Having become a student again, I recently got this urge to teach, and have been applying around for a teaching position. If I were to conduct a class in math (or a subject that uses math extensively), I’d keep reminding myself of the following, which all came to me sitting through lectures:

1. **I’d choose a good textbook. **Students need very good/excellent texts, so that they can study at their own pace. Every lecture should be covered by text that the student can go back to if they miss a point or don’t understand things at first hearing. Lectures are a bad way to introduce hard concepts. Bullet-point presentations are even worse, because the teacher can now go faster through the prepared text. Distributing bullet-point presentations as course materials is unsatisfactory. They should be treated only as course outlines (see next point). There is no substitute for a course textbook. Spend time and effort choosing it (them).

**2. I’d be very specific about the course curriculum. **Students who want to read ahead or even finish the course materials earlier should be able to do so. The students should always be informed in advance about the coverage of the next class session, so that those who want to read ahead, or who need to miss class, may do so without missing the lessons.

**3. I’d make students spend their class and off-class hours learning course concepts by reading through the text carefully and applying course concepts by solving problems/exercises. **The only way to learn is to accumulate “flying hours”, i.e. hours of practice. Here are some ways to encourage stepping through examples and problems: a) give easy, graded take home exams after each class session, which call help pull up the students’ average; b) compile a set of, say 100-200 problems that will cover the entire course curriculum, with 3 or more questions per topic, and distribute this problem set at the start of the course; c) announce to the class in advance that all exams (midterms, finals, others) will be picked at random from this problem set (i.e., if they take the time to learn to solve the entire set, they will surely get excellent marks.)

**4. I’d encourage students to ask questions. **Most students are shy about asking questions for fear of sounding stupid. To encourage them, make them write their questions on a piece of paper, signed with an alias (so the teacher may follow the progress of the alias.)

**5. I’d help clear away obstacles to the students’ self-learning. **In particular, the teacher should be immediately available to help them get out of dead-ends. This occurs when a concept is so intractable to them that they can not grasp it without help, and they are unable to make any further advance until this learning block is cleared away. Thus, in class, students should either be working on problems or asking the teacher’s help in clearing away such blocks. The teacher can use the questions and the written answers to exercises to identify which concepts are most difficult for students and to conduct special lectures about these concepts.

**6. I’d conduct a math class like a swimming class.** The coach stays dry, *standing by the pool side*. The students are *in the water*, learning to swim. In math, the pool is the chalk and blackboard, pencil and paper.

**7. I’d give exams that are fair. **Stick closely to the text as much as possible. Do not ambush students with surprise topics or trick questions. As a rule: ask many easy questions, a few hard ones. Give students a second chance; if most did not get a mid-terms problem, ask it again in the finals. Think of it as a bonus question.