What is the cost of, the simplicity of writing with a pencil, vs learning to write math for a computer – with the more powerful responses that come with it? http://blog.mrmeyer.com/2014/a-response-to-the-founder-of-mathspace-on-the-costs-and-benefits-of-adaptive-math-software/

The conversation started with feedback. Research has shown that feedback is important. -> Many math software provide simple right or wrong feedback quickly. -> Too often this feedback is more the fault of syntax errors than actual math errors -> programmers add hints, or expand the possibilities of correct answers -> kids still hate it.

Teachers follow-up saying, basically feedback has to start with what the student is doing and thinking and start customizing from there.

The holy grail is for a computer to recognize the typical mistakes, often mistakes can be put into general categories, and send a standard, but custom, message to each students as they need it, preferably in the form of a question so that students actually solve the problem instead of waiting for the computer to do it for them.

I saw a company trying to do something like this through hints, but I think they needed to get more data on which mistakes meant what hint to actually give.

While the cost of learning to write for a computer program is high and the feedback so far doesn’t seem that great, I start to think of programs such as Geogebra and Desmos and the feedback they give, even though they don’t advertise their feedback.

When I was learning Calculus, before the widespread use of Maple (I remember struggling to input equations correctly then waiting minutes for the graph to load), I never made the connection between functions, tables, and graphs. I got lost in the calculations, which took too long (and I was faster than most at the calculations).

Fast forward fifteen years and I’m teaching middle school Algebra and we are given a class set of graphing calculators, suddenly relationships between numbers and graphs are evident. Which, brings us to the age-old question, “How much of teaching math is teaching understanding and how much is teaching the mechanics?” or “How com we never really understand something until we try to teach it.”

The question for teachers I suppose it:

“How long do I let my students practice on the computer with the limited feedback, and how much time do I have to work with individual students?”