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Not trying to disagree with you about the crappiness of this student's education, or how sad it is that he counted with his fingers, but computation != mathematics.

I HATE the fact that American schools force students to do rote computation over and over again, with very little focus on the concepts behind the computations. I hated "math" until my 6th grade homeroom (not math) teacher took the initiative of writing high school level algebra word problems on the board, and not telling us how to solve them until after we attempted them. "A train going from St. Louis is headed toward L.A., and another train from L.A. is headed to St. Louis. they are going 40 mph, when will they pass each other" etc.

Suddenly, when the computation becomes a tool to satisfy an end, rather than the end itself, math becomes interesting.

... computation != mathematics.

This is exactly why giving calculators to children who have not yet mastered any method of multiplication is bad.

Its kind of subjective though. In my schooling, when we moved from basic arithmetic to "word problems" as these were called (i.e which required you to formulate the mathematics yourself), I was completely lost and intensely dreaded the process. It seems a bit silly saying it, but at that time I didn't understand that I had to actually understand what the problem was asking of me. Before then, learning math had been "if you see A, do B" and I would frantically search for "patterns" to similar problems. It took me a long time to realize that the problem itself was telling me how to formulate the solution.

There is an amusing end to this story. When I entered college, I realized that this pattern-finding approach to solve math was used (in vain for the most part) by many of my classmates to try to game exams. It seems that it had worked well for them through high-school, but failed miserably at college.

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