Ep 55. Mailbag: How to get started with evidence-based math instruction & tackle gaps with Jonathan Regino
This transcript was created with speech-to-text software. It was reviewed before posting but may contain errors. Credit to Canadian Podcasting Productions.
In this episode, Anna Stokke hosts an informative mailbag edition with guest Jonathan Regino, supervisor of math (pre-K-12) at Interboro School District in Pennsylvania and an experienced classroom teacher.
Drawing on their combined experience and expertise, they tackle listener questions, ranging from how to address large knowledge gaps among students to program recommendations. They also offer guidance on becoming informed about evidence-based practices, effective ways to assess students, and more. This engaging conversation is a must-listen for anyone seeking to strengthen math instruction and improve student learning.
This episode is also available in video at www.youtube.com/@chalktalk-stokke
Register for the Masterclass: Evidence-informed Mathematics Teaching, La Trobe School of Education
TIMESTAMPS
[00:00:22] Introduction
[00:04:52] Question 1: How can new teachers learn about evidence-based practices?
[00:09:52] Book recommendations
[00:16:08] researchED
[00:18:12] Question 2: Grading math assessments with points versus using standards-based grading
[00:23:00] The 1,2,3,4 scale breakdown
[00:26:16] Consistency with the grading system
[00:27:30] Question 3: Free class-wide interventions to address math knowledge gaps
[00:28:40] Delta Math RtI
[00:33:09] Supporting high school math students with large knowledge gaps
[00:38:46] Recommended resources
[00:43:22] Question 4: England’s times table check
[00:47:40] Question 5: Are spiraling programs ineffective?
[00:50:02] Understanding spiraling vs. interleaving vs. spaced practice
[00:56:14] Program recommendations
[00:59:44] Final thoughts
[00:00:00] Anna Stokke:
Welcome to Chalk & Talk, a podcast about education and math. I'm Anna Stokke, a math professor and your host. Welcome back to another great episode of Chalk & Talk.
This is a fantastic mailbag episode. I invited Jonathan Regino to help me answer some of your questions. Remember, if you have a question, you can visit my website and fill out the form, and your question could be featured on a future mailbag episode.
Jonathan has extensive math education experience, and he’s a supervisor of math for a school district in Pennsylvania. We covered a lot of fantastic questions in this episode, and I think it will help not just the listeners who sent them in, but a lot of other teachers out there who might have similar questions. You can get an idea of what topics we covered by checking out the timestamps in the episode. I hope you find it helpful.
Now, before we get started, I have a couple of announcements to make. I am really excited because I'm going to be co-delivering a master class on evidence-informed math teaching through La Trobe University this fall.
It can be taken by any teacher or pre-service teacher anywhere in the world. It will be on Monday, October 20th in Australia. That's October 19th here in North America.
I'm going to include a link on how to register in the show notes. I hope to see you there.
Also, if you're enjoying Chalk & Talk, you might want to check out another podcast I've been listening to lately. It's called Teachers Talk Radio. They've got a network of around 30 teacher hosts, and they publish episodes daily on all the usual platforms like Spotify, Apple, and YouTube. They cover anything that's teacher-related like behavior, assessment, instructional techniques, even AI.
So, give them a follow wherever you get your podcasts or visit them at ttradio.org. That's Teachers Talk Radio. Now, without further ado, let's get started.
I'm excited to welcome Jonathan Regino as a guest to the Chalk & Talk podcast today, and he is joining me from Pennsylvania.
He has extensive experience in math education with a career spanning classroom teaching, district leadership, and statewide support. He is the pre-K to 12 supervisor of math at Interboro School District. He has also held roles as supervisor of teaching and learning for STEM at Marple Newton School District, curriculum specialist at Age of Learning, and teaching and learning specialist at the Delaware County Intermediate Unit.
In addition, Jonathan has worked as an educational consultant with the Pennsylvania Training and Technical Assistance Network, which is the training arm of the Bureau of Special Education supporting schools across the state. Before moving into leadership roles, Jonathan spent 10 years teaching middle school math and science. Jonathan has also shared expertise on math interventions and curriculum at state and national math conferences over the last 10 years, always with the goal of making math more meaningful and accessible for all students.
And I first learned about your work from listening to Zach Groshell’s Progressively Incorrect podcast. And so big shout out to Zach for that. But I was so impressed after listening to that, I thought that you're a person that I need to know.
And I've reached out to you a few times actually with questions about math resources and that sort of thing already, because you obviously know a lot. And you can cover some areas that I can't, like how to manage teaching math within the constraints of, you know, a grade three or four classroom, which can maybe be kind of tricky. And so, I have a lot of mailbag questions to answer and I needed some help.
And so, I thought you'd be perfect, the perfect person to help me with that. And so, you kindly agreed to come on and I'm really excited about it because we're going to have some great discussions today. So welcome Jonathan, welcome to my podcast.
[00:04:22] Jonathan Regino:
Hi Anna and thank you for the opportunity. Looking forward to answering these questions. I'm coming from a place where I'm trying to build out my network of people who follow the science of learning and believe in some of the things that you have shared, and Zach have shared.
So, the more I can build this network, the better off it's going to be for my teachers and my students.
[00:04:42] Anna Stokke:
Absolutely. And all the other teachers out there listening.
So, okay, let's get right into it. We've got a lot to discuss today. So, I'm going to start with this question from Anna.
Anna writes this, I am a second-year teacher who taught second grade last year, and I will teach third grade this year. So very new teacher. I really love math growing up. I myself have a strong math background. However, I feel completely overwhelmed and lost as to how to teach math. Unfortunately, my math education classes in university were severely underwhelming. I was taught to basically make students find as many ways as possible to solve a problem and run around in mental circles that barely make sense to me, much less a student. I hear that a lot by the way. So, this is not something new for me. I hear a lot of teachers complaining about this. Anna goes on to say, I always hated that method and it didn't make sense to me. When I listened to a podcast you were on, I felt so relieved that my intuition was right and I was not taught well.
