Teaching Math

I know now that some students get it. The other day a student told the rest of the school in chapel that he ?thinks Mr. Paul wants his students to question what they are doing, not just get some mechanical algorithm that is ?done? to a problem.?.

A few years ago I wrote this in a place that I am reminded to look and read it again and again. It is part of a teaching math philosophy that I am always developing. It might need some more refinement but here is a snippet:

I want to lay out a feast (of math) for the students to take, chew, ingest and digest.

I cannot teach them concepts.

I can give them information. They must turn the information into concepts.

I can show them information through modeling and they need to process that information.

Here is something else along that line that I wrote near the end of last school term.

How do I get students to think through and really study examples, whether they are in a text book or on the board? It is easy to ?walk? a student, especially freshmen, through a problem. Later in their schooling it becomes nigh impossible to get them to think and reason.

I?d love to hear what helped you in school, and what really didn?t work for you, as a student  or as a teacher.


A few weeks ago I mentioned Sage and Beamer, well beamer has been going pretty well, I am using it several times a week in various classes. I thought I was going to try Sage, but haven’t gotten to it yet, although I have come across a free software (not open source) package called GeoGebra.

It is given as Dynamic mathematics for schools. It is has much of what I thought I might want in Sage and is easier to handle in some ways. It is a Java package that can create java jars that can be easily placed into html pages that can be used to demonstrate graphical concepts in Algebra and Geometry. It understands Latex input for labeling, it can export postscript that can be used in a Latex document (ie Beamers). I think I am going to like this.