Friday, February 24, 2012

Teaching and Tutoring, It's All Good...

It's been hard to blog this school year. I've been devoting myself to my classes (and to parenting), and just haven't found time. I went to a great conference just before the semester started (Creating Balance, on math and social justice), and meant to write about it, but just didn't find the time.

I'm posting now just to say that I'm loving my classes. I feel a bond with each of the 3 groups. Two of my classes ended up being only 16 students each, and one (calc II) has 35 students. I felt guilty at first, because our classes are capped at 40 students, and I felt like I wasn't doing my share. But once the semester got under way, I was so grateful. The students in the smaller classes speak up so much more!

Our first unit, reviewing linear equations and graphing, along with studies of circles and inequalities, showed me how much this group was going to struggle. The great thing is, they are struggling through it. The attendance is better than in my calc II class, and most of them are working hard.

The atmosphere is very lively. Students are comfortable sharing what they don't get. One student, after seeing my solution to a problem, said "I got that, but I was sure it was wrong. I did the problem 5 times, and then I threw my book across the room." I asked why she was so sure the (right) answer was wrong. Unfortunately, I don't remember what she said. I think she expected a prettier number for the answer than what she got.

We're working on triangle trigonometry right now, and a student who really struggled in the first unit is calling out answers now, and introducing the next topic by making connections (you'd think I had planted her in the audience for her great effect). Her enthusiasm is catching. I love trig, but my students haven't loved it in recent years. This time, we are so into it!

On Wednesday, I did a proof of Law of Sines for them. (-After having shown it with a numeric example on Tuesday.) They liked it. It was short enough to hold onto, and they could see the beauty in it. We all agreed that the proof of Law of Cosines was ugly in comparison - mainly because it's too long, but also because the meaning gets lost in the algebra, I think. I did improve on the textbook's version, by focusing on the Pythagorean Theorem, instead of the distance 'formula'.

Calculus II
This class meets at 8am, in a long narrow room with the students in back so far away. They don't ask many questions, and most of them are scared of looking dumb or holding the rest of the class back.  So it's harder for me to see what they're struggling with. But I walked in unprepared on Wednesday and gave my best lecture ever on Integration by Parts. Yeah, I know, lecture isn't enough. I think I got them working in groups on a problem, too.

On Thursday, I was tackling this one. When I got to
I put boxes around the integrals and labeled it as m = term + other term - 4/9m (where m stands for mess), and asked them to tell me the next step. They did. I think they saw the beauty too.

The proof (of whether my fun-for-me lecture sank in) will be in their practice. I hope they come with lots of questions on Monday.

Two students in this class asked me for extra help in understanding exponential and log functions, so we're doing a completely optional review session on that today. 10 students have committed to show up. (Now the session has happened; 7 students showed up. They were still pretty quiet. Hmm...)

Linear Algebra
I'm teaching this for the first time in over 10 years, and worked hard on prepping myself before the semester began. The text, by David Lay, is unusual, I think. In the first chapter, he introduces linear (in)dependence, span, linear transformations, and more. He also works a lot with column vectors, in ways I wasn't used to. I'm used to it now, and totally enjoying both the course and the group of students I'm working with. I just gave the first test yesterday, so we'll see how they're doing soon.

This is the first class I've ever had that's ahead of the schedule I set myself, instead of being behind schedule. I am so impressed with the students. A student I had last semester was nervous about how she did on this test, so I graded hers right away. She got an 85% and looked crestfallen. I told her I thought this might be the hardest test, and that I totally trusted that she would be able to ace the course. I think I reassured her. She and her friends work very hard, and she asks good questions.

I avoided the lower level courses this semester because I was tired of struggling with behavior issues. It looks like that was a good decision for me. I am excited and happy about my work this semester. Eventually I'll have to go back to the algebra students and try again, but for now, I'm enjoying helping students who want to learn math.

And Tutoring
My tutoring session with Artemis yesterday was a blast too. We're looking at patterns in repeating decimals. I'm learning along with him, pondering the mysteries of number theory. There was an 'extra hard' problem at the end of the chapter. It asked whether the decimal formed by the units digits of the triangular numbers (.1360518...) is rational or irrational. I said it looked too hard, and maybe we should skip it. He said, "I have a proof". (!!) He had thought (in just a few seconds) about the patterns involved in triangular numbers, and worked out why that would make this number rational. I think he'd seen a discussion of how each group of 20 numbers always adds to a multiple of ten, and that was enough to send him in the right direction. His proof looked sound to me, and it's the first time I could see how he'll eventually surpass me mathematically. His memory lets him hold so much at once, and then he gets to put those pieces together more easily.

We're getting close to the end of our text, and I've been mentioning the classes offered by Art of Problem-Solving, because I think that will be his best next step. I might take the Intermediate Number Theory Seminar with him, so he doesn't have to participate online if he's not ready.

Tomorrow is the first session of the (renamed, and slightly differently organized) Richmond Math Party. Join us at 3 if you're in the area.


  1. Out of curiosity, do your students dread handling integration involving trigonometric functions?

  2. I don't know. Maybe I'll find out tomorrow. Do yours?

    They do have trouble remembering which of sine and cosine get a minus. I've tried to show them how looking at the graphs (do they know those?) helps me see which slope is the opposite, but I don't think it helps them much.

  3. Yes my students detest trigonometric calculus. They are fine with the derivatives ( and anti-derivatives) of sine, cosine and tangent, but just cannot tolerate variants of cosecant, cotangent and secant stuff. Not to mention arcsin, arccos and arctan functions.

  4. Ahh. Well, I focus more on sine and cosine, except that I think of inverse tangent as one of the basics. (Tangent and secant go together in this, so they can't sensibly be fine with tangent and hate secant, can they?)

    I imagine they feel they have to memorize all that, and it's too much. Are you their teacher or tutor? If you give me an example of a problem they hate, maybe we could discuss it here...


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