However, I now feel completely overwhelmed. I have started to dive into evidence-based instruction through your resources and others, but I feel like I don't even know where to start or what to search for. So, for young teachers like me who have not been taught evidence-based practices, how do we teach ourselves? I would really love some recommendations as to what topics to search for and practices that we should implement immediately. I think this could be a really interesting discussion for young teachers who have never known anything different and feel overwhelmed in changing our practices. Thank you for all that you do.
So that was very nice.
Okay, what do you think, John? Do you have any suggestions?
[00:06:31] Jonathan Regino:
I'm going to start a little bit off topic. For where I'm coming from, I think this is really important that we start with the curriculum. And if we don't have curriculum that follows the science of learning, then we end up in situations like Anna shared.
I think we really need to simplify in math. We've gotten to the point where the textbooks and the things that we're teaching, it's just way too much content. It's way too many strategies.
It's way too much of everything. So, we do need to simplify. And I do think we need to get down to where we're teaching one strategy and then moving into the algorithm.
But this is where curriculum is so important because we could focus on teaching everything through number lines. But if one teacher in that K-5 system decides they're not going to teach number lines, then that coherence falls apart. And if that coherence isn't there, then the student is learning multiple methods and multiple strategies.
But to answer Anna's question, one of the best books you could get is there's a direct instruction book by Stein, Kinder, Rolf, and a few other people. It's produced by Pearson. It's really hard to find.
And most of the time, if you Google it, it's going to be three or four times more expensive than it originally was. I did find it on a used bookstore website, took about a month of searching, but it's a really good book. It takes all the elementary content, breaks it down step by step, and shows you how to teach it in that direct instruction model.
And then as far as teaching overall, I think before the summer, I would have automatically said start with Ali Lavelle's book on cognitive load theory. It's a quick, easy book. It was one of those books that totally changed the way I saw education and teaching and really got me on this path of what I've been doing in the last few years.
But now with Zach Rochelle's book that came out, I tell all my teachers start there. It's a weekend read. It's so simple to follow, and it's everything in it you could do the next day. From there, I would take the ideas that he presents like interleaving and block practice and space practice and do deeper dives on it. So, if you're really into research and you like that side of things, I would go with How Teaching Learning and How Learning Happens by Kirschner and Hendrick and Heal. If you're not so much into the research or it's the beginning of the school year and you don't have time for the research, the Walkthru series by Tom Sherrington, they're all one-pagers.
They're quick, they're easy, and they give you the minimum amount of information you need to start doing things that match the science of learning and the science of math in your classroom.
[00:09:07] Anna Stokke:
Yeah, those are great recommendations. So, I'm going to follow up on just a couple of things.
So, you mentioned make sure you have a good curriculum. And so, I do want to just stress that when you say curriculum in the United States, what you mean is like the program you're using, like the textbook or something like that, right? In Canada, when we say curriculum, we mean what you would call the standards. And you mentioned a book by Marcy Stein. Is that corrective math? Is that the one you're talking about?
[00:09:42] Jonathan Regino:
So, it's not corrective math. It's almost like a handbook on how to do direct instruction in the math classroom. It was the precursor before the corrective math series came out.
[00:09:52] Anna Stokke:
Okay. I got that book out of the library once, actually. So, we can list that on the resource page for the episode.
And I like the books you mentioned as well. I want to mention a couple of others if you don't mind. I think I'll mention Barry Garelick 's book, Traditional Math.
I like that book. In fact, I like all of his books. A lot of them are kind of funny.
He tells his stories about going to ed school and everything like that. So, they're kind of fun reads. The Traditional Math book by Barry Garelick and J.R. Wilson is a little more hands-on, and it could be helpful.
And then how about Greg Ashman's book? Have you read that one? That little book, Cognitive Load Theory? Yeah. Yeah. Okay.
So, I'd recommend that one too. I like that you recommended books that are pretty straightforward and easy to read. So yeah, those are great recommendations.
I'll say a few other things in regards to Anna's question, because this is a mailbag episode, so I'm going to weigh in a little more today. So, I got the sense, because she said it multiple times, that Anna is really overwhelmed, and I can see why. But I would like to say that your intuition is telling you something and so listen to it.
It's true. The multiple strategies approach, I've never really understood why people think this is a great idea. I mean, I've heard lots of suggestions for why it might be a good idea, but if you think about it, students are going to get confused, and you're going to cause cognitive overload.
So, it's unfortunate that teachers have been given the impression that that's the best way to teach math, because I certainly haven't seen any research showing that. But anyone out there, if you think you have it, send it to me. Happy to see it.
But in the meantime, I'd say this method doesn't make sense. And then I want to say about teaching math. You might feel overwhelmed, but I would say concentrate on these things.
So first, focus on the content. Pick your content. Decide what is the best stuff that you have to teach, like the most important things that you have to teach. And you can maybe weigh in on this, because this is grade three, so you would know this really well. But I mean, I'm going to say the four operations. Like, students need to know how to add, subtract, multiply, divide, and they need to know how to do it well and fluently and quickly.
Otherwise, they're going to struggle in later grades. So that’s the first thing I would say, is look at your content. And I'm even going to post some things on the resource page, like from the National Math Advisory Panel, where they talk about the most important content that students need to learn, something from Brian Poncey, maybe I’ll post, and from Amanda VanDerHeyden. But then the next thing is, okay, so you've got your content. Now teach it. Teach it.
Teach the content, right? And teach it as well as you can. Break things down into small steps. Use some of those approaches that, yeah, you could get out of Zach's textbook.
Use and I do, we do, you do approach. Lots of worked examples. And getting students then to, you model them, and then the students show you that they can do those steps using a similar example. And then ensure high rates of opportunities to respond. And what that means is practice. And that we're getting all students involved and being able to respond.
So, using things like mini whiteboards and stuff like that. Math facts, at least four minutes a day, right? Practice at least four minutes a day. And then the other stuff, you know, the interleaving, the space practice, you can put that in there and get that in there.
But for now, focus on the content, teaching it, I do, we do, you do, and getting students to practice a lot. So, do you have anything to add to that?
