For the last three years, I have dreaded teaching trig identities to my precalculus students. Each year we spend tireless periods going over example after example of using trig identities to prove an equation, and then students work on their homework, and FREAK THE FREAK OUT when the problems don't exactly match the examples.
Last year, this lesson fell on the day that my principal observed. Aye carumba! Talk about freaking the freak out. Luckily the math looks impressive enough that he was quite satisfied with what he was witnessing. However, it has been a trying lesson for three years. Students struggle, and struggle, and struggle...and after asking around, I couldn't find a way to improve.
After attending multiple Common Core workshops this year, one concept that keeps getting repeated is the notion of "guiding" or "coaching" the students' learning instead of holding their hand through the entire process. One presenter even suggested that we let the students "wrestle with the material." Well, I decided that it was high time for my students to warm up their wrestling skills.
On the first day, I reintroduced 13 of the 15 basic and pythagorean trig identities, and then we talked through the pythagorean identities (which they all knew, but maybe not in so many words). After this I put their assignment on the board, and started my trips around the classroom!
My students struggled with the first few problems, but then they started to see what was happening...and I WATCHED THEM UNDERSTAND!
They were helping one another, and working through problems, asking for help when they really needed it, but using their textbook and their peers for the most part. I was simply awestruck!
The second day of identities was spent with a little bit of troubleshooting: things like multiplying by conjugates and creating common denominators. The homework on the second day was considerably more complex, and my students handled it like freakin' rockstars! I even had a few tell me that they liked these problems (tears in my eyes), because they were like solving little puzzles. And they are...that's exactly what they are!
A lesson that used to take me 3 to 4 days in the past with a rather questionable outcome, has now been beautifully melted down into 2 succinct and rather successful days!
That adds up to ONE happy teacher!