Math 503, Spring, '03

What does it mean to teach mathematics?

What in your mind does it mean to teach mathematics?
- Similar end goals need not imply similar techniques
- What sort of comprehension do I want the students to end up with?
- Ideal vs. Real – Which question are we asking?
- Depends on level – "completely different things" or not?
- Teaching = Teaching course?
- What is the same?
- Facilitate an atmosphere where connections can be made
- Giving students tools and techniques conceptually and symbolically for dealing with "real-world" problems
- Give students idea that math is useful
o real world
o in other subjects (e.g. organizing)
- example: writing proofs good warm up for writing English papers
- Most important thing one learns in a math course is how to think
- Students developing/articulating idea is powerful, makes it easier to remember
- Teaching is balancing different methods
- Students should figure things out on their own
o Where does this happen? Can teacher have this happen in classroom (even with large calculus class)?
- "With class of 100+, not much can be done"
- "Even in large lecture, should have opportunity for students to interact with each other and instructor"
- Group worksheets to apply what has been learned?
- Kinds of questions you ask – regurgitate? – more conceptual?