LIVE @ ISTE 2024: Exclusive Coverage

Just as the science of reading has shown that some instructional practices are more effective than others, research points toward a more effective ‘science of math’ and how to teach math

We can teach math better–here’s how

Just as the science of reading has shown that some instructional practices are more effective than others, research points toward a more effective ‘science of math’

In 1997, the National Reading Panel issued a report on the findings of dozens of studies looking into the most effective methods of teaching and learning reading. The report offered specific recommendations for effective practices, such as intentional and explicit phonics instruction for all students.

Lately, there has been movement toward codifying science-based literacy learning practices into law, but it took 16 years before the first state to do so, Mississippi, took such action. In the meantime, many educators—and even entire schools and districts—continued using outdated teaching methods or only engaged in phonics instruction with students in need of remediation.

Something similar is happening in mathematics classrooms right now. A national mathematics panel has not been convened to lay out the science of how students most effectively learn math, but there is a large body of research available. Unfortunately, the math instruction most students receive is not based in the science of math—but it could be.

Being Lectured at Doesn’t Work

As many others have, I learned from my own experience teaching in the classroom that lecturing doesn’t work. There are usually a couple kids in any classroom who will learn whatever you teach regardless of the method, but for the vast majority of students a lecture is abstract and a little boring and, most importantly, it’s something they’re listening to and not something they’re doing.

As human beings, we’re wired to learn by doing. In fact, we’ve been learning by doing even longer than we’ve been human, because all mammals learn by interacting with their environment, taking in feedback, and processing that feedback.

The Perception-Action Cycle

Human beings learn in a variety of ways, using different learning cycles. One powerful learning cycle, and one that is invoked whenever we try to solve a challenge, is the perception-action cycle.

How I use digital curriculum in my math classroom
5 ways to create a strong math culture in your schools

When we are confronted with a problem, we think of potential solutions. If we try a solution and it works, the neural pathways, or schema that suggested that solution become stronger. The next time we are confronted with a similar challenge, that solution will come to us sooner and, if it works again, those paths will become stronger yet again. Basically, the ideas that work grow stronger in our brains each time they are proven to work, while ideas that don’t get reinforced tend to become weaker.

In order for the cycle to go into action, however, the learner must be the one having the idea for a solution and experiencing the feedback, whether it be positive or negative. If a teacher, for example, comes up with a potential solution for a student to test, neither will experience the perception-action cycle. The student will miss out because they are testing someone else’s ideas, and the teacher’s perception-action cycle will not go to work because they didn’t experience the feedback from testing their own idea.

It might be difficult for teachers to give students challenges that will kick their perception-action cycle into math learning gear, but visual models can accomplish the same thing. If you show a student an image of some birds sitting on a wire, and then a second image where some of the birds have flown away, you have a model of subtraction. If you ask students how many birds must join those on the wire to make a total of ten birds, you not only have a missing addend situation, but you’ve asked them to solve a problem—which engages their perception-action cycle.

Shutting the Perception-Action Cycle Down

As with other learning cycles, the perception-action cycle can be shut down from negative emotional experiences at the point of feedback. Imagine a teacher trying something new with their class for the first time and it’s not going great. With the class out of control, the principal walks by and pulls the teacher out of the room to tell them to get it together. That teacher is not going to be eager to repeat the experiment, right?

The same thing happens with students learning math. If they are shamed or otherwise made to feel bad about themselves or their ideas, they are going to shut down. Learning environments need to be free of emotional judgment. To build a conceptual understanding, students need space to explore ideas and see what does and doesn’t work.

Learning by Speaking

Learning by doing is a powerful way to learn but not the only one. Students also learn a great deal by speaking. When you ask a student to justify their thinking, as they explain themselves, they actually create a new mental codification of experience called a schema.

This is why asking students to give a synopsis in an English class is so powerful. Students aren’t just parroting back language without meaning. To give a summary, a student must create meaning from the information they have received and then communicate it clearly to someone else.

Most educators are probably familiar with the Benjamin Franklin quote, “Tell me and I forget, teach me and I may remember, involve me and I learn.” By giving students opportunities to solve mathematical challenges in a safe, non-judgmental environment and then asking them to explain the thinking behind the solutions they arrived at, you’re involving them in their own learning twice. That explanation isn’t just a rehash of what happened; it’s an opportunity to extend, generalize, and reinforce the learning that took place in the perception-action cycle.

Showing Students Math Is for Them

Engaging students in the perception-action cycle and having them explain their thinking is an excellent start, but students must also know that they are “mathematical people,” that they are capable of doing math and that, in fact, they do it all the time.

Something as simple as building an equivalent fractions lesson around the paper fortune tellers many kids fold in grade school can help them understand that math is a part of their everyday lives, relieving some of the anxiety and fear around the subject.

Fortunately, the perception-action cycle is an inherently more equitable way to teach math because every human being is capable of learning this way. It also tends to eliminate confounding factors. For example, on a recent school visit, one of the teachers was a little flustered by a student who had just come to the school a few days prior. He only spoke Cambodian, and his teacher was saying that she didn’t know what to do with him because she had no way to test his math knowledge. She wasn’t even sure if people in Cambodia used the same math symbols because she couldn’t speak to him and ask.

I sat him down in front of a computer with a visual math problem to solve, and he arranged the numbers 1-20 in order on a number line immediately. He had plenty of math knowledge for his grade level, but no one had been able to get past the language barrier to find out. By cutting out all those external factors, visual math challenges that invoke the perception-action cycle can help shine a light on all kinds of interesting thinking different students are capable of.

There was nothing wrong with that student’s ability to learn math. His teacher, through no fault of her own, simply wasn’t teaching it to him in a way that worked for him. Just as we learned 25 years ago that there is a better way to teach reading by focusing on the science, we know today that there is a better way to teach math. Let’s hope it doesn’t take a quarter century to become the norm as well.

Sign up for our K-12 newsletter

Newsletter: Innovations in K12 Education
By submitting your information, you agree to our Terms & Conditions and Privacy Policy.

Want to share a great resource? Let us know at

New Resource Center
Explore the latest information we’ve curated to help educators understand and embrace the ever-evolving science of reading.
Get Free Access Today!

"*" indicates required fields

Email Newsletters:

By submitting your information, you agree to our Terms & Conditions and Privacy Policy.

eSchool News uses cookies to improve your experience. Visit our Privacy Policy for more information.