[00:013:43] Jonathan Regino:
No, I agree. Actually, this was the message I shared with my staff coming back to school was, we are going to simplify, we're going to focus on the facts, 100% of our kids, we're going to guarantee that they know the facts before they leave.
We're simplifying. And the relief from teachers and the excitement of just going back to what they know is good, and that intuition tells them is good, has just been a game changer. We talk about how stressed-out teachers are.
This is the easiest way to alleviate that stress. I had a whole multiple approaches idea. I say, teach them the algorithm.
And once they mastered it, then you can bring in some of those other approaches. We have this, the expertise in us, and we forget how hard it is to do all those approaches and keep them in your head, figure out which one to use at which time, it doesn't make any sense. So, pick that one method, use the algorithm, show them how it works, break it down to the itty bitty steps, they can learn each step. And then from there, you can stretch your students, but you're going to save so much time by just simplify.
[00:14:45] Anna Stokke:
Absolutely. And then the other thing I would say too, just on focusing on the really important content, you might have an outcome in your standards or something that says something like, I don't know, represent and interpret data.
Okay. And now it's all fun, like making bar charts and reading off what those mean and that sort of thing. But don't spend so much time on that at the expense of other things that students really need a lot of practice at to get good at.
So, I guess I would say, cut the fluff. What is that saying? Focus on the stuff, cut the fluff. So really concentrate on those important concepts.
[00:015:27] Jonathan Regino:
Yeah. Here in the States, if you're in the United States, you could cut out about a third of what's in the Common Core or whatever version of the Common Core that you're using in your state and be done teaching by our spring break here. Be done teaching before state testing happens.
It doesn't matter what textbook you're using. It doesn't matter what standards you're using. There's about a third of it that can go away.
And the best way to look at that is you look at other countries and the way that they list their standards and expectations. They have far less content that kids have to learn every year, but yet they still learn all the content that they need to do well on the international test. So, we don't need to teach as much as we're teaching and the way that we're teaching it.
[00:16:08] Anna Stokke:
Precisely. I completely agree with you. The issue, though, is that a lot of teachers don't know what the important concepts are to teach.
I've found that out in a few ways, just by talking to teachers or giving presentations. And then sometimes they'll ask me after, OK, what are the important things that I should be teaching in grade eight? And I'll be like, well, fractions, algebra, right? Like to me, it's very obvious because like I have a high level of math knowledge. But if you don't, you don't always know.
So that's why I think it'll help if we post some things on the resource page that lists the important things to hit, don't you think? Another thing I think I would add, maybe go to some research ed conferences if you can. Have you been to a research ed conference? I bet you've presented at one.
[00:16:58] Jonathan Regino:
I haven't presented at one, but I did go to the one that Sarah Oberle hosted in Delaware, in the United States.
You get surrounded by everybody who believes the same thing that you believe in. You get to learn from experts. All the books that I just mentioned, they’re saying people were at these conferences and they get to see and hear them talk about what they’ve written.
And they talk about what it's like in the actual classroom and not just what they have in their textbooks. It's a great experience. And from that, you build out a huge network.
So much of what's happened to me in the last year was because of that conference. And I was just there in attendance. I wasn't presenting, just sitting there listening.
And so much has come out of that.
[00:17:45] Anna Stokke:
Oh, there you go. So, I hope we've answered Anna's question.
And I get that it’s overwhelming, but you can do it. Your intuition is telling you what to do. It’s always hard when you first start teaching for everybody.
You don't have to be perfect all the time. And you get better as time goes on. And, you know, you just do your best, right? Okay.
So, let's move to the next question. And this question is from Phillip. So, Phillip says, my school uses standards-based grading, and we have been explicitly told not to grade math tests or any assessments, for that matter, with points. We are supposed to assign a standard to each question, then grade each question by giving it a level. A group of these standards form an expectation, and you're supposed to assign a level for each expectation based on your professional judgment of the amalgamation of the levels assigned for the different standards under that expectation. If this sounds convoluted, it's because it is.
I worry about the obvious things like clarity, consistency, transparency. In summary, what are your thoughts on grading math assessments using points? And what are your thoughts on standards-based grading?
So that is Phillip's question. So, what do you think, Jonathan?
[00:19:10] Jonathan Regino:
A lot of these ideas that are in schools right now to hide the negative aspects of assessments.
Instead of trying to fix the initial problem and help kids do better on the assessments and learn the material better, we've changed the assessments to hide some of the negative things. So, things like the idea that grades are permanent, or a teacher not having enough time to give specific feedback to a student, or a kid not reading that feedback or using that feedback. Kids competing with each other just to get the highest grade in the class versus actually learning the material.
All those ideas had some negative connotation. And the idea of moving to grades that are like four, three, two, one, or some district you're secure developing needs improvement, those kinds of ideas, all to kind of hide the negative and get kids to focus on the learning. What it did in the long term was erase the idea of what a grade actually means.
So, whether it's a four, three, two, one, or secure developing needs improvement, you ask a parent how kids doing in math, they have no idea. That middle grade of developing or a two and a three is so wide that you don't know if your kid lands in the area, you don't know, are they closer to the needs improvement or are they closer to being secure. And those two extremes have a life changing difference depending on where you're at.
So, you can get to the end of the year and been in developing the entire year, and then you get to the end of the year, you've never made it to secure. And as a parent, you have no idea why your kid didn't make it to secure. So, I think there's a whole lot of problems with this.
And what we're seeing at the high school level now is that you've got a large group of kids who don't know their basic facts, they don't know how to do any of the operations with fractions, and they can't do anything with word problems. It doesn't matter what school you go to; high school teachers are going to tell you there's a problem. Even middle school teachers are going to tell you that's the problem.
And part of that is because of the grading system we have doesn't hold anybody accountable or that knowledge accountable. My district, I live in, I work in a district where we do have to use those four, three, two, ones, I'm working within the system. So, what we've done in the math side is kind of straddle that.
So, we have the four, three, two, one. We started off prioritizing the standards, figuring out what was the most important to get to algebra. And then we weighted every standard.
So, the ones that are most important to get to algebra are weighted a little bit heavier. The ones that aren't necessarily important to get to algebra, we give less points to. And then when we do our four, three, two, one, we can apply an algorithm to it and then get an overall percentage.
