Tips for Teaching Mathematics
1. Remember you are teaching a highly abstract, symbolic language. No one is born reading music, and no one is born understanding mathematics. Both are skilled, nonverbal means of thinking and communicating that require patience and practice.
2. Get students involved solving problems. Mathematics is learned by practice just like languages. Watching you solve problems gives students a false sense of the difficulty involved. Learning takes off when students solve problems on their own.
3. Encourage students to really try before you jump in to help. If you immediately show them how to proceed you will stunt their developing skills. On the other hand, too little guidance can cause them to give up. Calibrate your instruction accordingly.
4. The material seems clear to you because you’ve been thinking about it for a long time. Calculus becomes clearer to me every time I teach it, but most students only take a course once. Be patient and empathetic. These ideas took a long time to develop historically and take time for students to absorb.
5. Don’t lie about the applications. Students can tell when “story problems” are contrived. Tell them the truth: These problems are often “mental weightlifting” and are intended to build critical thinking and fluency, not to yield immediately applicable skills.
6. Cultivate the mindset of a coach or cheerleader instead of a gatekeeper. Try to design your course so that it is “us versus the material” instead of “student versus teacher.” You want to help your students climb a mountain, not keep them from the summit.
7. Use technology carefully as a tool, not a crutch. As computers become more and more capable, it is increasingly important that their human operators understand both the question and the solution. An “answer” is meaningless without these two things.