Gone for a week

I am looking forward to commenting on several issues, but I will be traveling for the next week. No new posts until next weekend. Everyone enjoy the end of July and beginning of August.

AP scores are in…

Well, I am a little excited and feeling very good about what I did in Calculus BC this year. This past year I eschewed a traditional textbook and gave the students a packet of problems, most of them taken from curriculum from Phillips Exeter Academy, and we worked on these problems all year. They spiraled through the curriculum, spent a great deal more time on vectors and parametrics than I had previous years, and less on series. We had very little review at the end of the year before the AP exam, significantly less than I had previous years – in fact the students last test on new material was a take-home due the day after the AP exam. We pretty much had time only to go through the multiple choice section of one old exam, and talk briefly about the free response questions to the same exam. I never stopped at the end and said, “Here are the topics you need to be aware of for the AP exam.”

What we did do is spend a lot of time solving problems, facing new and unknown situations (they did at least… not too many of the problems stumped me), and learning how to talk about math and communicate results. Some of the students struggled daily with this approach, talking to me privately to say that they were much more use to a class where the teacher told them what the topic was, presented it, and then practiced it for homework. Another student would answer the more theoretical problems in a way that I can only call “elegant.” It was beautiful to watch.

Everyone of my students earned a 5 on the AP exam.

There are some caveats of course. It was not as if this was a dramatic upturn in my AP scores. In the four years previous to this one all but two of my students had earned 5s (and those two earned 4s). So at the very least, my approach this year did not hurt anyone. Some will say (with good reason) that our program is too selective and what I did with the students was bound to have good effects because I had good students. I agree our program is too selective, but that is a topic for another time. One thing I said in the previous four years was that the best thing I could do for my students in BC was to stay out of their way as much as possible and they would get 5s. In fact, when complimented on my scores for a year I would always defer to my students and say that at least I did not screw them up at all.

This past year was the first year I felt these extremely bright students left my class having really learned something about math. The calculus they could do blindfolded with a monkey teaching the class, but it was how to talk about math, show their work, face failure, and get excited over an elegant solution that I saw them learning this year.

I cannot wait for next year!!

V for Vendetta

I just watched this movie again tonight. Listening to V’s story about the fear that the government created in order to clamp down on the populace makes me think about how our government seems to be run these days. I was called as part of a survey today where they asked a number of questions about two propositions on the California ballot this fall, Proposition 6 and Proposition 9. Both seemed geared toward making us more fearful. Particularly Proposition 6. Spending more on stopping crime, increasing spending on prisons, police offices, and the like. The United States already imprisons more of its population than most countries in the world – including those that we supposedly think are more oppressive. Just read here, here, or here.

How long do we let our politicians tell us to be fearful and who to be fearful of? I’m not advocating blowing up Congress as V blew up the House of Parliament in the movie, but how far must we be pushed before we push back.

I keep coming back to Ben Franklin’s quote, “Those who would give up essential liberty to purchase a little temporary safety, deserve neither liberty nor safety.” We have walked down this road already. George has held our hand as we did so, and John wants to continue on the same course.

I believe in America, but not America the country or the land or even the people. I believe in the idea of America. The Declaration of Independence. The Constitution. The Bill of Rights. These are what America is to me. When our politicians claim they want to keep our land safe, but then trample on these documents I have to ask what they really believe in.

Who is V? “Edmond Dantes, my father, my mother, my brother… He is you, and he is me.”

He is me.

To CAS or not to CAS…

I just finished an online course on how to use the CASIO ClassPad 330, and I have owned a TI-Nspire CAS since they were first released. In addition, over the years I have used MathCAD, Maple, Maxima, and Mathematica. I have been using some of the CAS capabilities in my upper level classes, but usually only to help answer a question we had. I went to a conference in June called USACAS just outside Chicago, and the things that I saw were amazing.

The kneejerk reaction from many math teachers is that CAS is bad. I mean, for about $150, you can buy a CAS enabled calculator that will essentially do all the skills we teach in the high school curriculum – including AP Calculus! So the first thought is usually that we must keep these things out of the classroom, otherwise what is the purpose of what we teach? That was my reaction initially as well. Now my reaction is to ask that question more purposefully. Why do we teach what we do? Too many math courses focus on the algebraic manipulation that CAS was built for. I am not saying that students should be unaware of how to do the manipulation, else how would they know when it goes wrong. But we spend too much time on it, often to the exclusion of the big ideas.

Ever since I realized that problem-based learning is what we should be focusing on, I have come to regard CAS as a helpful tool. Not to replace the learning of skills, but to supplement and and enable the learning of the skills. For those math teachers who complain that it is not the way they learned it, I only ask how many people today remember any of those skills unless they are directly involved in teaching them. Very few.

I say we use CAS.

When have we taught? When the students learn.

I am sick of hearing from teachers, “But I know I taught them that last year (or the year before, etc.)” when it is clear to the present teacher that they do not know that particular concept or skill. They say it as if that sentence says all that needs to be said.

The bottom line is that if the students have not learned it (in a real and lasting way) then the teacher did not teach it to them. They may have “taught” it to the class… but I would argue that such “teaching” is nothing more than presenting or lecturing.

Saying my students learned something just because they may have done well on my test is even not enough, if they cannot remember it later on.

I was reading the stories of the Trabuco Canyon High School students whose AP scores were invalidated because their school screwed up. That’s who the students and their parents should be going after – not the CollegeBoard. I hate to say that I actually think I am on the CollegeBoard’s side on this one.

At any rate, the students were upset about taking make-up tests at the beginning of August, and that they would not be able to do as well on them because they wouldn’t have enough time to prepare. Does that not say something about the quality of the AP classes at Trabuco Canyon? If the students have so forgotten the material that it would take them more than a few weeks of brushing up on the material to do well on the exams again? Sounds like Trabuco Canyon had problems with their AP program long before the exams rolled around.

I’m just saying.