Why Concrete Learning Is Essential in Math

Concrete learning opportunities—like using manipulatives and doing hands-on activities—are essential for every child’s mathematical development. When a child develops their number sense with concrete math learning tools, a deeper sense of understanding occurs.

Counting out objects, combining them, moving them apart, forming groups, and taking them away, are all processes that children can do with their hands. These activities work more areas of the brain than if the same problems were done abstractly.

Jo Boaler is a Stanford education researcher who studies how children learn math. I’ve been lucky enough to see her speak at conferences in the past few years. Her work is fascinating and if you haven’t done so already, I highly recommend you check out her website, youcubed.org, for research-based teaching tips.

Boaler’s research shows that visual learning—such as using an area model to multiply—improves overall performance. That’s because two areas of the brain are communicating. A youcubed blog post covering the research of Joonkoo Park & Elizabeth Brannon says it best:

“When students work with symbols, such as numbers, they are using a different area of the brain than when they work with visual and spatial information, such as an array of dots.”  

Interested in learning more? You can read the paper here.

When working with teachers, I’ve noticed that many teachers will often take away concrete math tools after students begin to develop their conceptual understanding, moving to pictorial or abstract explanations instead. This is a disservice to students, as manipulatives help encourage rich mathematical discourse.

When teachers encourage students to use manipulatives for challenging problems, students are more comfortable and end up using the concrete tools to justify their reasoning pictorially or abstractly (thus taking learning to the next level on their own).

Whether or not you decide to use manipulatives in your math lessons, I suggest you try at least one daily concrete problem solving opportunity to help students create hands-on and visual math connections for their long-term mathematical memory.

This has helped many of our students maintain progress as they advance during the year.