Five Ways Understanding the “Why” Behind Math Changed Everything

When I tell people that my schools completely transformed the way we teach math by focusing on why math concepts work, they tend to look at me like I’m speaking nonsense. They often will say something like, “Why do you need to know why math works? Isn’t it just about solving for the right answer?”

This mindset is exactly the reason we decided to change our approach to math instruction. 

A Complex Challenge

I am the principal of two small K–6 schools in Utah’s Tintic School District: Eureka Elementary and West Desert Elementary. Together, we serve just over 100 students.

In a small district, every instructional decision matters. For so long, our teachers struggled to make strides in math achievement, despite their effort and commitment to students’ learning. They could see when students were getting the wrong answers, but they couldn’t always identify where students were making mistakes or how to address them.

We realized our teachers needed deeper insight into how students actually learn mathematics. Teachers needed to understand why math concepts work—not only to improve their teaching, but also to reframe and expand their own understanding of the curriculum.

Math Training That Changes Everything

A conceptual understanding of math isn’t just a mindset change—we also knew our teachers needed real training and ongoing professional development to sustain a new instructional approach in our math classrooms. 

This is how we found our way to the Ongoing Assessment Project (OGAP); a research-based program focused on understanding student thinking in mathematics. The program is not your typical professional development workshop. It’s an empowering four-day training designed to help educators dig deep to understand how students build mathematical reasoning over time. 

Instead of simply learning what to teach, teachers gain a deeper understanding of how students think about mathematics, as well as instructional strategies that can respond to students’ unique thinking pathways.

We aren’t just training teachers for their specific grade level; we’re investing in their mastery of the entire mathematical landscape. Through a three-year rollout covering additive, multiplicative, and fractional reasoning, our K-6 educators are developing a profound vertical perspective that connects early foundations to advanced understanding.

Transforming Math Instruction: Understanding the “Why”

The program has completely transformed how we teach math. Teachers have pivoted from focusing on student answers to understanding student thinking and reasoning. 

Once our teachers began to prioritize the “why” behind math, we started to see meaningful changes not just in instruction, but in how students engaged with learning.

Here are five ways understanding the “why” behind math concepts has changed everything in our district:

1. Teachers can diagnose and address math mistakes

Teachers are no longer grasping for solutions to help students “get it” in math classrooms. Now, teachers can identify exactly where a student’s thinking breaks down. Even more, teachers are now equipped with conceptual approaches to address these misconceptions and provide more targeted instruction going forward.

2. Instruction is more flexible and differentiated

What makes the professional learning sessions especially powerful is how interactive they are, which encourages teachers to work collaboratively, use manipulatives, and examine real examples of student work. After completing the training, our teachers are well-versed in a variety of instructional strategies, such as number lines, models, and manipulatives, which has enabled them to present concepts in multiple ways and reach every student.

3. Students are problem-solving, collaborating, and explaining—not memorizing

Our math classes have shifted from quiet memorization of steps to active discussion and problem-solving, with students explaining their reasoning and learning from one another. In our first and second grade classrooms, we have implemented whiteboard tables where students can show their work and collaborate with their peers. This interactive approach to mathematics has boosted student engagement and confidence across grade levels.

4. Students have stronger math foundations, and teaching is more consistent

We invited not only classroom teachers, but also teacher aides, special education teachers, and secondary math teachers to participate in the training. Educators now share a common language and understanding of how math concepts build over time, creating smoother transitions and stronger foundations for future learning. When a student struggles in fourth grade, teachers are now able to trace that learning gap back to earlier concepts and collaborate on strategies to support the student.

5. Teachers are confident and excited about teaching math

Like many adults, most teachers had learned math as a set of procedures. We were taught to follow steps, memorize algorithms, and arrive at the correct answer. This procedural approach never explains the “why” behind the math, leaving educators with few solutions to address math mistakes. Our professional learning program helped our teachers understand the math more deeply, enabling them to teach with clarity. Plus, they are more confident in their ability to address learning challenges along the way.

The Power of Understanding the “Why” Behind Math

Walk into one of our math classrooms today and you’ll see how powerful it is to understand the “why” behind math. 

Students are explaining why their solutions work. Teachers are identifying why students are struggling. And everyone is building a conceptual understanding of why math works that has noticeably transformed our math classrooms.

Professional learning requires time and commitment. Our teachers give up four days of their summer break to attend this pivotal training—the fact that they continue to return each year says everything.

They see the impact in their classrooms, and perhaps more importantly, in themselves. So, when people ask me why it’s important to understand the “why” behind math, my answer is simple: When teachers understand math differently, students learn math differently.