In her book, A Mind for Numbers, Professor Barbara Oakley refers to the practice of “chunking” as “one of the first steps toward gaining expertise in math and science…” (Note: this is different from chunking in long division.) So what is this all-important technique and how do you use it?
First of all, what is a chunk?
A chunk is a mental connection that links small, separate ideas through meaning. This might sound a little nebulous, but examples in daily life abound. Take, for instance, a task as routine as driving to a friend’s house. If I called you in the middle of the trip and asked what you were doing, you’d probably tell me that you were…driving to your friend’s house (as if it were a single activity). In actuality, the act of driving somewhere is a complex and varied series of actions. Think about it: driving somewhere involves unlocking a car, opening the door, sitting down, etc. Yet we commonly refer it as a single, simple task.
Here’s how this applies to math
Storing separate ideas a chunks allows your brain to run through problems more efficiently; it eliminates the need to focus on the little, individual pieces of a math problem and lets you concentrate on the big picture. Chunking is all about understanding the connections between problem-solving steps, not merely memorizing facts or formulas.
To illustrate this concept, Professor Oakley invokes the image of a jigsaw puzzle. She compares a new math concept to unassembled puzzle pieces. By memorizing facts, you can gain a very narrow insight into the problem, but no understanding of how it fits together with other ideas—an idea she illustrates as a small, solved fraction of a puzzle.
A chunked thought, on the other hand, looks like a puzzle with most of the pieces in place, but perhaps a few missing. Thus, the random puzzle pieces have been ordered and grouped in a way that resembles an image. Of course, the image is an analogy for a mathematical concept. “The new logical whole makes the chunk easier to remember, and also makes it easier to fit the chunk into the larger picture of what you are learning,” writes Professor Oakley.
Forming Chunks
Forming chunks is relatively simple, but it requires concentration and freedom from distraction. When you’re studying a new concept, put your phone away, turn off the television, and remove other disturbances.
Once you can fully concentrate, the next step is to understand the basic idea you’re trying to learn. We’re talking big picture stuff here—synthesizing the important facets of a concept. Once you’ve mastered smaller concepts you can start connecting them together. Eventually, things snowball and you’re able to combine many large chunks of information together.
To do that, you need to practice with different problems so you can get an understanding of the broader context in which your concept chunks can and should be applied. The goal here is to become familiar enough to quickly access these chunks when you need them.
The beautiful thing about the Mathnasium curriculum is it is designed so children have plenty of practice with different problems as well as similar problems presented differently. This approach enhances our students' abilities over time to chunk concepts and operations making their ability to solve problems more effective and efficient. Questions about learning strategies? Call us at 303-840-1184 to learn more!
