Who do we seem to take more pride in: A jeopardy winner or a famous inventor? Obviously it’s the latter (though Ken Jennings has probably seen more fame then the person who invented toenail clippers), at least in terms of respect. Those that create, not just regurgitate facts or knowledge, hold not only respect, but have much more fulfilling careers (a bold claim, perhaps). I think it’s because of the sensation I feel, elation perhaps, when not only do I learn something, I do something completely new with that knowledge. It doesn’t happen all the time, in fact it’s quite rare, but when I do, it’s like magic.

So what are we mostly teaching? Knowledge and understanding. Lower orders of thinking (not bad, but not enough). There’s a whole other realm out there. Going through Bloom’s taxonomy, I like to look at a simple task. If we’re teaching addition, it’s one thing to remember that 5+7 = 12, it’s another to understand it. Applying we get to in mathematics a lot, through activities and word problems, which is definitely a step up. Once you get to analyzing, most teachers don’t follow through. If we can look at addition and break it down (perhaps we do this when originally teaching) but for the student to be able to break it down and apply it to the structure of mathematics, that’s a lot better (and I don’t have a good example for that). Evaluating would be taken it further. Is addition the best way to represent a grouping of numbers? Finally, is there another way? What if we had to reinvent addition? What would it look like? I take this from a great book, *Gödel, Escher, Bach: An Eternal Golden Braid, *where he partially reinvents mathematics for illustrative purposes. What about showing numbers a little more visually. 2+3 = 5 or SSO + SSSO = SSSSSO is a quick example, or to reinvent the modifier SSOSSSO=SSSSSO. There’s so much more (time permitting!) that we could do with students to take them into higher level thinking – which will ultimately make them more well rounded, more interested in subjects, more likely to be inventors, someone who doesn’t just follow the status quo.

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