K-12 Momentum | February 2024

Colleagues,

Consider the humble equal sign (=), that unassuming pair of parallel lines we first see at a very early stage of schooling. To many students, the equal sign remains a simple command—"do this calculation”— add this, subtract that. But this hampers later math understanding. My math friends insist that by teaching the equal sign procedurally, we miss its broader invitation to explore concepts of equivalence. The equal sign teaches us that the calculation to its left must always mirror what's on its right; it invites students to a deeper level of understanding, a contemplation of "let's find the balance" inherent in even the simplest problem.

I’m grateful for this insight. Understanding this simple symbol is a critical building block in a students’ mathematical development, something students struggle with to their detriment. In algebra, for example, understanding equivalence is crucial for solving systems of equations, working with inequalities, and exploring the properties of functions. Algebra often requires students to manipulate expressions and equations to find solutions, a process that hinges on the principle that operations performed on one side of an equation must be mirrored on the other to maintain equality. A misunderstanding of the equal sign as merely a signal to perform calculations can lead students to apply operations incorrectly or fail to understand the logic behind equation-solving strategies.

And like so much in math, I’m learning that understanding and embracing equality extends well beyond the bounds of numbers and calculations. It serves as a gentle nudge to think about the balance in every investment we make to support students and educators on this math journey. Ultimately, the humble and powerful equals symbol connects us with our broader aspirations to ensure all students have the opportunity to learn and love math.

In partnership,

Bob Hughes
Director, K-12 Education

P.S. Hugh Burkhardt passed away earlier this month. A British Mathematician, Hugh worked with the foundation in our salad days, playing a critical role in the work of the Shell Centre, and continues to influence our thinking. One of my favorite articles about the complexity of great math problems can be found here. And he recently published Learning and Teaching for Mathematical Literacy.