Student understanding

Student understanding. Students are children, whose brains are still developing. There are important differences between student understanding and adult understanding.

One is the lack of abstract thinking. We cannot start with abstract concepts with high school students. We cannot define our terms in mathematics, state the postulates, write down the theorems, and then prove them. We must begin with concrete objects, and they have to understand the abstract generalizations. If we can personalize the concrete, by referring to their bodies, it is much better. We consequently must first give examples, and then state the abstract rule, while showing how the concrete example matches the rule. Again, while explaining the abstract, we must constantly refer to the concrete.

Another important thing to remember is that there are three types of students.

1.	Those who learn by listening – the audio-centric. The teacher must verbalize the ideas.

2.	Those who learn by seeing – the visual. The teacher must write the ideas on the board.

3.	Those who learn by doing. The student must go to the board and work out examples. When the teacher is writing, the teacher should ask students what was written. It may not be enough to write down the ideas on the board. The students must be able to say back these ideas.

All material must be presented in this fashion.

SEE THE BOOK FOR MORE DETAILS.