This unit was a good one during which to start my blog. Puns galore.
Today was the first time the students saw the “therefor(e)” symbol – three dots in a triangle, with the bottom two dots determining a line parallel to the bottom of the paper. Picture it – because I can’t type it. Or don’t know how anyway. It’s not a big deal either way. In any case, where did this thing come from? “Why do three dots mean therefore?” No lie. A direct quote from a student in each of my three sections. A conspiracy, perhaps? Having anticipated this question – and indeed the only reason I even introduced the symbol is because I had what I thought was a good answer – I was quick to respond. Well, in a 1659 book by Johann Rahn, the symbol was introduced sort of arbitrarily. A lot of work was being done with proportions at the time, and to solve for an unknown quantity, one must know the other three parts. Three dots meaning the problem could now be solved. I have all three parts, THEREFORE, the answer must be _________. I’m not sure about the validity or accuracy of this answer, but nobody questioned it. Mission, one-third complete.
Working with rules of square roots…a square root is something to the half power. Side note: during this part of the lesson, a girl asked me why they are called “radicals.” I said the Latin word for root is radix – the same place the symbol came from (a bastardized “r”). I never made this connection before, but she said “radishes are roots. Is that why they’re called radishes?” It made sense, and all I could do is thank her for actually using her brain. Which I did. So anyway, I connected today’s properties of square roots – which the book treats as a completely new thing – with the properties of exponents we learned months ago. I think it helped understanding. It’s not new – it’s just a new twist on an old topic. I used to hate when teachers said it to me. I now know why – it’s true! If any of you are students – listen to your teachers. In general, they’ll know what they’re talking about. If not, you’ll know. Question when unsure, not just to be a jerk. Two-thirds.
As far as connecting the history together? It was a stretch today, but a while back I taught them that the division symbol (horizontal line with a dot above and a dot below) is called an obelus. Who introduced that one? Johann Rahn. A connection! three-thirds done and just in time. Bell’s about to ring. Have a super night