I've been thinking about this a lot lately, and I've concluded that I need to write rants like this from time to time. I just need to keep them separate from the news - like the newspaper separates the news from the editorials - so the folks who want to read the news aren't offended by having to read an opinion from outside their bubble.
This is going to be a math rant, and they can be among the worst. So, if you want to skip the rants, stop reading now.
When Terry Bergeson was the Superintendent of Public Instruction, she said that the students should not be held accountable for failing the math WASL to graduate because it was not the students, but the adults in the system who had failed. On THAT day they should have all been fired, herself included. They are never held to any kind of accountability yet they have the greatest responsibility. Why does the accountability net catch the small fish and let the big ones go?
The greatest impediment to the kind of reform that our schools really need is not the teachers or their unions. The greatest impediment to the reform we need are the administrators at the school, district, and state level who are responsible for the design and maintenance of the system. Our problems are systemic; it is the system that does not work, not the people in it. Have they never even heard of Deming? Where are they learning management? They are the ones who responsible for the system, they know it doesn't work, yet they refuse to fix it so it will work. That's not only incompetent, it is borderline evil.
I have a report from a teacher about a student in a pre-calculus class who was stumped by simple linear equation. That ain't right, but I don't blame the teachers. I'm sure that the student's high school math teachers are capable people. My daughter has taken Geometry and Advanced Algebra in one of our high schools. I have seen her homework and I know for a guaranteed fact that she would have no trouble with that linear equation. I suspect she would even have recognized it as being in the y=mx+b slope/intercept form. HOWEVER, she learned that from me when she learned algebra at home in the eighth grade.
My daughter has had the great advantage of coming home to a parent with the unusual combination of math skills, math understanding, and the time, interest, and ability to explain things. For any line on a plane, you only need two points to define the line or one point and a direction. One of those points is the y-intercept (when x=0), the other point (or the direction) comes from the rise over the run (the slope). Or, as in the examples from the teacher, one is given as a set of (x,y) coordinates and the other comes from the slope. It should have been easy.
The problem - and I know that I'm preaching to the choir here - is that students working in a spiraling curriculum such as EDM or CMPII, are never allowed to achieve mastery, only familiarity. Familiarity fades so that when they are presented with the material again they do not recognize it. You cannot do higher math if you have not memorized and cannot instantly recognize the familiar patterns - from the simple (the very mention of the number 28 triggers thoughts of 7 and 4, area of a rectangle is l x w) to the slightly less simple (y=mx+b, ax^2+bx=c=0, and volume of a sphere is 4/3 pi r^3). We don't expect them to do anything that is truly complex. You can't drive the path if you don't know the landmarks. Otherwise all the x's look the same. It would be like driving in a city you've only visited once before three years ago for a week. You think you're supposed to turn right at the fast food restaurant but was it a McDonalds or a Burger King and am I even driving the right direction on this street.
The modular workbooks and the inquiry-based pedagogy taught my children a strange lesson about math. They would get a new workbook and for the first two weeks the lessons would be absurdly simple. They were coloring boxes and doing inane busy work without learning anything new. It was frustrating and they hated it. Then, in the third week, they would be expected to make a significant mathematical discovery and the class would suddenly shift from a stroll to leaping an impossible gap. Not surprisingly, they couldn't make the leap. That was also frustrating and hated. These leaps were first made by the finest mathematical minds in history; why do we expect all children to be able to make the same leap? Why should they have to? Bridges have been built since the leaps were first made. My kids couldn't figure it out. My explanations (using the conventional algorithms) were too different from the one they were getting in school. They got in trouble at school if they did it my way (even as they were told that any method that works is a good method "Do it any way you want - NOT THAT WAY!") so they stopped asking me for help. Instead, they figured out that if they could just fake it for a couple weeks the topic would quickly change and they could safely forget all about that part they didn't understand. It would be back to two weeks of the ridiculously simple. That was math for them: two weeks of the boring, inane, childish, and ridiculously simple alternating with two weeks of insanely and impossibly difficult, but none of it mattered because once it was gone you never saw it again. Both phases of the class were frustrating and hateful, so they learned that math is frustrating and they hate it.
One more kvetch on a slightly higher level. People are motivated to do cognitive work by three things: autonomy, mastery, and purpose. Don't make me prove that here, read Drive by Daniel Pink or watch the RS Animation about it. Student achievement is driven primarily by student motivation. Yet there is little focus on motivating students. They are given almost no autonomy (at traditional schools). The higher purpose of education is rarely mentioned. You would think that school would, at least, allow them to pursue mastery. Surely this is what school is all about. Except in math education. Students are rarely allowed to pursue a concept or a process to the point of mastery. In a spiraling curriculum they are not allowed to stay on topic that long. They are not allowed to pursue the idea all the way to the end. And they couldn't do it even if they wanted to because the workbook for that section is taken away from them when the section is complete and they can never refer back to it again. The spiraling curriculum and the modular instructional materials de-contextualizes the subject and makes it un-intelligible. It is oddly perverse that Math, a discipline with perfect unity and interconnectedness, is intentionally de-contextualized. Consequently students are never given a very good reason to learn math and, unless they have someone at home supporting them and motivating them, they are not going to get the necessary motivation at school as a result of the curriculum design - without regard to the individual teacher.
If I'm wrong about any of this, please correct me.