In this case study, we discover how one middle school teacher uses the strategy of mathematical thinking to make math instruction engaging and approachable for all students. 

Redefining success in mathematics

By middle school, many students — especially those with disabilities and learning differences — develop the belief that they’re ‘not a math person’.

This belief can be unintentionally reinforced by tracking, where students are assigned to a ‘traditional’ or ‘advanced’ math course track based on standardized test scores and teacher recommendations. 

But Edric Uy, a sixth-grade math teacher and leadership coordinator at Calavera Hills Middle School in Carlsbad, California, believes that anyone can be a math person — and he’s making that belief a reality for kids in his classroom through a strategy called mathematical thinking. 

Mathematical thinking: Going beyond computation

Mathematical thinking refers to the cognitive processes and skills involved in solving math problems. According to Edric, mathematical thinking goes beyond mere computation and focuses on developing problem-solving abilities, critical thinking, reasoning, and creativity within the context of mathematics.

“Especially in elementary school, a lot of students think math is just about computational fluency. So they build an image of themselves as a mathematician that’s solely based on their ability to compute. That’s such a shame, because that’s not really what defines a strong mathematician,” explains Edric. 

“My goal with mathematical thinking is to get them to reevaluate their perception of what it means to be a mathematician and understand that success in mathematics isn’t just tied into their computational fluency — that their ability to think outside the box allows them to be just as successful as someone who can spit out their math facts in under a minute.”

This is especially important for students with disabilities and learning differences, who may come into the classroom believing they are not good at math. By engaging students in a way that focuses on their strengths, mathematical thinking creates a positive learning environment where all students can thrive and see themselves as capable mathematicians. This, in turn, leads to increased engagement and participation in math instruction. 

Fostering mathematical thinking

From the minute the bell rings, it’s clear that Edric’s classroom is different. Instead of starting class by having students solve problems on the board from the previous day’s lesson, Edric prefers to open with a warm-up activity that develops the “soft skills” necessary to be a successful mathematician. 

These soft skills include problem-solving, attention to detail, creative thinking, and justifying reasoning. By starting with these skills, the aim is to create positive momentum and lower students’ defenses, allowing them to confidently approach the rest of the lesson. 

During a unit on adding and subtracting fractions, for instance, Edric might choose a warmup that asks students to pay attention to details — a skill that will come in handy later when converting fractions or determining the lowest common denominator. 

From there, Edric provides students with hands-on, real-world projects that promote inquiry, critical thinking, and collaboration. A perfect example of this is the “life project,” where students learn to budget for a month of life while practicing concepts like working with fractions and decimals. 

Along the way, Edric leverages tech tools to personalize instruction and address individual needs. For instance, he might record a short YouTube video of a lesson and assign it to students as homework the day before. This gives him more time to circulate and help individual students instead of standing in front of the classroom delivering instruction.

Or, he might use PearDeck to check for understanding without randomly calling on students — a practice that can add to the stress many students already feel about math.

“Specifically for those students that have accommodations or modifications in their IEPs, this approach levels the playing field and allows them to feel like they aren’t being taught in a different way. I still provide those supports and accommodations, but they’re usually just best practices for my entire class.” 

Nurturing engagement & empowering students

Thanks to mathematical thinking, Edric has witnessed increased student motivation, engagement, and active participation in learning. 

“I have students complete a self-assessment at the beginning and end of the year on their attitude toward math. Some kids who started the year saying they hated math now say it’s their favorite class.” 

This has also translated into improvements in test scores, mainly from low-performing students. “From a data perspective, I see the most significant growth from the lower 50%,” says Edric. 

But the most important outcome of the mathematical thinking approach has nothing to do with test scores — it’s the soft skills that students take with them to high school and beyond. 

“No one’s going to ask you what your eighth-grade math score was, but they will want to know if you’re a team player, or know how to communicate well during a project, or can meet deadlines,” says Uy. “I want students to be able to say that it wasn’t just a math class, but a vehicle for them to grow as individuals.”