Math is Supposed to Make Sense

In recent years, Oakwood Elementary School has refined and enhanced the way that math is understood by teachers and students alike. This period of reflection on the school’s practices has caused a number of new and innovative ideas to take shape in classrooms and inspire students from kindergarten to sixth grade.

Along the way, Oakwood educators have given this project focus by studying best practices in teaching math from around the world. The work of scholars such as Stanford professor Jo Boaler and former National Council of Teachers of Math president Cathy L. Seeley, combined with careful examinations of curricula such as Singapore Math and Math in Focus, have given light to the inexorable link between conceptual understanding and procedural fluency. Or put another way, there is a renewed emphasis on teaching why a math problem makes sense, in multiple ways, rather than solving problems with computation alone. Concrete and visual representations, manipulatives and model drawing, word problems and abstract thinking all help students to truly make sense of math.

In line with the first goal of Oakwood’s Statement of Philosophy, “To guide students towards mastery…,” this evolution in math thinking has led to new perspectives on academic rigor. Previously understood as giving students harder problems, teachers now lead students toward higher levels of complexity in thinking, reasoning, and understanding. And drawing on a key concept of Singapore math, students are being taught to master fewer concepts, but at a greater depth.

The sum of this all is a change in the math mindset at Oakwood School. Associate Principal Denise Ross captures this by saying,

What does it mean to be proficient in math?

Saying that a person is proficient in math can have many different meanings, depending on the type of math that you’re looking at, but we’re really thinking about being proficient as having a deep conceptual understanding of math. It’s not just looking at a multiplication problem and knowing how to multiply, or knowing the basics of how to subtract with regrouping. It’s about an understanding of what it is that you’re doing so that you can apply that in a variety of situations. The goal is to be able to solve problems and to learn to persevere when things get challenging. Students who are proficient in math can think flexibly about the problems that they encounter so that they don’t just see one way to do something. That’s what we’re trying to instill in students here.

Is one of the benchmarks to math proficiency seeing how you can apply math to other areas of your life?

I think so, because one of the higher levels of thinking is being able to take what you’re doing and then apply it in a variety of relevant scenarios. If students can only follow the steps or the procedure, then you don’t know if they truly understand the problem. But if they can take the problem and apply it in unique situations, then that gives you some indication that they really do have an understanding of what they’re doing.

Can you explain why the focus of math instruction at Oakwood is more on the process than the product?

We want to focus on the process because there are so many good conversations and strategies that can come out of whatever the process is. For example, in one lesson in the sixth grade classroom, students look for patterns in circles. In that kind of exercise, it’s hard to show a finished product, like, “Ta-da! Here’s what we did,” but through those conversations that the students have, they are able to make discoveries that they may not have made on their own. We’re focusing on those conversations, and we’re focusing on the process of how they’re learning the information, rather than just, “Here’s twelve problems that we did, and I got a 100% on the page.”

Sometimes, it’s difficult to see the end product of what they are doing, but it’s important, instead, to see the richness and the learning that comes through the conversations that they’re having with one another and to see that they’re working together and collaborating to find new strategies and solutions.

Teachers at Oakwood talk about “positive math culture.” Can you explain what that means?

Positive math culture means that students feel like they have a safe place to do math. They know that it’s okay to make mistakes. They know that mistakes are a good thing. They help grow your brain, and that’s where the real learning happens. When you have this positive math culture, kids get excited to do math. They want to do it. They’re raising their hands, they’re jumping in, they’re looking for challenges. It’s not just, “Oh, we’re opening the workbook to page six, and here we go.”

How is this positive math culture embedded in the school’s overall culture and environment?

A positive culture is present everywhere at Oakwood. Math has always been important here, but we’re finding new ways to make sure that kids know that math is accessible to everybody. As you can see around the school, a growth mindset has been a big focus, as has specifically and explicitly translating that into learning math so that we can show how it’s okay to make mistakes. That’s how we’re going to learn and get better at it. This idea permeates everything.

How do students take responsibility for their own learning at Oakwood?

Students are naturally taking responsibility for their own learning, and their own thinking and understanding, because of the types of activities and tasks that they’re being asked to do. It’s not enough to just say, “I finished this worksheet,” or, “I did these three problems and now I’m finished.” The challenges and the tasks that we’re trying to have students do don’t always have an end point. We call them low threshold, high ceiling. There’s always more learning that they can do. You might have answered a couple of questions, but how could you challenge yourself and come up with another question to answer, or a new way to look at things?

In the fifth grade classroom, you’re seeing the students build rocket ships, and the goal of that is not just to see how you can fill the rocket ship diagrams with shapes, but to ask how many different ways can you do it? We’re constantly looking for ways that we can extend and continue the learning.

Can you talk about the process of self assessment and how individual students decide when they are ready for assessment?

Self-assessment is something that we’re doing so students can take responsibility for their learning. We want them to feel like they know where they are, and they know where they need to go. Part of that is being very clear with the objectives and the learning goals that we want them to accomplish. We’re trying to embed ways that students can self-assess, and I think that’s pretty prevalent at Oakwood overall. There’s a lot of metacognition going on—students are always thinking, “How did I do that?” or, “Why did I do that?”

How do students draw on what they learned in previous years? It seems like these students aren’t just skill building but also confidence building as well.

Part of that is the positive math culture we’re building, spending time at the beginning of the year, before you even get into the math part of things, talking about growth mindset and how it’s important. It’s okay to make mistakes. It’s important that you try something and take a risk. That’s the precursor to skill building. Oakwood hasn’t changed programs, we’re just evolving so students don’t feel like there’s only one correct way of doing something. We’re trying to help them see that there are many different strategies and ways to approach a problem, and that one strategy might work for you this time, but a different strategy might work for you next time. It might not even be the most efficient strategy. You’ll get to an efficient strategy eventually, but at least you have a way that you can try to attack a problem.

Many Oakwood students say they have had moments when a teacher really connected with them. Can you talk about that teacher-student connection, as it is related to math?

Having a strong student-teacher connection is a central part of the Oakwood philosophy. These students know that they can go to their teachers. They know that their teacher is a positive role model, a positive confidant, a positive person that they can trust and work with. That is just the culture here in general. To translate that to math has actually been easier than I anticipated. Our teachers have completely jumped onboard with these ideas and are even more excited, now, to teach math than they were before, and that’s translating to the students being excited. It’s just fed this energy.

This is my first year, but so many parents have reported that their kid didn’t love math like they do now, or they felt like they couldn’t do math like they can now. Part of that is because there is that strong connection between the teachers and students. It’s part of the Oakwood way and the Oakwood philosophy. Now, we’ve just taken that and extended it into math.