A few thoughts on the difference between memorizing and learning

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Kids making sense of math.

Math on the Move: Engaging Students in Whole Body Learning is organized around three basic ideas:

  1. The body in math learning is best conceived as a thinking tool
  2. Math learning is more than memorization
  3. Amazing learning can happen when the body and math come together in both dance and non-dance settings.

It’s point #2 I’d like to focus on in this post.

A couple years ago Ben Orlin had a fantastic article in the Atlantic titled When Memorization Gets in the Way of Learning. In it, he says:

“What separates memorization from learning is a sense of meaning. When you memorize a fact, it’s arbitrary, interchangeable–it makes no difference to you whether sine of π/2 is one, zero, or a million. But when you learn a fact, it’s bound to others by a web of logic. It could be no other way.”

Most often, the role of the moving body in the classroom, during math time, is that of mnemonic device. Here are some examples of what that might look like:

  • using arms to create symbols for operations, like +, – , and = (focusing on creating representations of the symbols, not expressing their meaning)
  • using hand movements in a song about memorizing a procedure
  • bouncing on an exercise ball while reciting multiplication facts
  • singing a song with an accompanying dance about finding the area of a circle, using movements that bear no relationship to the properties of a circle
  • exploring a math concept such as high versus low in isolation, removed from a narrative context (such as retelling a story) or the larger context of dance learning and making
  • having multiple students become the sides of a triangle by lying on the floor

None of these activities are inherently harmful, some of them may be helpful, and yet, none are at all focused on making sense of mathematical ideas.

In the book I endeavor to explain why we should use the whole, moving body in math learning. I do this by pulling from both research and practice to build a framework for meaningful, body-based math learning. When children harness their innate body knowledge for mathematical sense making, they also harness their whole selves in the pursuit of new ideas and understanding. They develop, communicate, and reason about mathematical ideas both nonverbally and verbally.

Children can make good sense of the world when they get a chance to interact with it, and children are also well able to reason with and about things they observe and do. But they can do this only if they get the chance to do, make, investigate, converse, wonder, build, express, and reflect. Without these kinds of interactions they might still be able to memorize math facts, but memorization would not necessarily mean they would know, for themselves, that something was true.

Ben Orlin said it best:

“Memorization is a frontage road: It runs parallel to the best parts of learning, never intersecting. It’s a detour around all the action, a way of knowing without learning, of answering without understanding.”

I’m SO looking forward to the book being out in another month or so we can grow the practice of meaningful whole-body math learning and teaching together. In the mean time, please feel free to join our book group on Facebook, comprised of educators who want to help their students make sense of math using the original “object to think with” — the whole, moving body.


Malke Rosenfeld delights in creating rich environments in which children and their adults can explore, make, play, and talk math based on their own questions and inclinations. Her upcoming book, Math on the Move: Engaging Students in Whole Body Learning, will be published by Heinemann in October 2016.

2 thoughts on “A few thoughts on the difference between memorizing and learning

  1. Pingback: OTR Links 09/21/2016 | doug --- off the record

  2. Pingback: Math Teachers At Play Blog Carnival 101 - Arithmophobia No More

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