not to go ask a plumber to come help me, I would just be taking this wrench and kind of flip, flopping it around under the sink, just trying to see how it goes. And they're just trial and erroring when you walk around the classroom the classroom looks busy.
Drill down on the math and you've got kids practicing kindergarten and first grade math and you've got other kids who – it's not that often, to be honest – that may actually be intuiting the procedure that they should be learning from this task. You create what is essentially a Matthew effect.
The rich get richer, the poor get poorer, and it's not a solution for differentiation, it's a solution for busy work. It's a solution for giving activities, a sort of activity-based type of teaching that is just really poor instructional design.
[00:14:07] Anna Stokke: So I get the feeling that multiple access points in your view are not really an effective tool for teaching math.
[00:14:15] Zach Groshell: No, they might be a great extension type of problem. They might be like an afterschool math club type of type of thing, because we don't care if they learn it. We just, we want them to grow their self concept, I suppose.
It's kind of a club type of thing. But we ultimately have a responsibility to the teacher after us to give them a class that has the foundational or prerequisite skills in place so that they can do their jobs. It's really malpractice in my view.
Afterwards what happens? They usually compare different methods. They discuss like who did what and he did what. And we all celebrate ourselves. But, but what's hiding in plain sight is that a proportion of that class is not learning the material to mastery. And it doesn't matter how we compare our, our worksheets on the board with each other's, that we're not addressing gaps and we're not doing our jobs when we do this kind of math teaching.
[00:15:12] Anna Stokke: Onto the big question. So are you familiar with Building Thinking Classrooms?
[00:15:18] Zach Groshell: I am. I read the book at everybody's encouragement. I read the book.
[00:15:23] Anna Stokke: Okay, so do you want to first describe what it is and then maybe tell us what you think about it?
[00:15:29] Zach Groshell: It's sort of like a cookbook of like different strategies that the author has found to it––probably, he thinks it increases engagement or increases enjoyment in math. And maybe it creates a math classroom that looks, has a certain aesthetic to the author that he thinks is important in a math classroom.
And contrast that to more of a traditional math classroom where kids are seated more often, the kids are responding in unison, the kids are doing a lot more timed tests or worksheet based tasks. It feels like it's sharing a set of values.
But really, all it is repackaged, in my view, discovery learning or problem based learning. Someone on, on Twitter just the other day said they are a big fan of BTC and they said it's basically just cooperative learning, repackaged, but it's looser. I thought that was crazy. It was like, it was admitting that this is actually a bad version of another bad idea in, classrooms. But he was saying it in the positive.
They're cool sounding tips and tricks, kind of a bag of tricks. Like for example, the most famous one is the vertical non-permanent surfaces. You can stand at a board and everyone has a marker. One kid has a marker, and we are all having kind of discourse around a board.
Another big emphasis that everyone doesn't want to talk about 'cause it's so ridiculous is non-curricular tasks. I didn't even know those were legal in schools, but Okay. Let's emphasize tasks that are off the curriculum. These are the brain teasers, these are the puzzlers and the magic tricks.
Things like group assessment, right? Somehow if I assess everyone at an average, I will be able to report the correct findings when really what happens is you get a skew of the top learners, the one doing all the work, and the lower learner just gets, improperly assessed.
[00:17:29] Zach Groshell: It's bad assessment. There's almost nothing in that book. I find to, to be useful. I can, we can have a debate now or a discussion around when it could be useful, but not as it's presented in the words of that book.
[00:17:44] Anna Stokke: Okay, so I'm going to weigh in on this. I actually don't talk that much on the podcast because I usually let the guests do all the talking, but I mean, this question was sent to me.
I am kind of familiar with Building Thinking Classrooms, and I'll tell you how I heard about it. It was used in my daughter's school. And so actually before I left the house this morning, I said, “Hey, you remember when you're using Building Thinking Classrooms?” This was a while ago. “Now can you remind me what were some of your complaints?”
And she didn't like it. So first of all, she said some kids will take over and they'll often show you incorrect ways to do things. And she said, we just passed the marker around and each person did part of the problem anyway. Like we could have done so much more if we were just doing it on paper.
When it was used in her school, I realized that this wasn't working and I looked into it.
And so, first of all, is it a research-based program? That's an interesting question because a lot of people say it is, but if you look closely at this, you know, what would you think a research-based program in math would look like? Should it not have been shown that it actually improves student learning? What do you think, Zach?
[00:18:59] Zach Groshell: It'd have to have had an effectiveness study of some sort, however poor.
