What does it take to learn fraction division?

Fraction division is certainly one of the more challenging topics for children to learn (and for teachers and parents to teach). Let’s look at what’s involved in solving a simple fraction division problem.

To solve this problem, a student needs to know:

• The meaning of the numerator and denominator in a fraction
• Simple division
• Simple multiplication
• Reducing fractions

The solution looks like this:

Each of us has only a tiny amount of working memory. We can remember three or four things at a time. In addition, the rest of our cognitive resources are limited. In learning research, a measure known as “cognitive load” is often used to quantify how hard your mind has to work to complete a task. The bottom line for learning is that when you are under high cognitive load, you can’t learn much at all.

One way to reduce cognitive load is to use your long-term memory. Take the multiplication table for example. Memorizing the multiplication table has fallen out of favor with some educators. “Why memorize useless facts?” they say. Or “everyone always has a calculator around.” The problem is that not memorizing the multiplication table makes doing fraction division much more difficult. We’ve seen children who had to add 7 together eight times to calculate “7 x 8”. Needless to say, that causes cognitive load to go up, and makes it much more difficult for that learner to actually learn the new concept of fraction division. Even having to turn to a calculator increases cognitive load and takes attention away from the real objective.

So memorizing can actually foster better conceptual understanding and learning. Now go and memorize that multiplication table!