Learning Fractions with a Paper Window

At thirty-eight, Joel was taking a basic maths course before applying for technical training. He understood measurements at work, but fractions on a page made him hesitate. When the tutor wrote three quarters, Joel tried to remember a school rule and immediately mixed it up with another one.

The tutor gave each student a rectangle of paper and asked them to make a window with four equal sections. Joel folded his sheet, then shaded three parts. That seemed easy. The next task was to divide the same window into eight sections without changing the amount of shaded paper.

Joel drew new lines through the original sections. Now six of the eight parts were shaded. He could see that the shaded area had stayed the same, although the numbers had changed. Perhaps I have been treating the numbers like passwords, he thought, instead of asking what they describe.

At home, he made more paper windows and wrote the fractions underneath. His daughter asked whether he was decorating the kitchen. Joel explained the exercise, then let her check one of his examples. The following week, he still worked slowly, but he could explain his answers. For the first time, a mistake gave him something to inspect rather than something to hide.