Memory tips (11): understanding

It is easier to remember:
1) what you understand
2) what you experimented with
3) what you discovered and formulated yourself

Everybody knows that. Why we apply it so seldom in the classroom is a mystery to me. Here are three examples.
Example 1
Method 1. Suppose you are teaching how to use a shovel in the garden. You can show a diagram to your students explaining that the shovel should enter the soil at a 45 degrees angle. Another diagram will show that when they place their foot on the shovel's head, it should be close to the handle. You ask your students to copy your drawings and memorize what you said and ask them to repeat that one week later.
Method 2. Let the students experiment in the yard and reach conclusions themselves. They might not only learn that the foot should be placed close to the center of the shovel's head (therefore close to the handle), but also that it is useful to have sturdy shoes. One week later, they are more likely to write a whole essay about their experience than to forget how to dig.

Example 2
A number of years ago, I got confused while teaching French grammar: I could not find a grammar that explained a specific point in a way that I could understand (then how could I teach it?) In despair, I decided to explain my dilemma to the students. I brought ten different French grammars at school and asked them to discuss in several groups what they thought what the best rule definition. After a few minutes, my students were in revolt: all these grammars were contradicting each other, some were plain wrong, the examples were not clarifying the subject. They all complained: my students had never considered before that there maybe such a thing as a bad grammar. But after half an hour, I did not have students, I had little grammarians very ardent at defending their point of view. Checking what the grammars said became a game that they played, and of course, they all became pretty good.

Example 3
There are a very small number of equations and rules in mathematics that students have to know by heart. But they got to know them. Why is that? First because time is short during a test, but mainly because recognizing the rule usually gives you a tip on how to solve the problem. All carpenters know that they can verify the square they are building by measuring the two diagonals: if the diagonals are equal, then they got a square. The method is much easier than to verify each angle: students who build a box or delineate an area in the yard do not forget that tip. It makes it easy later one to remember interesting rules about triangles.

Students come to the teacher with varied levels of knowledge. One school in New York experimented with teaching chess to kids, and their professor discovered that they did not know what a corner is. Corner, he said, if for them the grocery at the corner of the street, but they did not understand what is the corner on a chess game. It comes then as no surprise that kids learning chess were better at math!