[00:19:03] Anna Stokke: And we've discussed this this many times, engagement isn't learning. So you can be very, students can be very engaged, which is what I think a lot of people are seeing when they're seeing Building Thinking Classrooms, because students are up on the whiteboards, but they could be learning nothing.
To my knowledge, the only research on this program and whether it has any sort of impact on kids in schools was done by the author Peter Liljedahl, and it measured proxies for engagement, not learning. It did not measure learning. For a program that's supposed to be about thinking you would think there would be a study that actually measures thinking. And you can measure thinking by seeing if students could solve problems that would require them to think. But he didn't do that. He measured engagement, which again, is not learning. As far as I know, there's no evidence that this program improves math learning in schools. Now this is a huge red flag and we've talked about red flags in education research on this podcast.
And even if you look at the engagement study, there's serious problems with its design. I'm not going to go into detail about that, but I'll mention in my opinion the measures of engagement in the study were really suspect. So here's an example and, and I've looked at this, proxies of engagement. So more points for non-linearity of work.
So in other words, if the work is scattered. and I think about that as a mathematician, as someone who's been doing math their whole career, and no, that is the exact opposite of what you want. You want students to be able to write math properly. There are good ways to write math and there are bad ways to write math because otherwise the students are going to get lost and they will make mistakes. What do you think, Zach?
[00:20:53] Zach Groshell: I appreciate this podcast format right now because I want, I want to actually hear what you have to say about this. One of the things that people tell me though, and maybe, your own child's experience could, could say more about it, is that there are ways to do it right.
And everyone who's trying it, who's criticizing it is doing it wrong. And they give examples of ways for the pen and the, and you, you draw, you draw, make it into a quadrant and you have the kids have rules and you stop everyone. Only this kid can talk. They give an infinite list of things that you should do.
And everyone's doing it wrong. I mean, have you heard this before?
[00:21:32] Anna Stokke: Yes, of course. When things don't work well and parents are complaining about it––because parents have been complaining about this program––I posted something on Twitter just the other day where the parents were saying, you know, if their kid was struggling and they didn't know what was going on, they didn't learn anything because the math whiz did everything. And then there's the math whiz who feels that they have to do everything for the group, because nobody else knows what they're doing. So this isn't working. So when parents and people start complaining about programs not working, they'll say you're not doing it correctly.
Maybe sometimes that's true. Okay. But you know. Why is everybody having such trouble doing it correctly then, and where are the results that show it's effective?
[00:22:17] Zach Groshell: So I've had the experience––I think it's unique––of having a consultant who had trained the teacher just before we were to visit to as a proof of product, right? So they, they come and say, “We are doing Building Thinking Classrooms. I spent several Zoom meetings with this teacher. I came in yesterday and we planned out this entire thing, and now we're going to go see it.”
Of course, they say, “this is a teacher who's new to Building Thinking Classrooms. Let's give them some grace.” And we all are. We're on the side of this teacher, right? And we go and we watch multiple lessons, which are supposed to be proof of this product because a very, a very expensive consultant has spent many hours training this teacher personally, which no one else is going to get this type of training.
And we go in there. And the kids are off task. The lowest kids are breaking the marker into the carpet. The lowest kids are, especially the low kids that show certain behavior issues, are eloping, are coming to us and trying to have a chat with us. You look at the math and it's completely unsophisticated.
It is baby math of kids doing little ticks and charts and you're thinking, “If this is, this is the way to bring these kids up, this is the method of one kid doing the work. Everyone else is social loafing. And this is the best version you have because the consultant created it, what's going to happen if we just let this loose on a school district?”
Right? So I've never seen it work.
[00:23:46] Anna Stokke: And I think we know what will happen. A bunch of kids will get failed by this program, and eventually it will be replaced by some other fad. Lots of schools are buying into this. They're spending lots of money on this.
And honestly, when I first heard about it, I thought, “you have to be kidding me. Our school division is paying money to get someone to tell them to put kids in groups and work on whiteboards?”
Like come on. Come on. Do we really need to pay someone to tell us how to do that? And is this even a new idea?
I want to mention a couple other things. Okay. So about thinking. I think that perhaps teachers are afraid that their kids aren't thinking, and they want their kids to be thinking. Now, if someone is telling you that your students are not thinking unless you're using the teaching methods that they're telling you to use, I think that is a big red flag.
