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When students are taught math this way, they find it more compelling, and naturally develop a deeper understanding of the subject.
Here's an example of how our mathematics programs apply this approach to a 4th grade math problem:
Jane and Andrew had $50 together. After Jane bought a present for $12, she and Andrew had the same amount of money. How much money did Jane and Andrew each have initially?
This seems like a fairly simple problem. And tempting to solve the straightforward way: algebraically. But instead, we encourage our students to solve the problem visually. This way, they develop clarity around why the algebra works.
Here are a few segments from our teacher-training seminar as an example:
We know that initially, Jane must have had more money than Andrew
And after Jane spent $12, they had the same amount. Which, combined, was $50-$12=$38
Meaning that if both Jane and Andrew had equal amounts, then each had $19. And initially, before spending the $12, Jane had $31.
Algebra is a powerful and useful tool for elementary math problems like these. But by taking a visual approach and encouraging classroom debate, we encourage students to grapple with the problem and envision what the algebraic translation really means. This understanding is essential; as problems become more complex, rewriting them in algebraic terms becomes increasingly difficult. Building a solid foundation in elementary school is the key to developing excellence in mathematics and critical thinking.}