Build a Mathematical Mind--Even If You Think You Can't Have One by Albert Rutherford

Author:Albert Rutherford
Language: eng
Format: epub
Tags: mathematics, how to learn math, mathematical mindset, logic, math skills
Publisher: Albert Rutherford
Published: 2023-01-31T00:00:00+00:00

CHAPTER 7: Visualizing: Externalizing the Internal

If you’ve ever spent time with a gymnast, a concert pianist, or anyone else performing at an elite level, you may have seen them visualizing a performance: imagining every step of it, trying to picture themselves performing it perfectly. You may have wondered why they were doing this rather than spending time practicing leaps or scales. They know something mathematicians also know: visualizing is a powerful tool.

Mathematicians are skilled at visualizing. Einstein attributed his success to the skill: “My particular skill does not lie in calculation,” he wrote, “but rather in visualizing effects, possibilities, and consequences.”[xlv] It makes sense that visualizing holds such power for humans. Approximately 30% of the brains of primates (which includes humans) is used for visual processing.[xlvi] No wonder we are such visual creatures.

Researchers have identified five aspects of visualizing: internalizing, identifying, comparing, connecting, and sharing.[xlvii] We will examine each of these and discuss how you can hone these skills to incorporate visualizing into your life.

Internalizing involves making sense of something in your head. This is the first step to understanding a problem, particularly a complex one. Let’s imagine you’re trying to do something that challenges most people: packing a car for a big trip. People who are good at fitting everything into the back of a car aren’t magicians; they’re just good at internalizing a spatial problem.

When someone gets ready to pack a bunch of suitcases and bags into the trunk of a car, they need to spend time internalizing the problem first. They might ask themselves: How many large suitcases are there? What irregular objects do I need to get in? Are there pockets of space somewhere, maybe under the back seats, where certain items would fit? Where can I put the bag of fragile items, so it’s protected and not squished?

The talented packer spends time picturing the answers to these questions and manipulating items in their head before packing the car. If you watch this person in action, you’ll see they rarely have to pack and repack the car. They are strategic about what they put where, and they get everything in securely. This is because they spent time internalizing the problem and have a plan for how to solve it.

The identifying stage of visualization involves identifying or creating an image or model that might help you. Young students learn to do this to help them solve math problems. Many teachers use a strategy called, “Read, Draw, Write,” which asks students to draw a model or picture to help them solve word problems. They are supposed to read the problem, draw a model, then write the answer in a sentence. The RDW strategy was not created to torture kids or the parents trying to help them with their homework. Rather, it is based on research about how visualization, particularly the act of drawing, creates a stronger understanding and memories of the problem.[xlviii] The process of creating a model leads to better understanding.

Sometimes, we’re faced with problems that beg for a drawing to help us solve them.

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