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"4. Technology shallows out learning, IMO.

This can be debated. My feeling is that technology is simply a tool. It has to be used in context to make it work. Too many schools rely on it as a hook. Kids are not going to be hooked by tech without the teachers being able to advance it more than they see everyday."

This observation about shallowing out learning is based on my own experiences. I frequently tutor kids in calculus and their depth of understanding is very shallow as their approach is too frequently to rely on their graphing calculator, which leads to very little intuitive understanding of what a curve will look like, or how a function will behave. Plus, due to years of this, their basic skills in algebraic manipulation are weak and without strong algebraic manipulation skills calculus is way more challenging than it needs to be.

An example: I was at my local coffee shop a few weeks ago and there was a HS student there studying for his AP test. As I always do, I told him that if he needed any help I was a math teacher and would be happy to help him. He kind of acknowledged me with an undercurrent of "sure, this old guy could help me? Ha!" So I just went back to reading my kindle.

After a while I saw that he had been working on the same problem for about 20 minutes. By working on it I mean he was looking at the problem, punching buttons on his graphing calculator but clearly getting nowhere. At this point I asked him if I could look at the problem. It was a relatively simple problem in implicit differentiation. But to get the boundary values you had to also solve a quadratic equation. I did the problem and then asked him "Is this the answer? xxx?" He looked surprised that I had the answer correct - and that I hadn't used a calculator to do it. Needless to say his attitude changed and he was more than willing to listen to my explanation of how to do the problem. But honestly, it was too little too late to do him much good on the AP test.

A graphing calculator is not a necessity for mastering calculus. While on one level it could be used in a way that deepens and enriches the learning, in my experience that is not what happens. It usually becomes a crutch which prevents deep understanding. Shallowing out the learning.
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