One of our girls visits the 7th grade (13 years, secondary school) right now. In geometry, they are talking about the congruence rules for triangles and triangles in general. Yesterday’s homework included a geometrical problem: construct the space diagonal of a cube geometrically and specify its length (side length of the cube is 5.3cm).
While this might be an easy problem for grownups, it seemed not so easy for her. She drew a grid model of the cube, connected the opposite vertices, and measured off the length of the resulting diagonal. It seem logical and right for her. When I asked her about the actual angles in a cube, and how they relate to her projection, it became quite clear, that some angles in the drawing weren’t quite what they should have been.
In my opinion, kids have to learn how to ask the right questions, and how to find answers. And then they should explain it to somebody else. As a freshman I earned some extra money by giving private lessons for juniors and seniors. I quickly learned, that I was only able to explain a problem and its solution in depth, when I was able to answer all kinds of questions they were throwing at me. It didn’t have anything to do with knowledge, but with the ability to express it. And that is quite harder. So whenever you want to make sure you truly understand something, talk to someone about it for a couple of minutes, and have her or him ask you questions.
Finally, she was able to find a solution to the problem. I didn’t explain it to her, but I asked her some questions. She had to explain it to me.