The most powerful learning occurs when we use different areas of the brain together to solve problems. When students work with symbols, such as numbers, they are using a different area of the brain than when they work with visual and spatial information, such as an array of dots. Learning and performance is optimised when the two areas of the brain are communicating. Training students through visual representations may improve their maths performance significantly, even on numerical maths.
Students can be excited and inspired when they see mathematics as pictures, not just symbols. For example, consider how you might solve 18 x 5, and ask others how they would solve 18 x 5. Here are some different visual solutions of this problem.
Each of these visuals highlights the mathematics inside the problem and helps students develop understanding of multiplication. Pictures help students see mathematical ideas, which aids understanding. Visual mathematics also facilitates higher-level thinking, enables communication and helps people see the creativity in mathematics.
Mathematics is a subject that involves precise thinking. But it also involves creativity, openness to new ways of seeing things, visualisation, and flexibility in approach.
Nice neat formulae and procedures are used to solve familiar type questions posed in a familiar way. But understanding is required to solve them when they are presented in an unfamiliar manner. Students should be challenged to discover new ways in which to see and solve problems.
Take the following example.
A man is on a diet and goes into a shop to buy some ham slices. He is given 3 slices which together weigh ⅓ of a pound but his diet says that he is allowed to eat only 1/4 of a pound. How much of the 3 slices he bought can he eat while keeping to his diet?
One approach would be to use ratios and algebra as follows:
3: 1/3 = x: ¼
9:1 = 4x:1
4x = 9
x = 9/4 =2 ¼
Another would be to solve it visually as follows:
Both methods are equally valid. Both result in the same correct solution. Students who have difficulty with one approach may find success comes easily with the other. Don’t be afraid to experiment. For some doodling on scraps of paper may be an important part of learning and thinking their way through problems to the solutions.