Passive Learning

I picked up the AP Calculus exam scores for my students, and while I had a good number pass, there weren't as many passing as I expected or knew that COULD pass. This made me reflect over the school year and day-to-day activities and behaviors of the students. For the ones that didn't pass (but that could have), I see a pattern. They were seemingly attentive in class. They did their homework. They did reasonably well on tests. However, they did not pass. I think a big key is the "seemingly" attentive in class. They learned to play the game and knew to make the "paying attention" actions, meanwhile, maybe for a large portion of class, their minds were elsewhere. (this also goes for my other, nonAP classes).

I've never consistently had daily assessments at the end of class (of some form or another) to see who's getting it, and who's not. Yes, I've walked around class and they practice the skills. Yes, I know who's struggling. Yes, I suggest they come in for help. BUT. There was no consequence to them whether they followed up or not. My tests were structured in such a way that they could do corrections and earn back some points, and that was enough of a safety net for students.

On the plus side. Many (all?) of my students care about their grades, so I've started thinking. There are 6 weeks in a marking period. On block schedule, that means I see them roughly 15 times. Each day I could have a quick assessment (5 minutes?) at the end of class. Everyone getting a different problem (or at least everyone in one group of 4 getting a different problem) ... or 2 problems ... based on the day's topic. This could be worth 1 test point and so by the end of the 6 weeks, totally, this would add up to approximately 1/2 a "normal" test. They'd get 100% if it's correct. If anything is wrong, they have the option of coming after school to make it up. Each time it takes them to make it up (to 100%), their grade goes down to a B then a C, etc. Their tests are weighted about 75% of their total grade, so this would be significant enough to make a difference.

This way, they'd have more of an incentive to ACTUALLY focus and learn during class time because they'll be held immediately accountable for the information.

Possible "cons":
1. more paperwork (though it's only 1-2 problems per student and maybe I can have a limited # of total problems and put the problems on the overhead so they just have to have paper).

2. Would it have the desired affect? (well, I think so, and won't know until I try it) ... maybe I have to incorporate other things, too.

Differentiating Instruction in High School

I know it's a good idea. I know it's what we're supposed to do. Maybe I'm even doing it sometimes (most times?) and don't even know it. BUT. There's always a part of my brain saying, "too many kids, too little time, not enough resources specifically for math or for high school ...". Everything I have read in the past seems to be, "give projects!" and that seems to be the bulk of what I got from their suggestions.

This book (http://www.amazon.com/Differentiating-High-School-Classroom-Strategies/dp/1412917166/ref=sr_1_1/105-4459711-7881269?ie=UTF8&s=books&qid=1216748751&sr=1-1) seems to be different (from my glance and quick read through at the bookstore and through reading the 1st 5 pages and looking at the bulk of what each topic is about). I like the fact that the woman is (was?) a high school teacher. She has taught not just the "cream of the crop". She's not a PhD researcher who only knows theory. She talks about many obstacles and how to overcome them. She talks about the fact that, yes, we do have lots of things that get in the way. AND. The best part. It's geared to high school. Hopefully, I'll absorb the material and be able to use it as a springboard to make some progress this year on my differentiation.

Cumulative Knowledge

I've been batting an idea around in my head for a while to deal with the following problem. Students in AP Calculus need to remember information from (say) August on when they take their exam in May, and students/people have a very hard time recalling information they haven't seen in months even though it may have been "easy" for them in the past.

I don't want to give cumulative exams because I believe:
1. either the students will just shrug their shoulders and give up those "past" problems for lost points,
2. it seems more punative even though it's for their own good
3. I won't be able to cover ALL old topics every time
4. it would only be a (possible) review for students (say) every 2 weeks or so

So my thought is that I want to assign cumulative homework basically every class, and as we are on a block schedule, I'll give them "2" homework assignments each class, one for new material, and one for old. I don't want to have to scramble for old material every time, and I want it to be accessible to the students, so that the review process is not so painful. Here's my germ of an idea:

Have a designated folder on the computer for cumulative work. Have a pre-mapped idea of what we're learning for the whole year (and its timeline) and how many assignments I roughly need. Each time I teach a new topic, I'll have some notion of how many times I want it to appear for all the documents and I want to spread it out, so that day/week, I'll just take the basic problems (?) and cut and paste them into all the appropriate files with an "answer bank" (in some form) on the bottom of the page. It's fresh in my mind since I just taught it, so I don't have to waste time coming up with new problems for them to review. Also as time goes on, the assignments will either be completely filled with problems, so I'll just touch it up and print it out, or it'll need just a wee bit of extra work. I believe I'll also put the date(s) we learned the topic near the problem, and since they'll date their notes ("hey baby, want to go to the math movie tonight?"), then they'll be able to easily flip back and brush up. Also, since the answers will be there, they'll have immediate feedback if they remember the process correctly or not.

I'm also thinking that at the beginning of the year, it'll be slim pickings on "review" material, so I may assign things like (along with a brief tutorial on the page) finding equations of lines given various information, fraction work, factoring work, ... the basics that seem to need extra gentle and not so gentle revisits every year.

Volume of Revolution Project

This past year I tried something new with my calculus students for the "volumes project" in the oh-my-goodness-what-to-do-after-the-exam phase of the year (closely linked to the eek-I-hate-giving-class-time-to-do-projects-and-can-they-waste-any-more-time phase of teaching calculus).

I did the project with the kids to see what was involved, and I told them it was the first time I'd done this, so we'd learn the pitfalls and tips and such together. I also was vague on how they should display the projects at the end. I said, "wow me" and "whatever you do, have a good reason for it" and "think of the best way to display it to use as a learning tool".

The general idea was that we'd all have the same starting 2-dimensional region (y = 4 - xx), and we'd each revolve it around a different axis of revolution, and thus each have different solids at the end.

She wowed me with her final presentation:
This is mine (I now realize I took the picture upside down). Hmmm, spaghetti/math-tool ... probably not too long lasting:


Before she started, she kept saying, "I want to make it into Saturn", so I guess she continued with her space theme:

He was so funny, "tell me what to do. tell me what to do." Me, "no. no. NO.". He finally came up with it himself: