Math Fluency: The Why & How

The Ongoing Debate: Should Students “Just Know” Their Math Facts?

For a long time, I’ve been championing the battle cry: “They should know their math facts.” As both a teacher and a math coach, I’ve consistently heard and faced this concern. But what if we looked deeper than just memorization?

A Teacher’s Perspective

When I taught first grade, I noticed that some students struggled with math facts, and I often questioned what I might be doing wrong. Later, as a math coach, I had the opportunity to dive into research that expanded my understanding of how students truly learn. A key realization came from something I first learned 20 years ago in a brain-learning workshop: the brain is a vast neural network, memory is stored in multiple areas, and the power of visualization is profound.

The Power of Visualization

One essential strategy that aligns with the way the brain learns is using visuals to develop a deep, conceptual understanding of how symbols—like numerals and operation signs—connect. The brain processes visual information 60 times faster than text; therefore, linking facts to a visual quantity gives the brain an anchor to reference later.

Rethinking the Multiplication Chart

One tool I loved using was a visual multiplication chart. You may remember the traditional charts where you slid your finger across the grid to meet the answer. Personally, I found those overwhelming and, honestly, a bit boring. But when students actually build the chart themselves, the experience changes completely. By creating arrays that represent each factor and then placing them in the correct position on the chart, students construct their own visual map of multiplication. (See picture below.)

Visual Multiplication Chart

From Memorization to Meaning

By shifting our focus from rote memorization to visual connections, we not only honor how the brain learns but also empower students to see math as meaningful and attainable. When students build their own understanding—literally constructing visuals and connecting them to facts—they develop confidence that goes beyond recalling answers. Instead of battling with math facts, they begin to build a web of knowledge that sticks, supports problem-solving, and ultimately transforms the way they view themselves as mathematicians.