Tapping the brain's natural ability to perceive symmetry in the physical world can help children make sense of negative numbers.
On the road to algebra, children must learn a weird idea: that numbers can be smaller than zero (negative) and can be mixed with numbers greater than zero (positive) in an equation.
Now researchers at Stanford University have created a hands-on way for students to grasp the concept, which appears to harness the brain’s natural ability to notice symmetry in the world.
They found that when they directed fourth graders’ attention to the symmetry between negative and positive numbers (that -5 is the same distance from zero on a number line as + 5, for example), the students got better at solving the problems.
And they were able to apply that insight to new problems such as figuring out where to locate positive and negative fractions on a number line.
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“Most neuroscience tries to explain the effects of existing treatments,” said Daniel Schwartz, one of the study’s co-authors and the new dean of the Stanford Graduate School of Education. “Ours is one of the few cases where neuroscience actually came up with a new way to teach.”
When adults look at a number line with negative numbers extending left of zero and positive numbers extending right, they usually notice the symmetry and use that perceptual skill to help them solve problems.
To see if kids could tap their brains in the same way, Schwartz and his colleagues at Stanford and Purdue University created a hands-on activity designed to emphasize symmetry.
Using a plastic number line and colored plastic blocks (red for negative numbers, blue for positive), the researchers compared their way with the methods teachers usually employ to help students visualize a problem such as adding -3 and 5.
Kids could place a little man on -3 and jump him five spaces to the right, landing on 2, which gave them the answer.
Or they could lay out 5 blue blocks on the number line and stack 3 red blocks in a second row to see how red and blue canceled each other out, leaving 2 extra blue blocks.
Jumping and stacking are the ways teachers usually demonstrate the idea.
In the third way, which researchers devised to emphasize symmetry, the kids placed 3 red blocks left of zero and 5 blue blocks right of zero.
Then they folded up the number line as if they were closing a book with the spine centered on zero. When the hinged halves clicked together, the blocks formed columns and kids could see that the blue column was 2 blocks taller than the red one.
In all, the kids got about four hours of instruction. All three ways helped students solve simple problems.
But when it came to solving more complex tasks such as locating fractions on the number line, the folding method was about 50 percent more effective than jumping and about 33 percent more effective than stacking.
The study, by lead author Jessica Tsang, appears in the journal Cognition and Instruction.