So, on my report cards, like a third grader will get all the standards with the four, three, two, one on it. And then below it would be an overall percentage. So, the parents know specifically how a kid's doing in class.
And if they have like an 85, then they can say, what does my kid need to do? And they can go look at the actual standards, look for a three, look for a two and say, oh, you have a two on this standard. We probably should work on that specific standard. So instead of worrying about the entire test or the entire course, look at one little spot and they're working on that one little area to improve.
And then we decided that our grades aren't permanent. We made that very clear to the students, the families. So, if you have a two, you work on it, you show that you understand the material.
You can bump that up to a three and you can bump that up to a four. And then your overall percentage will change. So, we did away with extra credit.
We did away with all the ideas of how to improve a grade, except for showing that you actually learned the material. We're trying to eliminate that pretend grade and the false idea that an A means you've learned everything, which in most of our schools, an A doesn't mean you've learned everything. It just means that you're compliant enough to earn an A. So, we're trying to undo some of that fake grading.
[00:23:00] Anna Stokke:
Wow. You did a great job of covering this. I just wanted to ask about the 1, 2, 3, 4 scale. When you talked about that in your district, is that at the high school level too?
[00:23:10] Jonathan Regino:
It's only K-5. I did expand it into middle school because I wanted to get down to the idea of focusing on a single standard. So, the way our tests are set up is every question is related to a single standard.
So, if I have 10 questions, they might all be on one standard, or it might be three different standards. But if a kid gets question number one wrong, they know exactly what standard that's associated with. So, they do test corrections and after test corrections, they can retest.
And when they're ready to retest, they focus on that single standard that they got wrong. That helped us kind of bridge that gap between in middle school, you typically got one single grade and then the kid didn't know where to start or where to begin to practice and how to improve.
[00:23:54] Anna Stokke:
Okay, got it. So, what you're doing seems to make a lot of sense. I guess I'm sort of a bit surprised by this question in some ways that I don't know why teachers are told that they can't grade the math test, right? Like you're the teacher, you should be able to grade the math test if you know that's the right thing to do. And I agree with you.
I think it masks things when people are being vague about whether students have learned something or not. And it's not good for students because they don't know that they haven't learned. They might be under the false impression that they've learned when they haven't, or maybe they don't care, and the parents don't know.
And then the parents can't advocate for their children, right? I mean, we assess students so that we can determine whether they've learned what we wanted them to learn, so that we can determine whether we're doing a good job, whether you as the teacher is doing a good job of teaching the material, and so that you know who needs support. Otherwise, you're just going to push students through who haven't actually learned the material. And frankly, I would think that would hurt at-risk students the most.
Do you think?
[00:25:05] Jonathan Regino:
Right. In Philip's case, he's taking an average of an average of an average to come up with a grade. So even the teacher is not going to know how a student is doing, let alone the student or the parent.
And in the end, if you don't know how a kid's doing, how are you going to intervene? How are you going to make sure that they learn the material to get ready for the following year?
[00:25:25] Anna Stokke:
Yeah, exactly. And I'll say, we have some schools in Manitoba where I live that are really doing wild things, like doing away with grades in high school. So, there's this ungrading movement.
So, the students aren't being graded. In some cases, it seems they're assigning themselves grades, which I just can't believe. And I mean, at the level I teach at, we have students coming in from high school, and sometimes they have these 95% averages, and they're really not prepared at all.
They don't know the pre-calculus material. And that actually doesn't benefit students in any way. You're just kicking the can, right? They're just going to get to university and crash and burn.
[00:26:10] Jonathan Regino:
Right. And it costs a whole lot more money.
[00:26:13] Anna Stokke:
Oh, yeah. It costs a whole lot more money. You got it.
[00:26:16] Jonathan Regino:
One of the last things he asked about was clarity and consistency with the grading system. And working within the system that he mentioned, I would suggest doing some blind grading. So, in this case, I would grade Anna's class. Anna would grade my class.
You put the student names on the back of the test. Nobody knows whose test is whose. And then after Anna's done grading it, I’ll grade my own class. And we kind of compare. Did I grade mine harder? Did she grade my class harder? Were there things that I taught that Anna might not have or that Anna taught that I didn’t or things that I focused on? And that allows you to, in the convoluted version of assessing that you're doing, at least have some consistency. And the conversations that come out of that really helps you hone in what you're actually teaching as a group of teachers.
So, it takes a little bit more time. But doing some blind grading, even if you do a couple tests and not the entire class, at least it'll put you on the direction of being a little bit more consistent and have a little bit more clarity and transparency when you're grading.
[00:27:20] Anna Stokke:
Love it. That's an awesome suggestion. Thank you for that. Okay.
So, let's move on to this question from Rebecca. And Rebecca says, I'm a first-year high school math teacher and new to your podcast but love it already. And it makes me excited about where math education is hopefully headed rather than lately feeling like I'm just bailing water and plugging holes with gum.
I'm hopeful that you could help me with appropriate class-wide intervention resources. I gave my students a quick skills check quiz. And while most know how to substitute a value for X and solve an expression, many couldn’t accurately write two thirds in decimal form rounded to the hundredth place without a calculator.
This is a school-wide and probably further trend. And next year, I want to add in more strategies for identifying and closing these knowledge gaps. In an early episode, you or your guests suggested spending 10 to 15 minutes every day on tier one class-wide intervention techniques.
And I think this is what I'm looking for, but I can't find any free resources. Could you please help point me in the right direction? So, Jonathan, you're the best person to answer this question. Any suggestions?
[00:28:40] Jonathan Regino:
I do. So, there's something called Delta Math RtI. It is different than Delta Math. So, there’s a Delta Math program, but this is Delta Math RtI.
That's all you have to put into Google, add the RtI, and you'll find it. It came out of something called the Intermediate Units in Michigan, the state of Michigan. Those units work at the county level, and they're supposed to work with any school district in the county.
Because it's a county-level program, it's free and it will always be free. So, it's called Delta Math RtI. It has tier two and tier three interventions.
