I sat in M’s classes in high school mathematics. The first day I sat in the rear, while the rest of the time I sat in front. I observed his teaching and the students' reactions. After class, I discussed my comments. M was very quick to incorporate these comments into subsequent classes, and displays a very positive attitude. Students paid attention and showed interest. M has a pleasant relaxing way of talking. There were very few instances of students looking bored, talking about irrelevant things, or being wild. Even these rare instances did not last long.

 

For the expression

 

-x2 - 2x2 + x,

 

tell the students that each separate power of x be treated like a separate entity. x2 is like a red book, and x like a blue book. We then add books, and note how many red books and blue books we have. The result is -3 red books, and 1 blue book.

 

       -17 + 9.

 

One girl said the answer is +8. It is important to ask her why. We have to understand their misunderstandings, and not merely give them the correct answer.

 

For word problems, one has to translate from words to numbers and expressions. It is like translating from French to English. This is a hard step. Part of the checking should be to check the translation.