I am currently teaching a class on software for schools. The main topic is computer algebra, along with a short introduction to LaTeX, and to dynamic geometry. As an algebra system, I use Maxima via my own program Euler Math Toolbox. Now, at the end of the class, I am somewhat disappointed about the progress of the students. Why is this so difficult for them?
The main reason might be the structure of the class, which is only 2 hours of presence time, with little or no homework. This, of course, is far too little to learn a new language, like LaTeX, or the syntax of a computer algebra program. I would have had much more success with dynamic geometry, but this was not my main point in this class.
But in this blog, I want to point out, that teaching math using computer algebra systems, or even using math via computer algebra systems, is much different from any other math activity in school or university. First of all, it involves talking a new language to the computer. Next, you have to listen to and understand the answers of the computer. So one of the main problems is a communication problem.
So, if I do this class again, I will concentrate on only one aspect, like the computer algebra, a less ambitious aim. Then I would start with small problems of the current mathematical world of the students, so they can relate the one language to the other, the content they know to its representation in the algebra system. Moreover, they should be able check the answers of the system, via a plausibility check, simpler problems, graphical representations of the result, or using the system itself.