So, they have a screener that you can do, but you don't even have to use a screener. If you are teaching numbers and operations or you're teaching fractions, you can just go to that section, pull it up. Tier two is one grade level below.
Tier three is two grade levels below. And it gives you step-by-step. I do; we do lessons.
There are eight lessons for every topic that you're doing. It starts off with the I do. So, the first lesson is all for you.
Now the lessons are meant for 30 minutes. In my school district, we do them in 15-minute chunks. So, we do that 15 minutes a day.
The first half of it, the first lesson, we do half of it the first day. The second day, we finish it. It comes with quick checks.
So, at the end of every lesson, there's a quick check to see how a kid's doing. They graph their results themselves so they can track their own progress, which helps with that generalization and the whole thinking through the problem. And then as a teacher, they have a spreadsheet that allows you to collect all the information so you can keep a log of how they're doing.
It goes K to Algebra. The K, because it goes two grade levels below and one grade level below, there's not a whole lot of content in K. And then Algebra, it does pretty well with the Algebra content. But from Rebecca's question, it sounds like you're hitting middle school and elementary level skills. So, this program would do really, it would do good things for you. The other piece, if you don't use Delta Math RtI, if you follow or listen to Amanda Vander Hayden or Dr. Sarah Powell, Dr. Sarah Powell actually has a book on interventions that’s really, really good. But both of them will tell you that what happens with a lot of interventions is we don't go far enough.
So, if you know a kid struggling on fractions, you need to figure out, is it an acquisition issue or a fluency issue? And there are two different types of interventions that go with each of those ideas. So, in your class, you have to figure out of those groups of students, is it that they just don't know how to do it? They haven't learned all the skills to be able to solve whatever content you're teaching? Or is it they know it, they're just not fast enough yet. They're making little mistakes here and there, but they have the general idea.
And you can do a class-wide intervention for either version of that issue, but you need to know which issue it is to intervene correctly. So, Delta Math does a good job of doing that for you. But if you don't want to use a program and you kind of want to do it based off of the content that you're teaching or use whatever resource you're already using, you need to get down to the level of figuring out if it's acquisition or fluency before you make a next step decision.
[00:31:55] Anna Stokke:
Wow, that's really useful. And I'm going to file that away because I get asked these kinds of questions a lot. And we're going to put a link again on the resource page to Delta Math that you mentioned.
Rebecca, I think Jonathan did a great job of answering your question, so I hope you find that helpful. Okay, anything else to add on that one?
[00:32:16] Jonathan Regino:
I've done presentations on this very question at the state level and national level. I'm happy to it's like FirstNet, I give everything away for free.
We're teachers, we're here for students, we need to work to improve our student outcomes. So, I'm happy to share a link to the presentation. Underneath every slide has all the notes and connects you to all the research papers and all the locations where I found my information.
And really, if you want more information, my contact information will be in the podcast. Just reach out. I get contacted from all over the country with simple questions like this to more complex.
I have a student who has X, Y and Z. Reach out. We're all in this together, and it's all about improving students.
[00:32:59] Anna Stokke:
Yeah, that's very, very kind of you.
So, thank you for that. And we'll post the presentation then.
Okay, next question.
And this question is from Abu. And Abu says, I am a math teacher and an engineer. I teach in Canada, high school calculus, statistics, computer science and IB math courses.
I've been struggling recently with differentiation. It seems that so many students have huge gaps in fundamental skills like multiplication tables, GCD, LCM, etc. That teaching more advanced yet simple skills such as factoring functions and other pre-calc skills has become extremely challenging and almost impossible.
And these kids are losing interest. They feel frustrated. Their working memory is overloaded trying to work on these new concepts while still struggling in fundamentals. I'd like to hear how we can accommodate these students to help them catch up with their peers, because simple differentiation doesn't work when the gaps between students is so large.
Okay, so we hear this a lot, right? So, what are your thoughts on this?
[00:34:11] Jonathan Regino:
In reality, I don't think people are going to like my answer, but I don't think differentiation is realistic. To truly differentiate, you're asking teachers to essentially personalize or at least create a lesson for four or five different groups that are in your class. And no teacher can do that for 180 lessons or 180 days or however long your school year is. It's impossible. You're going to burn yourself out and you're just going to struggle.
Bigger question I have for a district is how can you make it to calculus and not have a firm understanding of fractions? That is criminal to allow a kid to make it out of middle school not knowing how to solve fractions and to put them in a calculus class where you know they’re not going to be successful. It's the same idea of sending them off to college and they had to take remedial math courses because they really didn't learn the content. That's a systematic issue that needs to be addressed immediately.
And you're talking about going back to kindergarten and looking at kindergarten and first grade and fixing the issues as quickly as possible. Now, the reality is in your class right now, whether you started school or you're about to start school, you're in that situation. So, what you need to do is take the problem that you want the kids to be able to do by the end of class and break it down into its most minute steps.
So, if I'm factoring, I'm breaking it all the way down to multiplication. Even if I had to go a repeated addition. But you want to list out all the skills.
From there, you want to do some simple problems to warm up your class. So, if my class is at the multiplication level, I might do one or two multiplication problems that's going to lead them to one of the harder problems at the end of class. So, if I know at the end of class, they're going to have to do eight times six, I might start with a warm-up problem of eight times six. And I'm going to have the kids do it, practice a couple multiplication problems, and I'm going to add on the next step. So, if it's distributing, I'm going to add in a couple simple distributing problems, make it a little bit more complex, and kind of build over time. It takes a little bit of time, but what you need to think about is you're teaching for three minutes, they're practicing for five minutes.
You teach for three minutes; they practice five minutes. And you keep adding their skills up until you get to a level that's somewhat close to what you need them to be to be able to do the level that you're teaching. It's going to take longer. It's going to slow your curriculum down. But at the end of the day, if they can't do the previous skills, they're not going to be able to do your content anyway. If you give them a calculator or you show them how to do it, it's a band-aid.
It's a type of problem where they know it just for today. Tomorrow, they show up and you won't be able to do it. Or they can do it just well enough to get to the test, and the day after the test, it's like you've never taught it for them before.
