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Inspiring mathematical thinking with minimal language

A principal explains how his school used a spatial-temporal approach to engage teachers and students in productive conversations about math.

4 min read

Voice of the Educator

Inspiring mathematical thinking with minimal language


When I became principal of Bicentennial Elementary School in the 2015–2016 school year, one thing I noticed right away was that our students were scoring better in reading than they were in math. That’s not necessarily a bad thing, but it is the reverse of what you typically see.

After poring over NWEA math assessment results, performing classroom observations and walkthroughs, and discussing it all with our teachers, I found that our students had trouble making sense of math problems and explaining their thinking. That’s a common weakness, and one I decided we needed to address right away.

We started with the obvious solutions. We revamped our math block and increased its length from 60 to 90 minutes. We put more focus on professional learning and held some professional development opportunities for teachers. We also looked for supplemental online programs that could help and hit on one, ST Math, that took an uncommon approach to math concepts, focusing on solving spatial-temporal puzzles rather than using the academic language of math.

Here are three ways we helped our students understand and explain their own mathematical thinking better.

Introducing math concepts with minimal language

It may seem counterintuitive to address an inability to explain mathematical thinking by de-emphasizing language, but it provides students the opportunity to make sense of the concepts in their own terms.

When they’re confronted with a puzzle to solve, students know they have to figure it out, and part of that is self-questioning, asking themselves how to approach the problem. As they try different approaches, they receive informative feedback, which encourages more internal dialogue about the challenge and refines their thinking about solving it. They ask themselves: “What do I click next? How can I manipulate this puzzle?”

This methodology really fostered the approach we were trying to help the staff develop by encouraging them to do more prompting and less explaining, with the goal of encouraging students to do even greater self-questioning.

Teachers want to be helpful, so it can be a challenge for them to let students struggle through a problem on their own. At first, their students were asking them all the time, “What am I supposed to do? What do I do next?” But as the students became familiar with the approach and as teachers learned different prompts they could offer, the engagement became undeniable and students began questioning themselves and, in turn, explaining the thinking behind their problem-solving attempts.

Giving students prior knowledge of the topic before it’s introduced

The opportunity to explore concepts before they’re formally introduced is an advantage, as well. Our teachers tend to front-load math instruction with the spatial-temporal approach, which allows students to get familiar with concepts before learning new vocabulary that may trip them up.

If they’ve solved some puzzles focused on, say, fractions, before their teacher starts explaining what the word means, they already have a concept to pin the word to. It’s not some murky idea that requires a lot of in-depth description, but a familiar concept they’ve already used to solve a range of challenges. After a couple of years of frontloading concepts like this, our teachers are reporting more transfer and more understanding when they work with students in small groups.

Embracing failure

Throughout this process, we’ve made encouraging a growth mindset a major focus for us as well. And that is something that has to start with the teachers. If they don’t believe that it’s possible to grow through failure, neither will their students.

To get there, we focused on growth mindset in staff meetings and trainings coming from the district level. It’s on our bulletin boards and posters displayed throughout the school. Our teachers worked with trainers and each other to learn different prompts for students struggling through a difficult problem.

It’s taken time and practice, as well as plenty of patience from teachers and students, but I really see them embracing struggle now. Ask our kids now, and they’ll tell you it’s okay to fail. That wasn’t true two or three years ago.

It’s showing in our math scores, as well. When we started this process, 53% of our kids were meeting their fall to spring NWEA math assessment goals. Five years later, we’ve improved that number 23 points to reach 76%.


Steven Etheridge is the principal at Bicentennial Elementary School, where teachers use ST Math to help students learn to explain their mathematical thinking. He can be reached at [email protected]


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