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Adventures in Mastery 5: Making Connections

I taught my year 7 class today and had the most wonderful time.  I really love my year 7s, they’re so enthusiastic.  So far this year we’ve done place value, rounding, four operations (with natural numbers and decimals), powers, roots and primes, negative numbers, order of operations, fractions (including four operations) and are early into our unit on percentages.  Today it was common FDP conversions (quarters, eighths, fifths, thirds, ninths, etc).

We looked at 1/3 and 2/3, which led us to the fact that 0.999999….. = 3/3, which is, of course, 1.  I love teaching this fact, I tell them I’m about to blow their minds, and when I show them the initial reaction is always something like, “but it can’t be 1, it’s less than 1″.   Continue reading “Adventures in Mastery 5: Making Connections”

Relevance Is Not the Goal

Experience has shown, and a true philosophy will always show, that a vast, perhaps the larger portion of the truth arises from the seemingly irrelevant.

Edgar Allan Poe
The Mystery Of Marie Rogêt

In my last post, about the history of mathematics,  I mentioned briefly the mathematician GH Hardy, who was based in Cambridge in the early twentieth century and who was the mentor of Srinivasa Ramanujan, the subject of Hollywood’s latest foray into the world of mathematical genius.  Hardy wrote a wonderful book called A Mathematician’s Apology, in which he discusses the beauty of mathematics and expounds the importance of mathematics for its own sake, rather than for its applications.  Hardy was vociferous in his belief that the most beautiful mathematics was pure mathematics, that which had no applications. It wasn’t that Hardy was against applying mathematics per se, more that true elegance existed in a discipline that was pursued chiefly as a matter of intellectual curiosity, or in the act of creating or discovering something truly new, without the ulterior motive of improving the material lot of humankind. Continue reading “Relevance Is Not the Goal”

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