## Tuesday, January 8, 2013

### Day 76: The Trig Table

I hate calculators. Ok, that's a bit extreme. After all, a calculator is just a tool - you can't hate a tool (or at least, you shouldn't, because it's an inanimate object incapable of malice), but you can hate how some people use the tool.

I don't know what it's really like nationally, but I get the feeling that students are handed calculators as early as 4th grade and they never look back. In 6th grade they get a fancy scientific calculator, and in 9th grade they get an even fancier graphing calculator. My district has always been on the lookout for grants and giveaways so we can get more graphing calculators and put them in everyone's hands as soon as possible. But why? How much quadratic graphing are they doing in 9th grade algebra? Even if they do cover it, shouldn't we be reinforcing the underlying theory by manually graphing the functions?

My students have very poor number sense. Take away their calculators and suddenly fractions don't make any sense. Radicals are a disaster. Sine, cosine, tangent? Forget about it. That's why a few years ago, I decided to stop allowing calculators when we reach the trig unit. I give each student a copy of the trig table (also available in their textbook) and we work through it "old school." My hope has always been that this will underscore that sine/cosine/tangent are just names given to very specific ratios in right triangles, but I don't know to what extent that message has come across.

This year is no different, so as we went over yesterday's investigation, I talked about how we could create a list of every possible ratio, from 1 deg to 89 deg, for a total of 88 * 3 entries. The kids immediately freak out thinking that will be the next assignment, draw a 1 deg right triangle, measure, divide, repeat. Good - I want them to panic. They need to appreciate what the table is (and later, what the calculator is doing when you hit that 'sin' button).

I downloaded a pdf of a trig table and fit it onto a half-sheet of paper, then laminated and cut out each one (yes, it really takes as long as it sounds). The first thing I heard as I passed them out was "Oh, it's laminated. That means we don't get to keep it." That was a real eye-opener to me. We (at least in my district) have taught the students "If it's nice, it's not yours. Give it back." Ugh. In any event, they were ecstatic when I told them it was in fact theirs to keep and the lamination should serve as an indication of how important it is. "You will NOT be able to solve ANY problems without this table!" I bellow to each class.

We didn't get much past identifying opposite & adjacent sides and setting up the three ratios, but I'm optimistic as always.