Also there seems to be a made-up definition of thinking when it comes to Building Thinking Classrooms. So thinking seems to mean solving the types of problems the author wants students to solve. Using the teaching methods you're supposed to use. So randomized groups working on vertical, non-permanent learning surfaces, not direct instruction. So if you are not using those methods, we're supposed to believe that your students aren't thinking, and we're told that mimicking is not thinking. Mimicking is disparaged.
Here is the Merriam Webster definition of thinking: Thinking is the act of using one's mind to produce thoughts.
It's a process that goes on in the brain. So when you're mimicking, you’re thinking, you really are. If you're mimicking what your teacher's doing, you're thinking. And mimicking your teacher's good approach for doing a math problem is a good thing. That is a good way to teach because we want students to learn how to do math, and we want them to be successful. We don't want them always mimicking, we're going to wean them off that.
[00:26:03] Zach Groshell: Yeah, and we have, I mean, going all the way back to Bandura and also even to reinforcement learning or spaced repetition. The always the idea is just that that practice solidifies and reinforces these ideas. But the original, the first phase is simply to imitate it.
You know, in math it's, it's very hard to get them to directly copy. And I do see this. They're just taking notes. They're copying down, right? This isn't actually, there actually isn't any thinking going on other than “is my paper the same as the paper in front of me?” But with math, it's very hard to kind of do that because every time you switch from a one worked example to the next or to a problem to the next, you change the numbers.
You slowly start to get the kids to apply it. And this is just scaffolding , and you start with the strongest scaffold possible, which is simply is, here's my schema, here's how to do it. And now that you know where we're going, now, you know what's possible. I'm going to break this down to the point where I'm going to pass the baton over to you, step by step.
People call this spoon-feeding, people call this whatever other derogatory, you know, pejorative term they can think of. But this is good teaching. This is good teaching to start with that strong scaffolding.
[00:27:01] Anna Stokke: Yes, that is good teaching. So this business about mimicking is not thinking, this is not true. And don't let someone make you feel bad for actually teaching well, because teaching well involves showing students how to do things and getting them to try it on their own, and then gradually fading instruction.
Okay, so I have a couple more things to say about this. 'cause I want to make sure that, that we cover this. And I want to bring up the issue of non-permanent surfaces.
So I don't know what you think, but I think that we can't have all of students' work on non-permanent surfaces. You want some of students' work––a lot of their work––to be on permanent surfaces. And here's the reason why––because students don't remember everything.
They might have done something in class that day and, and you think they got it and, and they think they got it and then they leave and they come back the next day and they can't remember it. That doesn't mean they didn't learn it, it just means they need more practice. But it's good for them to have their notes to refer to.
What do you think?
[00:28:10] Zach Groshell: Absolutely. The other permanent surface that I'm sure is, is complained about in some of these approaches is, is just textbooks. Good materials that have great worked examples in them that we can refer to, we can study back, we can give ourselves an extra model.
When, when it needs to correct our thinking, when we're getting things wrong, right? Our notes are a study guide for us afterwards. They're a way to actually facilitate partner work, which is we can actually talk about something that is shared between us, right? And there there are a way to guide students' thinking and show them this, the success that they are making.
Look how far we've gone. It's almost like a portfolio in a sense. Look how we started here and look how we added just a little bit every day. Now we're here. I need you to go back, look over what we're doing. It's a great, this is, again, are we talking about common sense? But where is that gone? When I would use a non-permanent surface, I would use many whiteboards.
And the reason why is because I can have everyone responding at the exact same time. I have everybody in my row or in my horseshoe shape or on the carpet, on dots. And what I do is I say. “I need you to do this. Step 3, 2, 1. Show me.” I look at it, I scan and I go. Now this is more, the purpose of this is not for collecting a permanent source of their, their practice––it's an assessment purpose. Can I set them off to do the thing in their notebook? Can, are they ready to get to that worksheet? And if they're not, maybe they need to stay on the carpet. And you got, going back to the original question, you two thirds of folks get on the worksheet that's already on your desk.
“Pencils ready? Okay, go. And you guys stay here just real quick. We gotta do some power teaching,” right? So that's what I would use because the logistical problems of four people sharing a board standing up are just ridiculous.
[00:30:04] Anna Stokke: Well, it's interesting you bring that up because, and I talked about that video I shared on Twitter and the parents were complaining and then teachers came up and they had some rebuttals and one of the things the teacher said is they like it because they can glance around the room and they can see what the students are doing and whether they get what's going on. But don't mini whiteboards make more sense for that purpose because every single student is participating?
