Some thoughts on the nascent 2016-17 school year. Cross posted: Infinite Sums
I entered the year with some plans for Pre-Cal. Initially I had some grand ideas, but the result on paper was a little reordering and some and a more intensive Algebra unit. In practice, the move has been to focus on explanations with a mix of mechanics. The first round has proven to be very fruitful. Recently we had a fantastic moment where students were given a triangle like this:
In my approach to trig I'm trying not to explicitly teach methods as much as possible, instead seeing if students can piece together ideas from what we have talked about and what they've seen before. In this case, we never explicitly discussed finding two missing sides. Two students cracked the puzzle (that sin 42 is a known quantity that can be exploited), but the methods were very different. One determined it through algebra (setting sin 42 = y/37 and solving). Another went through elaborate guessing using his trig table, using the approximate value of sin 42 and then fiddling with numerators until that numerator divided by 37 came close to the same decimal value.
This "figure it out" method is slowly creeping into Calculus, but it's harder.
Time. I mentioned it a while ago. I'm at school like 65 hours a week, plus however many to play catch up and do minor things like, you know, plan.
Let's do a break down of #1TMCThings, shall we? That's where all the summer learning comes from.
TMC13 - Wide-eyed, the community is every bit as energetic and passionate as I had hoped
TMC14 - Presenting, having people confirm curriculum ideas I had and provide feedback
TMC15 - Collaborating with Michael Fenton, sharing the Varsity Math love, getting input from Lisa and Dan on how to improve my Calculus teaching
TMC16 - Bruce Cohen's great Calculus problems, helping Lisa rebuild Algebra II, remembering Julie Reulbach should be pronounced JULIE REULBACH!!!!
I never walk away from conferences with a mountain of ideas, it's more about being around energetic people who will spitball about math notebooks with you at 11pm on the floor of a dorm.