I get asked all the time about my thoughts about a certain math resource or textbook. Now, I don’t have the time to look at, nonetheless use, every textbook or resource that’s out there. So instead of telling you what I think about certain resources, I thought I’d share with you how I evaluate math resources so that you could use a similar strategy when you are presented with something new.

I’m Christina Tondevold, The Recovering Traditionalist. And today, we’re gonna take a look at Evaluating Elementary Math Resources in our quest to build our math minds so we can build the math minds of our students.

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EdReports evaluation of math instructional materials

What Is The Concrete Representational Abstract Approach?

When districts are evaluating math resources, they typically are just looking to see if the resource meets all the math standards for each grade level. If that’s all that you are needing, take a look at EdReports because they have done that work for you.

When I used to sit in with districts when they were doing their evaluations, I was actually looking at different things. Every resource that you can find will pretty much cover the standards. But the question is, how are they covering the standards? Here’s the 3 things I look at to see how a math resource is covering the standards.

Is it focused on problem solving or answer getting?

I can just skim through the book and look at the types of assignments that they are giving kiddos. Does the resource have 50 problems or 5 problems? If it has 5, that tells me that it’s allowing for time for the kiddos to solve problems and even have time to discuss how kids were solving them. If there’s 50 problems you can tell that the resource is really focused on just getting the answer because to get all those problems done you have to just focus on answer getting. 

Do the lessons include C-R-A?

C-R-A stands for Concrete, Representational, and Abstract. This is the idea that it isn’t just the symbols on a piece of paper. Kids need to work and play with mathematics, and so they need the experiences of using Concrete things, concrete manipulatives, to play around, build their understanding of mathematics. The R stands for Representational-It’s having some kind of representation of my thinking. That can be with a model, like a number line, but it’s anything where kids are modeling their thinking using some kind of representation on the paper that isn’t just the equation. That’s what the abstract level is, it is just the symbols. Like 7 + 8 = 15. 

So does the resource allow for kids to use all three of them? Is it including all three of them? Are there opportunities for kids to play around with all three of them? My preference is to do all three in a single lesson, but that doesn’t happen all the time. 

There are times when you’re just working in concrete. There are times when you’re just in abstract. But when you can do all three, that’s when you start to see a whole lot of light bulbs come on. 

Are the three areas of rigor showing up? 

When we think about rigor, we tend to think of it as just being harder, right? But actually, when we’re thinking about rigor in mathematics, there’s three areas of types of problems that kids need exposure to, and that’s what makes mathematics rigorous. 

• Kids need types of activities that are building their procedural fluency. 
• They need activities that are building their conceptual understanding.
• They need activities that are asking them to apply it into a contextual situation. 

All three of these make up a balanced approach to mathematics. 

If one of those is missing, that stool is going to fall over. It’s going to be unsteady, and that is essentially what happens to our kiddos and their understanding of mathematics. 

If your textbook, or your resources, are only focused on procedural fluency, the kids are going to have an unbalanced idea of what mathematics is about. Their understanding of mathematics will not be steady. The same is true if your textbook is fully focused on conceptual understanding. 

If all they’re doing is building conceptual understanding and there’s not a whole lot of procedural fluency type tasks, that’s not a balanced approach to mathematics instruction. So whatever your resource is, check to make sure it is including things that have procedural fluency, that make kids apply it to real-life situations, and build their conceptual understanding. 

You will also see these three show up in your standards. Dig into your standards and look at the wording. 

Some grade levels have more procedural fluency-type standards, while in some grade levels, you are more focused on conceptual understanding. So your resources should reflect that. 

As you look at your resources and you try to look at that in comparison to your standards, don’t just look to see if it has tasks about place value and about adding and subtracting within 20.  Does it have tasks that include all three of the areas of Rigor? 

To make a decision about what you think about a resource, a textbook, whatever it might be, it’s not just are they covering the standards. Because pretty much every resource does that. It’s how they’re covering it. 

Is it focused on answer getting or problem solving? 

• Does it include opportunities for kids to work in concrete, representational, and abstract? 
• Does it include the three areas of rigor (conceptual understanding, procedural fluency, and application)? 

I hope that this has helped you build your math mind so you can go build the math minds of your students. Have a great day.

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