Does anyone else remember these toys? I played with one as a child, and I see similar toys in my church nursery. The concept is simple–you match the plastic shape to the hole it fits in. Most toddlers are amused by this toy. What toddlers (and probably their parents) don’t realize is that they are learning algebraic skills. In Pre-Algebra, the first step in learning to solve algebraic equations is to learn how to recognize when a number is a solution to an equation. For example, we ask, “is x = 5 a solution to the equation 2x + 7 = 20?” And, we plug 5 in for x to find that 2(5) + 7 ≠ 20; so, we say that it is not a solution. In other words, the “shape” of x = 5 does not fit the “hole” 2x + 7 = 20.
Think about this: if we didn’t have algebra, the only way to solve any problem would be brute force; we would have to try every possible answer to find the right one. In terms of the toy, we have to try every piece in every hole in order to find the right ones. This would prevent so many new developments and insights into our world.
Students like to claim that they will never use algebra in real life; they argue that they don’t need it. What they don’t realize is that they’ve been using it all their life. As we grow and learn, we simply hone and develop the skills and neural connections we’ve always been using. Mathematics teaches us new ways to approach problems, new ways to look at the world, new ways to think about things. We learn skills that can make our decision-making process more efficient; we no longer have to try every piece in every hole to find the right one.