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

More posts: teaching mathematics and levels of teaching mathematics

As a former accountant-turned-educator, I would say the most important item on your list in preparing students for the real world, IMHO, is #4 problem solving. I was often given the basic instruction during fraud investigations to “find the money,” and I had to rely on deep thinking and my problem solving skills to know where and WHERE NOT to spend my limited time on investigating. I often wish that for non-Calculus track seniors there was a survey course just in problem solving. “Crossing the River with Dogs,” although written for obstensibly for middleschoolers, would be a great starting text.

Glenn Laniewski

Blog:

autismplusmath

Latest post:

Math teachers, start baking your Pi Day pies early

http://autismplusmath.blogspot.com/2014/02/math-teachers-start-baking-your-pi-day.html

Thanks Jeff. You are right. The list only concerns the kind of math content knowledge teachers need to know. It’s only half of what the teachers are expected to know which includes knowledge of students, curriculum expectations, parents, etc.

Erlina – first, you’ve done a great deal to help us, even if it does just scratch the surface.

Of course the list of seven items does not include that which every teacher must know, the most important involving how students learn, and why and when they don’t.