Calculus. Wednesday: Circle area. Archimedes. Zeno. Started Boelkins' Velocity of a Ball activity. On Thursday, we got through most of the Velocity of a Ball activity. The students did not recognize that (s(b) - s(a)) / (b-a) is a slope. So We are working through the parts they need to review. I am goign slower than in other semesters. I hope I'm not going too slowly.
Linear Algebra. Wednesday: Discussed differences between Echelon Form and Reduced Echelon Form. I started with: a matrix in Echelon Form, and got them to tell me the values of the variables. I explained that this way is quicker for computers. We talked about number of possible solutions, and drew examples in 2D and 3D. Quiz tomorrow. (Quiz made and copied.)
Thursday: Most of them aced the quiz. The ones who didn't will be in my office to retake. We finished 1.2. (I hate referring to book sections, instead of math topics. Basically, we are working on row reducing matrices. We've started to think about parametric representation of solutions, where there are free variables.)
Pre-Calc. Wednesday: We practiced an arithmetic sequence (find the nth term) and a geometric sequence. We looked at a problem that used a recursive definition for a n. I mentioned the Fibonacci sequence, but didn't do much with it. Quiz tomorrow.
Thursday: Only a few aced the quiz. It was harder than what we had done in class. I'll give a retake on Tuesday in class. We reviewed lines. I walked them through my proof that perpendicular lines have slopes that are negative reciprocals. (It's different from the text's proof.) In the process, I also walked them through the proof that the angles in a triangle add up to 180 degrees. I love how the result suddenly pops out of the picture. I asked them to show me with their thumbs (up, down, sideways) how cool it was. They all gave it a thumbs up and I said they were being too nice. The bigger proof (for perpendiculars) gets an 80% coolness rating from me.
Calc III. (I am sitting in on this class.) Wednesday: Ed showed us how to connect the tops first and use dotted lines for hidden lines. I noticed that it felt like we were seeing the xz-plane from the back. Thursday: Over an hour of lecture. Ed is a good lecturer, but that's too long for me. I fell asleep. I woke up for the quiz. It included drawing 3D surfaces. I understand all of this, but how well did I draw? I'm not satisfied yet.