The mathematics that engineers, accountants, etc and teachers of mathematics know are different. They should be. There are some engineers, accountants, chemists, etc who become very good mathematics teachers but I’m sure it is not because they have ‘math knowledge for engineering’ for example but because they were able to convert that knowledge to ‘math knowledge for teaching’.
What is math knowledge for teaching?
It includes knowledge of mathematics but on top of that according to Salman Usiskin, it should also include knowledge of:
- ways of explaining and representing ideas new to students;
- alternate definition of math concepts as well as the consequences of each of these definitions;
- wide range of application of mathematical ideas being taught;
- alternate ways of approaching problems with and without calculator and computer technology;
- extensions and generalizations of problems and proofs;
- how ideas studied in school relate to ideas students may encounter in later mathematics study; and,
- responses to questions that learners have about what they are learning.
I don’t know why some people especially politicians think teaching is easy. Surely college preparation is not enough to learn all these. You certainly need to be a practicing teacher to even start knowing #1 and #7. Teachers need more support in acquiring these knowledge when they are already in the field than when they are still in training.
I started this blog to contribute towards helping teachers to acquire the seven listed by Mr. Usiskin. After 250 posts, it looks like I have not even scratched the surface 🙂