Exploring a Bottom-Up Approach to Learning Math, Part I of IV: Why Practice?

Repetition, especially of the “rote” memorization ilk, gets a bad rap in academia. This is with good reason.  As teachers, we don’t want you blindly memorizing something without understanding the REASON and MEANING behind it.  However, being able to DO something through repeated practice, even without immediately getting the “Why,” actually helps you achieve that all-important understanding.

Think about the way we learn how to talk. A 2-year-old makes noises first, mimics mom and dad, then years later—after he has a grasp of speaking the language—learns grammar and how to dissect language and deconstruct and reconstruct it. All of this greatest depth of understanding comes after a lot of simple copycatting.

It’s also the way we learn how to walk, as well as re-learn how to walk.  Spinal cord injury and stroke victims are recovering more quickly with the help of machines that put your body through the motions of walking.  This repetitive training works to activate muscle memory.  The machine is doing all the work to begin with, until the body can take over.  A bottom-up practice approach to learning skills works similarly.  The brain is a pattern-recognition machine.  If given the right opportunities and feedback, it can figure things out enough to DO a skill before it can explain how or why it’s doing it.

Learning this way is almost like having the information downloaded into your brain. (read about a fascinating study on this, as applied to learning math, here.)  It takes the effort out of it.  It takes the ego out of it.  It even takes aptitude and ability out of it.  This is not to say that the brain isn’t working.  We WANT the brain to work.  If there is no work, there is no reward.  But by taking advantage of what the brain naturally does best—recognize patterns and assimilate them into what feels like intuitive knowledge—it doesn’t FEEL like so much work.  This is a huge win-win.  Not only is it more enjoyable to practice this way than to effort-fully memorize and regurgitate for a test, but the knowledge is more lasting.

This is what your brain was designed to do. The brain will pick up on and have functional recognition of patterns even before we consciously know how to articulate what we’re doing.  Think of what this could do for math education!  Math programs that take advantage of this will produce the most lasting results, and enable students to arrive at a place where the bigger math picture starts to come together. They will actually appreciate underlying reasons and be able to apply their “intuitive” knowledge to problem-solving.

In our next few articles, we’ll explore what this would look like in an approach to teaching math skills for Mastery. We’ll go over HOW to do this magical “repeated practice” in a way that’s engaging while ensuring that it never becomes wasted, numb repetition.  Stay tuned!