Teaching Math The Right Way – Part 1: Balanced Math Instruction

I have a question for you. Are you teaching math right? Well, that is a huge question and could mean so many different things, yet I get asked it a lot. Today I’m going to start a mini-series about “What It Means To Teach Math Right” and the three areas when people ask me that question, that they’re really wondering about. I’m going to start off on a soapbox I tend to get up on a lot. It’s whether or not we should teach conceptually or procedurally.

Watch the video or read the transcript below.

What do I mean by Conceptually & Procedurally

First, let’s talk about what it means to teach math conceptually and what it means to teach math procedurally? It’s a huge question, so I’m going to summarize it in a way that some people may say is way too simple. But for our case here, I want to talk about the two distinct differences between teaching conceptually and teaching procedurally.

Procedurally was basically the way I grew up having math taught to me. It was taught as a set of rules and procedures that I was supposed to memorize and apply on problems that usually had no context to them. It was the typical traditional math book where it was a sheet of 50 pages in the book, or maybe a worksheet, and it was just bare problems. It was just repetition after repetition to see if you could get all the problems done correctly. It wasn’t about how you did it. It was all about whether or not you got the answer correct.

Oftentimes, when people are talking about teaching math procedurally, that’s the vision they have in mind. This is when we focus on procedures and getting kids to practice, practice, practice, and we’re focusing on the answer…“Did they get the answer correct?”

The flip side of that, is when we’re talking about teaching math conceptually, and again people may have a more in depth version of this, but to me conceptually teaching is a focus on how kids are doing it. Typically, it’s focused on helping them understand why we’re doing those procedures, and not so much even a focus on a specific procedure. Traditionally, procedural type of mathematics is that there’s only one way to do it. Conceptually teaching mathematics is, letting the kids do it in a way that makes sense to them and then looking at other ways that kids did it.

Often they are given mathematics in a contextual situation. It’s put in real life terms or it’s even a problem that’s given to kids with no predetermined path. It’s what’s often called a non-routine problem. There’s no one set way to solve it. It could be approached in lots of different ways and you’re really helping kids to see how mathematics can help them solve a real life, non-routine type of problem.

History of how it was done in the past (pendulum swings)

Now, what has happened in the past is that in education, we tend to go all in on something. So, for awhile it was all about “skill and drill” and just teaching the procedures. Just do the math and it didn’t matter how you did it. For some teachers, it mattered how you did it, but the real focus was on getting the end result. Then they realized that wasn’t working for some kids and maybe even a majority of kids, so we swung the complete other way and it becomes all about letting kids just discover mathematics and play and talk about how they’re thinking about math without a focus on still getting to an answer. Anytime we go all in on something, it’s often not the best

because I am a firm believer in balance and in mathematics kids need balance as well.

If you aren’t familiar with the whole history of math education, there is a great book by Matt Larson called Balancing the Equation and he talks about the history of how we’ve had these pendulum swings and how it really needs to stop.

Choose a Balanced Approach

I am a firm supporter of that idea. Kids need both. Kids need to develop that conceptual understanding and play with math and see how it relates to their lives and see that, “Man, if I don’t get it this way, it’s okay, I understand it this way.” But they also do need to know that sometimes there is one right answer and sometimes we just need to practice because, with anything in life, we get better if we practice.

If we’re going all in on conceptual understanding for kids, we’re leaving off that ability to practice the stuff that they have learned. We understand it better and we do better if we continually practice. If we go all in with procedural understanding, we come away with kids like me, who think they are good at math but are really only good at following steps and procedures. When I had a real life math problem, I was horrible at it and I had no thinking skills. I would see a problem and if I didn’t instantly know how to solve it, I would shut down because I wasn’t sure how to approach it. I couldn’t remember the steps I was supposed to take.

Neither one of those alone is good. It doesn’t bring a well-rounded understanding of mathematics to our students. We need to balance our instruction. If you want to make sure you’re teaching math right, the first thing that I would recommend is to balance your instruction, and I’m not saying it’s an easy thing. It’s a hard line to know when you’ve crossed it. “When am I spending too much time focusing on procedures?” or “When have I let them play enough and now it’s time to move on and get them to practice?” It’s not an easy feat and I can’t tell you that once you do this few activities then it’s time to just start practicing.

It depends upon your kids, it depends upon their experiences. Sometimes it even depends upon the models that you’re using and the visuals that kids have. Sometimes that can make it easier and faster for them to move on into that procedural practice stage.

You’ve just got to know that you need to have a balance of both and be cautious with your teaching. If you feel like you’re swaying too far one way or too far the other way, think about how you can bring in the other.

I’ll tell you the one thing that makes it even harder is that textbooks tend to be one way or the other. There’s not a whole lot that is down the middle. You either have a really procedural type curriculum or you’ve got a conceptual type curriculum. Know which one yours is and just know you’ve got to bring in other. People ask me all the time, “What’s the best curriculum?” There isn’t one because they’re all lacking in some way. Definitely, there are people out there working to change that and starting to move in that direction, but at this time there are not ones that I can say, “These do a great job of it.” All curriculums are going to have their issue, but just know which side they are on and know that you’ve got to bring some of the other in and just reflect upon your own teaching. No matter what curriculum you’re using, are you doing a balance of both for your students?

I hope that this helps you build your math mind a little bit more about what the right way to teach math is, and I hope it helps you go out there and build the math minds of your students. Don’t forget to check out Matt’s book, Balancing the Equation. It’s a wonderful read.