We've all been in that situation, and that's why it's happening. Because they don't know the content well enough, they haven't internalized it, they haven't put it into long-term memory. So, we need to simplify, take the itty-bitty steps, and build up, build up, build up.
But meantime, the district level needs to correct the issue that allows a kid to make it out of middle school without a solid understanding of fractions.
[00:37:19] Anna Stokke:
You are 100% correct. And I know that this person did write in from Canada, which I'm pretty familiar with. And we actually don't stream as much in Canada as you do in the United States. So you might be, this teacher may be in a situation where the students aren't streamed till grade 11. I'm not kidding you. So that happens in some provinces in Canada. And so now this teacher is in a really bad spot, because they've got students who can't do basic things. I'm certainly familiar with students in calculus classes who can’t factor in things like that, but they can usually add fractions, and they know their times tables.
If they don't, they will not pass the class. Like I don't know, like you said, I don't know how you could go back that far and possibly succeed in calculus. I would say too, like, it depends what the issue is.
If it's like you're teaching something that relies on factoring and the student actually did master factoring once, but they forgot it. That's a different issue than never having mastered factoring, right? So, if it's an issue where they've just forgotten how to do it, a good idea is to give them some practice problems to review that prerequisite content before you're going to teach the next concept or review it at the beginning of class, right? Like it's always a good idea to bring back that prereq material. It will help the students.
[00:38:46] Jonathan Regino:
Craig Barton and Ali Lavelle. So, Craig Barton has a podcast and Craig Barton and Ali Lavelle have been arguing about the ‘do nows’ for an entire summer. So, 15 minutes of class and they still haven’t made it past the ‘do nows’ yet, but they talk about that preparing students for what’s coming up.
So, your ‘do now' is so critical to bring in their skills to help kids warm up and practice and get ready for you as a teacher to know how much further back you have to go or how fast you can fly. But if you have time, Craig Barton's podcast are close to three hours sometimes, but they get down to that nitty gritty step-by-step of every aspect of an entire lesson. Like I said, they spent a whole summer on do nows and they haven't completed the do now yet, but you walk away with a complete understanding of how to build that beginning of a class to do what you just shared of if a kid learned it and they mastered it, but now they forget it, how do we bring that back and how do we get them ready for today's lesson?
[00:39:48] Anna Stokke:
Yeah, exactly. I mean, if you have homework that you can easily sort of manipulate the worksheets, like I actually use online homework, so it's really easy for me to put in problems that are not in that particular section. And so, then it becomes easy to put in those things that they need to practice before they're going to be able to learn this new concept. It's really quite easy. But I mean, of course it can be hard to design all these worksheets, but there are lots of resources out there that would help. I will mention too that I actually asked one of my teacher friends named Max about this because he actually is in this kind of situation. He teaches in Canada.
He teaches exactly what you're saying you teach, that Abu is saying that they teach. So, he teaches high school calculus, statistics, computer science, IB, math. And I asked Max what he does in this situation.
And so, I'm going to read out what he said. So, he said, I don't think there is a silver bullet. These things are much easier to correct earlier on, as we're all saying.
So, when someone is near the end of their high school career and still struggles with fractions, it's tough to move them forward. I think that's why so many high school teachers are frustrated with what's going on in early and middle years. And I would include all those multiple strategy type approaches that are maybe preventing kids from actually getting good at any one skill.
So, Max says it's extremely hard to differentiate at those higher levels since the content being delivered is so specific and requires so much prerequisite knowledge. But he says there's no shortcuts. Learning math takes time.
But he mentions that something that he does is he helps students during lunch hour workshops. So, you know, he's putting a lot of time in. So, after quizzes or tests, I often record skills that need attention, even if they're basic skills that they should have picked up years ago.
Then I'll have students sign up. Attendance is much better when parents are told what's going on. And then I'll print off enough worksheets for everyone and do a ton of examples and have them work on it for the remainder of lunch.
Sometimes if there's a student who I know needs help but hasn't signed up, I'll talk to them ahead of time and suggest that they come. This has been pretty successful in my experience. And I often have students who aren't mine even show up.
And I think that speaks to something. Students actually do want to learn this stuff. At least that's been his experience.
So, I thought I'd read that out in case it helps people too.
[00:42:27] Jonathan Regino:
That made me remember there's a program called You Teach You. And we’ve been testing it out over the last couple of years.
But the program was designed with work examples. And it's called You Teach You because it's meant for a kid to go through the program themselves. Teacher comes in and they check, and they make sure that things are going well. But it's designed in a way where there's micro steps so that a kid looks at the work example, mimics it on the next page. And then each time they move to the next page, some of that work example disappears. And then eventually they're doing the whole problem on their own. And it's a way to get those kids to practice when you don't have a ton of time or they can't come in during lunch. You could assign some of these work problems and these work pages and allow them to kind of build up their skills on their own or during some down time.
[00:43:18] Anna Stokke:
Okay, good suggestion.
All right, I'm going to move on to the next one. And I'm just going to answer this one myself. So, you get a little bit of a break.
This question is from David. I have a question about the Nick Gibb interview. So that's an extremely popular podcast episode I did actually with Nick Gibb. So, David says he talks about measuring multiplication fact fluency but allowing students six seconds to answer the problem. So just for a bit of background information, Nick Gibb was the minister of state for schools in England, and they implemented a mandatory times table check at age nine. And the students are given six seconds to answer each question.
So, David is asking, why six seconds? And he mentions that this seems to contradict the recommendations from Brian Poncy, who's kind of a folk hero on this podcast. Everybody's always talking about Brian Poncy because, well, he's great. And in the episode with Brian Poncy, we talked about fluency being 40 to 60 math facts correct per minute.
And David mentioned that Brian Poncy's requirement, they even include the student actually writing the answer. Well, in England, this times table check is a verbal response, so presumably faster for the student. So, David writes, why six seconds? It seems too long. That does not seem like no from memory. Okay. All right.
So, I first want to point out that the times table test is a mandatory requirement for age nine students throughout England. Making a requirement like that would bring in some opposition. All right.
