I am figuring out three things about teaching Geometry:
1.) Geometry is when they really are introduced to a lot of things for the first time. Therefore, it is great for discovery type lessons. Versus when I have been teaching Algebra 2 and I am saying, you have already learned this, let's make it more challenging.
2.) Discovering at the boards with VNPS is exhausting. I am doing 3 lessons a day at the board with classes of 28 kids all at the board. Then, sometimes, add my Alg 1 and 2 classes at the board.
3.) Learning is messy and productive struggle is uncomfortable for both the kids and the teacher. I want to jump in and help, but I can see them building their understanding one piece at a time and I don't jump in and save them. I let them build.
Lesson in point - yesterday's lesson about Right Triangle Trig. The lesson was ambitious and I knew that going in. I was supposed to teach them all 6 trig functions, including how to solve for the ratio or the angle on the calculator plus introduce angles of elevation and depression.
I did my best to really stress that the trig functions are just side ratios. They were able to stumble through my board problems. I did introduce SOHCAHTOA as a when of remembering them. I introduced the three reciprocals. I got to one problem introducing angle of elevation and they were able to do it. I did not get to angle of depression.
Here is the powerpoint lesson: Right Triangle Trig Lesson
Here are the board problems: Right Tri Trig Board
Here is some student work:
I read somewhere online to start them off relating trig to a ramp. I asked them to draw the ground and a ramp that had a slope of 3/4. This is what I got:
So, I asked them to erase it and label the horizontal and vertical instead:
We learned about theta and from theta we labeled opposite, adjacent, and hypotenuse. I told them the 3/4 was a tangent ratio. I asked them to come up with 5 more combinations of side ratios using opp, adj, and hyp. Then, we named them:
I left each lesson not feeling done. They left feeling confused.
The thought came to me that I fed them all a huge Thanksgiving dinner and then I kicked them out without giving them time to digest.
They tried the homework. I went over it today. I went over each problem. They were starting to see the connections for each side ratio. Some of the word problems were challenging because they were overlapping triangles.
I did discover one student's misunderstanding. She thought COSECANT was another acronym and couldn't figure out what it stood for. She kept asked what it was. I kept saying it was the reciprocal of Sine. Then, she finally said, but what does it stand for. I think I corrected her.