since it is so much easier to just paste thoughts i was forced to have and then record, i figured i'd get twice as much bang for my buck and reuse it here. the entry is horribly aimless, i start on one thing then go off on another repeatedly. but i don't think i could write all my thoughts/frustrations about teaching/these goddamn kids, given infinitely much paper and/or time. it would just go on, forever.
the way education is "reforming," they're only going to get stupider.
Building Math Understanding from the Ground Up!
Eric Chang
Journal entry 1, 1/19/2006 - readings 4 and 6
I teach a geometry support class, support being a euphemism for kids that failed geometry already and have to retake it. In addition, I have students that failed algebra I and have inexplicably been assigned by our most capable guidance counselors to take both algebra I again, as well as geometry for the first time, in the same semester. Sci-Tech is on a block semester schedule, which means these unforunates have been taking math classes for 3 hours of each day, every day, since September. So I deal with a lot of children that hate math, have always hated math, have parents who hate math, have probably been told by teachers at some point that they'll never be good at math, and so on.
I also teach a probability and statistics class, which up until this year was a joke course for seniors. I have students whose counselors signed them up for it even though they failed algebra II, because they (the counselors) think statistics is a class for kids who are bad at math. Although these are decent kids willing to do work, some of them are not exactly naturals when it comes to this subject.
My third class is AP stats, but I have very few issues with them regarding their math backgrounds. I'll mostly be talking about my geometry class in this entry.
The readings bring up a lot of frustrating points for me. I look at myself, and all I had to do in high school was memorize processes. I believe the thinking at the time was, learn the process first, get the big picture later. As in once we got the details, the nuts and bolts, the why of it would eventually appear in our brains, kind of like enlightenment? And that all worked for me. Now I don't know why it did - maybe I'm an atypical case.
Reading 4 talks about fluency, and how learning the standard algorithms will not help students develop fluency. That's true on some levels but I still think the algorithms are needed. I don't see how one can expect a student to be proficient, or whatever you want to call it, in math if they can't memorize simple processes. And long division (the how and why of which I could explain, by the way), which some people would choose as the poster child for unnecessarily difficult and unnecessary algorithms, is simple. It might look long and arduous but it's really just the same few steps repeated over and over. Like it or not, I really believe that some memorization skills are required for proficiency in math. Without memorizing that V = B * h, how is a student supposed to realize that he or she needs to find the area of the base of the prism first, or in the case of a pyramid, they need to solve for the height using the pythagorean theorem with the cross section of the pyramid as a right triangle? I have kids who have learned how to do exactly that, and I try to emphasize that it only applies to this specific situation, but they zero in on the process and don't place importance on the why of it. Then when they get to a pyramid where the height is already given, they're lost because this time they're already one step closer to the solution than in the previous problem, but they don't realize this.
I try very hard to give my students multiple approaches to every problem I give them. For example, Any time we deal with circles, I tell them that they can keep it in terms of pi or multiply the 3.14 in and round to the nearest tenth. I don't care. I know some like it better one way or the other. I don't even try to force them to learn both, even though a student fluent in this topic would understand that there's no difference. But to my students they are completely unrelated. When I show them that the only difference is muliplying the pi in as a decimal approximation, though, I see only blank stares.
Reading 6 talks about estimation, and the importance of evaluating reasonableness of results. In statistics this is everywhere. Since almost all of statistics deals directly with real-life situations, and most statistics problems are modeled on these situations, the answer can always be evaluated on the basis of whether or not its reasonable. Whenever the students are doing classwork and bring me their work to ask if they got the correct solution, I always ask them if that answer makes sense. Whenever I have to re-explain a concept to a student one-on-one, I find myself asking, "does this make sense," repeatedly as we talk about the reason for each step in the process. They usually nod their heads; I have no idea if they're being truthful. Overall I get positive results from this, though.
Lately we've been working with expected values, and there's all this stuff about whether or not a probability is less than, equal to, or greater than a certain value. And it's not theory or anything like that, it's concrete, real stuff. There are multiple ways to get which one it is: >, =, or <, one is straight-up calculation and another is testing for reasonableness and working backwards from there. I showed the class both methods, but it's only taken hold for a few of the kids. I don't want to describe the actual process here though, that would take too much space.
I try very hard to give my students that understanding, to tell them how or why this formula is accepted as true. When teaching the formulas for area of a parallelogram, I showed how it was derived from the area of a sliced up rectangle. For a triangle, I showed how its area was derived from half of a parallelogram. For a trapezoid, I showed how its area was derived from two parallelograms. I told them that they didn't NEED to know it, but it would help them remember the formulas if they understood where they came from. On the test for that chapter, I asked them to explain any of those three as bonus questions, and not one kid even tried to answer it. Even the brighter ones in my class left it blank.
There's so much more I could say about my geometry class and my mostly failed attempts to get any one of multiple methods to stick in their heads for any given topic. But it would just turn into a rant about how kids these days expect everything handed to them on a silver platter and we can only spoon feed them so much before we're just ensuring our own downfall as a society.
Oh, and I will never get used to going over a whole problem on the board, and after having solved for whatever the problem said to find, having four kids raise their hands to ask, "what's the answer?" I just said it, for crying out loud. And if I was a student, even one who was not paying attention, I think I'd be not stupid enough to go with the number written at the bottom of all the work.