So of course, we want students to know math facts automatically, and that should really be instantaneous. But there's a difference between that and having a mandatory countrywide test that's required for every student. So, I think Nick Gibb had to balance a few things out there to actually get this to happen.
And so, in fact, when I talked to Bruno Ready for the podcast, I asked him about this because he's in England and he has the Times Table Rockstars program, and he knows a lot about what's going on with times tables in England. And Bruno mentioned that when they were drafting the policy, they started with five seconds, and it received a lot of opposition. And so it was then softened to six seconds.
So, Bruno said that as much as three seconds would be good from a policy perspective, that would be tough. I think putting a number on it at the very least has been enough for a seismic shift towards learning the tables in a way that we didn't have before. In other words, despite it being six seconds, the times table check is serving the purpose that it set out to.
Besides, with most kids using Times Table Rockstars to prepare for that test, Bruno says he can tell us that the reality is that they're actually much quicker than six seconds, more like 2.8 seconds on average. If anything, teachers are trying to get them to slow down when they're writing that times table check so they don't make mistakes. And he also mentions that there have been positive spinoffs in getting teachers to level up their teaching of the times tables relationships and concepts, and that has trickled down into the teaching of addition and subtraction facts, not universally, but noticeably.
Okay, so to recap, I think we all agree, and I'm sure Nick Gibb would agree too, and Bruno, and that we do want those times tables to be instantaneous, but that's different than having a times table check. And the times table check does allow more time because it's a policy, and at the end of the day, it actually has helped to ensure that teachers do focus on that and that students learn their times tables. So, I hope that answers your question, David. And I would love to a times table check here in Canada. How about you, John?
[00:47:29] Jonathan Regino:
I would second that for the United States.
[00:47:32] Anna Stokke:
I would take six seconds. I'd probably take 10. So, I think it's pretty great.
Okay, so this next question is from Robin, and Robin starts by talking about issues with their children, learning math, and then mentions having to teach math. Then Robin writes, My U.S. kids struggled with math, and I ended up supplementing and reteaching them. One concern I had was the spiral-based math curriculum, which quickly introduced topics, fractions one week, geometry the next week, each year. Because these topics were familiar, when reintroducing them, my kids assumed they already knew the info, and it turned out when the harder info was introduced, they couldn't do it.
But even more concerning with these spiral lessons is that topics moved before mastery was achieved. Then my kids had gaps in their knowledge like Swiss cheese, and it was hard for me to figure out what fundamental concepts they didn't know. Fast forward a few years, and I've been hired to teach middle school math at a Catholic school in the U.S. All the textbooks are spiral in style.
I think they are moving so fast they don’t get past the acquisition stage. To be clear, I think review is important, but I just think that a deeper dive into math topics is critical, more critical than what I'm finding in these curriculum. Are there similar curriculums being built for math using the science of learning as there are in the science of reading? Thank you for your help.
Okay, so what do you think, John?
[00:49:06] Jonathan Regino:
So, if you talk to a teacher about spiral programs, they all feel guilty. No teacher likes to have a kid say, I don't understand, and then you respond with, it's okay, we're going to come back to this in a month. Don't worry, you'll learn it then.
Nobody believes that, and nobody feels good about moving on when a kid doesn't know something. We're teachers. We want to teach kids.
Why would we move on when they don't know it? If we follow cognitive science, we should be starting with block practice, moving to interleaving in space practice. The program should be built that way. It makes no sense to have a program where I just introduce something and then we move on.
It takes sometimes three weeks to master something. If you're teaching it every day, it could take up to three weeks. You need multiple touches on something. If you are spacing it out over an entire year or over a couple months, the curve of forgetting says that we're going to forget this stuff by the time we come back to it. So, if I introduce something and three weeks from now come back to it, I'm starting over. There are very few kids that can retain that information over a long term.
I think the bigger issue for what I see is there’s an iceberg effect in math.
So, if I'm in sixth grade and I just don't understand one piece of content, let's say one topic, when I get to seventh grade, I'm automatically out on that one topic, plus the two others that are attached to that. And then when I go to eighth grade, now I have the three topics from seventh grade and now it's going to be like six or seven topics in eighth grade.
At that point, I went from one topic in sixth grade to maybe a quarter of the material in eighth grade that I'm automatically out on because I didn't learn the material in sixth grade. When we do that spiraling, we're doing that to kids. We're saying, it’s okay that you don't know it, but math is hierarchical.
So, I didn't master that first topic. Can I really do the next topic in the book? Or was the textbook written so I don’t need to learn anything before whatever I'm learning? I can't imagine the textbook is written that way, but if we're spiralling, it has to be written that way. I worked for a company, and they called the math problems red bricks.
And if you think about a bridge that's made out of stone, like the old Roman bridges, you could pull stones out of that bridge, and it would still stand. But there are certain stones, if you pull out from that bridge, the whole thing falls apart. If you think of math that way, there are certain topics that yeah, you could spiral and a kid not get it and that would be okay.
But there are certain things that if a kid doesn't understand and doesn't master, the whole bridge falls down and everything in math falls apart. And we know this happens because at the end of third grade, when we start multiplication, it breaks the class in half. You have the kids who are ready for multiplication and the kids who are.
And by the time you enter grade, it's clear cut who's going to do well in math and who is not based off of if they know their multiplication facts or not. It's a red brick and we all know it and yet we haven’t fixed the systematic issues that are causing it.
[00:52:12] Anna Stokke:
Yeah, very well said. And I have to say I think the idea of spiralling, I think it's kind of confused sometimes maybe with interleaving and space practice. And honestly, I'm not sure half the time what people mean by spiraling either, but I have heard people use it in certain contexts like, oh, don't worry if your kid didn’t get that this year because we're going to hit it again next year. And that's an issue, right? So, there is a lot of research evidence backing up space practice. And space practice, though, the idea with space practice is that you've actually learned the topic. So, you've learned it to mastery. And it's very normal when you've learned something for the first time, if that's the first time you've learned it.
And you may even be really good at it. You may be fluent with it. And you might come back to the student three, four weeks later and they forget how to do it.
