Executive Functioning in Math

I have always been very interested in the processes involved in learning and engaging in math. In fact, I had to wonder if so much of what makes math difficult and anxiety provoking for many, is actually due to how we are able to organize, monitor and focus on the math — rather than the math itself.

Math is more than just about understanding and recalling important numbers and constructs. It is also about the processes that help us to get there. Many of these processes fall under the umbrella of ‘Executive Functioning’.

What is Executive Functioning?

It basically encompasses 3 main categories: a) someone’s working memory capacity; b) the ability to be flexible thinkers and ‘shift’ thinking to incorporate new learning, and c) the ability to inhibit distractions and unwanted information.

Are students the only ones who struggle with executive functioning?

Executive functioning affects kids and adults alike — and has nothing to do with someone’s IQ. There are many very successful professionals out there who struggle with executive functioning in different ways.

Therefore, it seems reasonable that when we attend to our students executive functioning needs, then there would be universal strategies and processes that we can design that would good for everyone, but necessary for some.

How does executive functioning apply to mathematical learning?

As a math coach, I work in our board to help teachers engage with students to learn how to problem solve and push thinking to new levels.

Can executive functioning improve mathematical problem solving?

We all know students who struggle with math, and problem solving in particular. High-stakes standardized tests will provide evidence of this as well. But what can we do to improve the problem solving?

Let’s first think about the students who struggle with working memory capacity. We know that working memory is related to mind-wandering and focus during challenging activities. This includes math. Research strongly demonstrates negative relationships between working memory and thought intrusions. If students are not able to inhibit intrusive thoughts, then this may also lead to an inability to self-regulate. Therefore, it would make sense that we need to think about strategies that will help students to inhibit intrusive thoughts.

Next, let’s also consider the students who become very emotional if pushed too far with a task that they find too challenging. Let’s face it, learning is hard. This happens just as much with teachers as students as well. However, what about those students who could possibly become volatile or aggressive, or those who might cry and shut down. With all of the research into math anxiety, educators are all too familiar with the fact that math tasks can be a source of many unwanted emotional experiences. Therefore, what could we do to help students to stay focussed on the task at hand, handle intrusive thoughts, and understand when they have been pushed far enough? Are there strategies to increase working memory to help facilitate deeper problem-solving limits?

I believe that there are essential tasks that we need to do as educators to help students succeed in math. These tasks are not only necessary for some, but good for everyone.

Let’s consider some of the basic steps of problem solving and what we can do to help promote mathematical thinking.

In problem solving it helps if we engage students in:

  1. Representation: Visually representing the math is essential. This cannot be stressed enough. This can be in the form of anchor charts, personal journals, using concrete manipulatives, visually drawing student thinking during a Number Talk, and perhaps other strategies that helping students to create/re-create visual representations of the math problem. Not just valuable for understanding the math, but also valuable for building stronger executive functioning skills. Helping students to hold information to free up space for working memory, increasing focus, and the ability to inhibit intrusive thoughts. Visuals should be mandatory and used all the time in my humble opinion.
  2. Planning: Making a plan to solve the problem is important. It includes understanding what the problem is asking them to do, figuring out what part of the problem is ‘unknown’, and understanding the story in the problem. Once again, depicting this visually is essential.
  3. Execution of a strategy: The more strategies that a student understands and practices and commits to memory, then the more flexible they can become at shifting their thinking to new math problems and choosing the strategies that can help them. To get to this point however, much practice is needed to learn the strategies.
  4. Evaluation: This step is about having students engage in another strategy to double-check their answers, and asking if their answer is reasonable.
  5. Learning Goals: Students also need to know the learning goals that they are reaching for. Many educators, as well as learners, may consider goal identification as a trivial process, but we know that goal identification is proven to drive the development of executive functioning skills. Students need to be able to interact with the learning goals in order to understand them. This can be done with visuals, turning and talking to a partner about them, and writing them down. Also answering questions from others who may come into the room, like principals can also help reinforce understanding of goals. If students don’t know where they are going, then we will be unable to help them learn how to get there. Then ongoing formative assessment of the LG’s will help educators to know if they need to make ‘in-the-moment’ decisions for this student, or other forms of differentiation in the next lesson for example.

When we actively strive to meet the executive functioning needs of our students by pairing goals with mental representations, and build those representations over time with experiences, then our students will build conceptual development of the content, improve their cognitive functioning, inhibit interference from other sources. Students therefore need the environmental cues to help students make explicit links to their signals. Especially those who do not develop some EF functions as fast as others.

Math really is about more than just understanding and recalling numbers and equations. It is also about the functions and processes that need to be nurtured that allow learners to be successful.

What strategies have worked for you?