[00:30:34] Zach Groshell: Absolutely. And, and how do you know who did what? And I have, now I have to add a bolt on to Building Thinking Classrooms where I have color coding, where kids have different color markers so I can see who's doing what. I've heard this before. Just take a second to think how math actually works.
What, how do you know what squiggle came first and which part of that really was them? Is the group member trying to humor the teacher and saying, come on, you got to add something. Kid doesn't really know what they're doing. It gets crossed off, you're glancing around the room, and you don't know if they can follow the step-by-step process to solve that problem.
Who did what? What was first? You can do that with, with mini whiteboards if you want 'em to talk about it. If that's the problem, you want 'em to talk about the math “3, 2, 1, show me, great. Turn to your partner. What did you do?” You get, now you've got everyone talking, or at least 50% at a time as opposed to one fourth at a time with four people at a board.
The math doesn't add up for using this strategy as a main. As a main tactic in a, in a classroom.
[00:31:42] Anna Stokke: It should not be the main dish of your instruction. I could see a situation where maybe you have really advanced students and you're working on like math contest problems. That might be a time that that type of approach would work well. But if you've got novice learners and you're teaching students something for the first time and you're trying to get students fluent at something. And that's another thing because when you're doing everything on the board like that in groups, it's very slow, right?
So the way you get good at math is practice––opportunities to respond, you're really lessening the number of opportunities to respond, which means the students don't get enough practice, and especially targeted practice.
And actually, I just want to drive this point home. As far as I know, there is not a valid study that shows that this program has a positive impact on math learning in schools. No matter what people are saying, And, also in my opinion, it's not aligned with best teaching practices either.
Like what we've discussed previously on the podcast with guests like Zach, Paul Kirschner, Amanda VanDerHeyden, Sarah Powell, et cetera. So I would say if you're going to use this program, use it at your own risk, actually at your student's risk.
And if you're in a situation where you're being told to use this program, my advice would be to use it infrequently. And the other thing, if you're a teacher and you're being told to use this program and you don't feel comfortable about it you should really ask for evidence that this program is effective and remember that effectiveness––that's not the author's book. Like that's not evidence of effectiveness, right? Anybody could write a book. You need a research article that actually measures learning. Whether students can actually do math, whether their math learning has improved.
And you know, if you get sent something, about it, feel free to send it my way. Happy to look it over for you or get someone else to look at it. And the other thing you could do is you could show your principal or whoever is suggesting that you should use this program. You could show them the IES practice guide that we've talked about many times on this podcast. Effective ways for teaching students math, and that actually is an evidence-based guide, and I've linked that to that on several resource pages on previous podcasts. For instance, you could go back to the podcast episode with Sarah Powell. I've linked to it there and that might be a good thing to do.
So, back to Jennifer's question. Should explicit instruction be prioritized or can it be integrated with BTC?
[00:34:20] Zach Groshell: Yeah, I think it cannot be integrated as the words suggest in that book. The idea that thinking has to come from within the student as a sort of constructed type of math, an invented type of math where it's self-initiated. That is throughout, that is the, that is the thread that goes throughout the entire book.
It's what gives it its title. It is that book. And so it's, it's more than just something to ignore. You'd really have to ignore everything, take out the tactics themselves, like the vertical whiteboards. And you'd have to say just to that tool, is that tool, does it have a purpose in for my class?
Hey, it's throwback Thursday where we're doing review. All my kids got great scores except for two kids. I'm putting up a bunch of problems on the whiteboards ahead of time. I'm going to say, “guys, markers, get over there. Small group. Come over to the kidney table. We gotta work on what you got wrong on this test because I'm going to retest you on this.”
Hey, you've, I just found, I just found a use. All tactics perhaps have a purpose somewhere. Some of them are high yield and high impact, and those ones are the ones that you really want to see every day. For most situations, I find one minute timed tests to be highly effective. I find high engagement strategies like choral response, mini whiteboards, turn and talks–these need to be a core of what we're doing.
Something like this is for a throwback Thursday or a fun Friday or the last day before break. It's not what I would spend any of my district's money and precious teacher PD time emphasizing were I running a school.
[00:36:06] Anna Stokke: I agree with you completely there. So throwback Thursday. Good plan.
Okay, let's move on to the next question. And I've received quite a few questions about this topic as well. So this is from Carrie.
“I was wondering if I could steal a bit of your time to ask you about number talks. In the past, number talks have been strongly encouraged as a daily routine. However, many of our students do not have math fact automaticity, and I am wondering where number talks fit in. I would like our classrooms to spend several minutes every day developing fact fluency, and I don't see if or how number talks will support our end goal of fact fluency.”