Right. But they actually learned it the first time. So then when you they've had that chance to just forget a little bit. And then when you review it, you get them to review it. They bring it back and it gets stronger. Right.
So over time, when you do this sort of thing with space practice, then you the student is more likely to retain that information long term. So that's the idea behind space practice. But space practice requires that you learn the topic to mastery in the first place.
Right. Okay, so then the other one I want to mention is interleaved practice, because I think a lot of times people are getting that mixed up maybe with this idea of spiralling, which, again, like I don’t know what people mean half the time by it. But with interleaved practice, again, you want to do blocked practice first.
So, you want to do a lot of practice of that topic. And so, one example I often use when I when I talk about this is word problems. So, if you're doing addition, subtraction, word problems. Right. So, to a student, those may look very similar. Right.
So, if you start interleaving those right off the hop, it's going to be really confusing for them. So, you do a lot of addition word problems until students get good at them. You do a lot of subtraction word problems and then you start mixing them up.
That's interleaving. Right. But you have to do that blocked practice first.
So, I think sometimes people are getting a bit confused about this, but it sounds like the textbooks are using this spiralling idea.
[00:54:53] Jonathan Regino:
Yes. Yeah. So, I have to talk to a lot of salespeople, and they don't understand the terms either. And they've used the terms incorrectly, which is why you always need to get a copy of the textbook and look through it. Robin mentioned programs.
And actually, this is where I love the power of the crowd, because I am looking for programs from algebra through calculus to follow the science and math and cognitive learning and things like that. And I've yet to find a program that actually follows some of these rules at the elementary level and even the middle school level. There are a couple that I think do a really good job of mastery and interleaving and space practice.
And the things that come right to mind are Ali Lavele's explicit math program that's still in its infancy. I was hoping that he would magically finish the program and have a through eight done before the school year started. But he has the beginning of elementary completed.
My district uses jump math, which I think does a very good job of focusing on mastery and doing those micro steps and interleaving along the way and space practice along the way. Outside of just a handful of programs that you can use school-wide and classroom-wide, it's very tough to find programs like this.
[00:56:14] Anna Stokke:
Right. And David Markunas is also working on that explicit math program, right? So, I think he sent me it or I looked at something and it looks like it's going to be great. So, we're going to keep our eye out for that one. And yeah, the program I usually recommend is jump math.
So, jump math is really good at scaffolding. So, it's excellent for that. And you're using it in your district. I didn't know that. So, it's actually a Canadian charity. And I know John Mighton fairly well.
So, I'm glad to hear you’re using it. And actually, we kind of went back and forth because there was a question that came in about Saxon math, and we weren't sure if we wanted to cover that one. But I'm going to bring it up right now just because Saxon math actually is another program.
I like those textbooks because they're really good at the spaced practice. That actually isn't very common that you see that textbooks will bring in topics from previous units into the exercises. And Saxon actually is pretty good for that.
[00:57:20] Jonathan Regino:
That's one where the salesperson didn't understand the idea of spiraling and was trying to sell me on the idea that it's a spiral program instead of the space practice and the ideas that are actually in the program. So that's one where, like I said, you need to actually get the physical book in front of you and look through it page by page to really know what's going on.
[00:57:43] Anna Stokke:
Yeah, exactly. But yeah, my daughter actually used Saxon math in middle school. And that actually was an advanced math program here in Canada. And she really learned her math really well. Like she was really well prepared for algebra through that. So, I was kind of impressed with that program. But yeah, those are the only two that I know of that kind of do a good job with some of these science and learning techniques.
Maybe you should write one, John.
[00:58:12] Jonathan Regino:
When I worked for Age of Learning, I spent an entire year developing how to teach word problems as a standalone content area, just the same way that you teach multiplication. Like, what if we removed it instead of being at the end of a lesson or separated from a lesson if it was just its own content area? And it was an entire year of just working on that one idea, full-time job.
So, the idea of writing an entire curriculum, I would love it because that puzzle would be amazing. But there are people who have already started and have done a really good job of writing programs. I just need them to move up to algebra in high school content.
[00:58:51] Anna Stokke:
Absolutely. And I think we should, because Robin was asking, again, as you mentioned, about curriculums being built for math using the science of learning, we should perhaps mention Amanda Vanderhaeden's Spring Math. So that's more of an intervention program, but she's just amazing.
And she knows the research inside and out. And then the other is Brian Poncy's MIND program. So that one is for the basics, basic skills, like learning your times tables and basic arithmetic. So, I'd like to mention those two as well.
So, Jon, I think we came to the end of the questions that we were going to cover. So, do you have anything else you want to add? I mean, you're here, and I'm just so happy to have you. And if there's anything else you want to add, you want to say about teaching math, here you go. Go for it.
[00:59:44] Jonathan Regino:
I think the best thing about being on these podcasts and going on and presenting is the connections. I have a monthly call with somebody down south in the United States that we're both doing Jump Math and Spring Math, and we're the only ones in our areas doing it. So that being able to collaborate and talk through these questions, I think so many times, and you can see it from the mailbag questions that you get, so many times we feel alone in this work. And especially those of us who are trying to move in this direction, like the science of reading had gone, you feel very alone, and you feel like the entire math national movement is not moving the same direction as us.
So, connecting and reaching out and talking, your podcast, it's just given a breath of fresh air and hope, and it doesn't feel like we're so alone in this.
So, I really appreciate the opportunity to be on here. I appreciate the questions and the opportunity to share some of the knowledge that I've built up over the year.
[01:00:43] Anna Stokke:
Well, I really appreciate that you came on, and you did a great job of answering these questions, and it's really going to help the listeners and particularly the people that wrote in. But as I always say to my students, ask the question because there's 20 other people in the class that have the same question. And in this case, there's thousands of people out there that have the same question. So, I go through them, and I don't answer all of them. Sometimes I can't answer them, but we answer as many as we can and hopefully it helps.
So, thank you so much for coming on and helping out today and sharing your expertise. I really appreciate it. And it was lovely to talk to you.
[01:01:24] Jonathan Regino:
You as well. Thank you. Thank you.
[01:01:26] Anna Stokke:
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