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Sunday, February 11, 2007

Irrationality

Rudbeckia Hirta reports that her college students have trouble understanding irrational numbers:
Most of my students felt that 3 * sqrt(2) / 5 * sqrt(2) was irrational because of the sqrt(2). They didn’t remember that you can “cancel” (hate that word: prefer “divide out”) the sqrt(2) that appears in both the numerator and the denominator. More alarmingly, many of them decided that 3.14159 was irrational, citing only “it can’t be written as a fraction,” and forgetting that 314159/100000 is a perfectly legit fraction
I wonder if my Weston High School students will have the same difficulties. Maybe they won’t, since all Weston students are above average. I particularly hope that they won’t write “proofs” like the ones that Prof. Hirta cites. For example:
We’ll be studying irrational numbers in a few weeks; I’ll let you know.

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