Here's a similar message from another listener.
“We are wondering where number strings and number talks fit into our practice. The routines do not feel like they align with the science of learning, but we feel the mental math strategies are important. We are wondering what your thoughts are on number talks and number strings.”
Okay, so I understand number talks to be short, maybe 5, 10, 15 minutes daily. They're tasks that focus on mental math, encouraging students to share and discuss various strategies for solving problems. So, Zach, have you seen these implemented?
[00:37:23] Zach Groshell: As an elementary teacher by training, it's sort of central to a lot of. Like teachers, teachers need a structure for their math block. And it's sort of an easy thing to implement. It's sort of like we start a certain way, then we get to the real meat of the lesson, and then maybe we have our exit ticket.
So, yes, I've seen it and I, and unfortunately I was even given programs to implement it and had to, you know, was held accountable to, to implementing versions of this.
[00:36:17] Anna Stokke: Okay, so what do you think about number talks?
[00:37:53] Zach Groshell: The first thing you mentioned that was important is, is brevity. And I've found that number talks tend to run over the promised amount of time that teachers are, are meant to do them. This is because the activity, the central activity of them is usually sort of a constructivist type of math.
“What's your answer? Why did you do it that way?” We have a kid come up with Popsicle sticks and he, he puts his popsicle sticks in a little, jar, and everybody looks at it and go, “is he right?” And everyone goes, “huh. You know, I don't know.” And he goes, “well, he has one way of doing it. Does someone have a, could someone add these cubes to this?”
And it, usually the programming, the actual material source material, it's sort of low level stuff, so to allow, enable kids to talk about something, and it usually doesn't link in necessarily to what the kids are doing. And they go over, the talks go over and you're spending this limited attention resource and working memory the kids have, sort of depleting it right at the start of their math block when they need that to learn the day's objective, the day's new material.
I'm curious what your thoughts are I've seen it go gone awry. I have another option that happens on the carpet. I just wouldn't relate, call it number talks or anything of the sort
[00:39:15] Anna Stokke: Wait, what's your option?
[00:39:16] Zach Groshell: Quick math facts on the carpet with choral response right before I ask you to go write them down. And the reason why I do this is because often you're simultaneously building their number formation, their ability to form numbers in the early years. as a problem with assessing for fluency is that it's sensitive to how fast you can form numbers.
So one of the ways to get kids practicing addition facts as early as possible is mental, so-called mental addition facts. And so very quickly you can warm them up with some flashcards or, or maybe you have a number series and you have 'em chorally read, I erase. We do those. Then we go to the worksheet or we go to the problems on your, at your desks.
And that would last two minutes, three minutes. But it's mental math if you, if, if you know what I mean.
[00:40:09] Anna Stokke: Okay, great. So I have some thoughts on this and on mental math strategies in general. So now the listeners, I am sort of getting the impression that they're writing and their students don't have their math facts memorized yet. And so I think that time would be better spent using some of those practices that I put in my How to Build Automaticity with Math Facts episode. Or you can listen to the one with Brian Poncy.
But I think something that happens a lot is people think that it's better to teach kids a whole bunch of different strategies for getting math facts. So for getting something like even single digit multiplication. So like eight times seven––you don't know eight times seven, well do you know, four times seven, and that's 28. So now you can double it and get 56.
But if you think about it, like that's really complicated for someone whose math facts are weak and they're just learning these and you do want them to memorize those facts. I think you have to have some strategies in place. So for instance, can they count by fives? Can they count by tens or maybe threes and, do they know that multiplication is repeated addition?
But when you overdo it with these strategies it's going to interfere with actually memorizing the facts because you're creating cognitive overload. And you know, as Brian Poncy would say, you don't want a whole bunch of time in between the stimulus, so eight times seven, and the response 56. You want students to be able to quickly do that.
So I think it's better, you know, if you just concentrate on the flashcards, the taped practice, timed practice, those sort of things we discussed in that episode, which are evidence-based techniques for memorizing math facts. And then after that, you start introducing strategies for larger numbers. So I really think I would first concentrate on getting those math facts down. I like your choral response idea if you want to do some sort of group work thing.
But now in terms of mental math in general, you know, do we want students to know, have nice mental math strategies for doing something like 18 times five, that's two times nine times five, which is 10 times nine, which is 90. We probably do want those strategies, but when do you introduce those strategies?
You introduce them after the students have the math facts memorized. Once they have the math facts memorized, it's going to be way easier to use those strategies because you free up that cognitive load because you have the math facts memorized. And then teach them those strategies.
