I love mathematics. I love technology. Therefore I agree wholeheartedly with this piece, which explains that there are no technological shortcuts in the learning of mathematics, and many technological hindrances.
Good quote: "earned fluency is the only way to understanding". A calculator can tell you the answer; but plenty of hard work with pencil and paper is the way to understand the answer. Confusing those two concepts is fatal.
On the subject of mathematics, here's a link to an article I wrote a few years ago, "Creation and Mathematics".
An interesting subject. In my oldish age, when I have forgotten much of what I had learned in earlier years, I have strangely held onto the basics, and when I need to solve a problem, I can often do so by returning to the fundamentals, even though I had forgotten a formula or shortcut. When I use a calculator, I still mentally verify that the answer is within reason, trusting my brain more than my fingers. Given the sense of this article, I wonder whether future generations will have an understanding of the fundamentals of the technologies and tools they are using. Toward the end of my 35 year IT career, I often wondered what IT graduates were being taught at colleges and universities, for in the commercial field, they showed a lack of problem solving ability except in a very narrow domain.
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