Thursday, September 18, 2014

Time to learn and prioritization of what to learn

From The Glass Wall: Why Mathematics Can Seem Difficult, by Frank Smith. On the pedagogy of teaching mathematics.
Anyone can learn to understand and enjoy mathematics provided nothing goes wrong. And nothing will go wrong provided four essential conditions are met. They are:
The mathematics must be interesting and comprehensible.

There's no fear of mathematics.

Inappropriate things aren't learned.

There's sufficient time.
Interesting thought and I would substitute generic topic "X" for the specific "mathematics". I instinctively agree with all four with caveats and qualms about the third item: who determines what is inappropriate to learn and what are the objective metrics/algorithms for determining that and who gets to determine?

Each of the four items warrants reflection.

The fourth item, for example, is deceptively simple - "There's sufficient time." True enough but the reality is that we are time constrained. There is never enough time. Given that there is, for operating purposes, a fixed amount of time, then the unstated task is to ensure that what is being learnt is worthwhile. If we are going to invest the, say, 100 hours necessary to learn, what topics or subjects are more warranted than others since there are virtually infinite topics and only a fixed amount of time. There's the rub.

For your typical student, are they going to benefit more from 100 hundred hours of studying Western Civilization or 100 hours of Trade Relations between Tanganyika and Zanzibar, 1500-1950? Both are interesting and valid fields of study, but with limited time, which is more important, AKA, which is more beneficial?




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