And then you can give them a whole bunch of problems and have them figure out when to use which strategy. But make sure they have the math facts memorized first and also teach them the strategies.
[00:43:06] Zach Groshell: Yeah. And I think if people, like, if you wanted to apply just this idea of like getting the kids together on the carpet, right? This sort of community vibe where we're all, we're all kind of, you know, doing our math together. The script that I would give the teacher, you know, like a DI type of script.
It just wouldn't, it would immediately not look anything like this kind of open-ended discussion around multiple strategies. Like you just said, like if we started with 5, 10, 15, 20, and we're all quarterly doing our, our counting and then I go, so one times five is five. Two times five is everyone goes 10, right?
That's right. Because 5, 10, 15. And we, what we would be doing is using a sophisticated design to show how the different elements that we had been practicing relate to each other, but we're answering chorally. It is well designed and scripted. It is very tight. The wording is minimized and it is not a class discussion of how everybody does different types of math. It's practice. It is a way of practicing and essentially memorizing elements of math and how they relate to each other.
[00:44:18] Anna Stokke: And something you mentioned at the very start of this conversation is just about the use of instructional time. This time is precious and absolutely, I could imagine this discussion just going off the rails, right? And using up so much class time, and I think sometimes people think, oh, it was great.
You know, there were all these rich conversations, but was it really great? Were students, were you targeting your instructions so that students learn what you want them to learn? Like that time in elementary school is pretty precious. That's the time when those students have to get those basic skills that set them up for success later on.
So you do want to use it wisely. You don't want to waste their time.
[00:45:01] Zach Groshell: And that's where kind of this discussion-based type of type of math teaching, it just, it always goes that way. A lot of teachers who are in the space of trying to find something that works. I have a lot of empathy for them. If they are navigating a land, you know, a field of landmines of I've got to try this, and then that, and the pendulum swings.
But they don't often get a chance to do something that I do almost daily, which is visit lots of classrooms. And what you do see in the more effective classrooms is an emphasis on efficiency and the idea that the, these moments count, if you could see the spread of teaching, you would realize that a lot of the classrooms that the kids are struggling, the teachers starting to blame the children, the teachers in a space of sort of survival mode is that we don't get to math because of all these other things.
And when we do math, it would be very unwise to do some sort of productive struggle type thing. 'cause there's going to be a lot of extraneous talking and socializing. There's going to be a lot of constructing and trying to do trial and error, but we can get them there a lot faster. We get rid of this extraneous load and hyperfocus in on the stuff, on the stuff they need to learn in that precious amount of time we are given with these kids.
[00:46:18] Anna Stokke: Absolutely. Well said Zach. So I think we've covered three questions in some pretty great detail. And thank you so much for coming on and helping me with that. But before we sign off, can you tell us a little bit about your book?
[00:46:34] Zach Groshell: Sure. This is not necessarily a math book. This is a generic instructional toolkit I would say that applies to all subjects and all age levels, except perhaps the very youngest children in the, in the AI coders over doing doing grinding work over in some, you know, proving ground somewhere in Austin, Texas.
This is really for your average student in your average classroom, and you want to know. How do I teach stuff efficiently and how, what is, what are some updates in the world of cognitive science? And I focus heavily on the worked example effect. I look into things like clarity of explanations dual coding with visuals and in example, sequencing.
I hope that this is a good course correction for education. We read this and we go, you know what? Let's start by just telling them, and then once we start by just telling them, then we can start asking questions. Then we can start removing scaffolds. And finally, once those things are in place, we can get to that space of generalization and creativity and, and all that that's possible with proper good instruction.
[00:47:45] Anna Stokke: And you did a great job. I love your book, so I'm going to put a review on Amazon today, so there you go. So thank you Zach. Thank you so much for coming on and helping me address the listener questions. It was lots of fun.
[00:47:58] Zach Groshell: It was you know, this podcast has just made my life awesome. You've, you're doing a service to all of us by giving us this information and bringing great guests. I'm just so tickled you even considered having me on in the first place, so thank you so much.
[00:48:13] Anna Stokke: ​ If you enjoy this podcast, please consider showing your support by leaving a five-star review on Spotify or Apple Podcasts. Chalk & Talk is produced by me, Anna Stokke. Transcript and resource page by Jasmine Boisclair. Subscribe on your favourite podcast app to get new episodes delivered as they become available.
You can follow me on X, Blue Sky or LinkedIn 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.