Curriculum and Pedagogy Matter and ‘Reformers’ Suck at Those Things: The Math Edition

When the latest ‘algebra-is-too-hard-so-let’s-dumb-it-down’ pustule broke, I argued that the problem isn’t learning algebra, it’s that the students in trouble usually haven’t learned basic arithmetic:

…one thing I’ve noticed anecdotally is that when students say they have difficultly with algebra, that’s usually not the entire story. Typically, that means they have also trouble with arithmetic. There’s a reason why the ability to do long division is correlated with long-term mathematics performance: you have to master the basics.

Two major reasons that students don’t learn math (or anything else) well is due to failures in curriculum and pedagogy–what students are taught and how they are taught. And this failure starts at the top:

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.

The specific failure (boldface mine):

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….

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.

…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.

To be clear, teachers do not choose curricula and books, administrators and principals do. In fact, in an era of high stakes testing, any teacher who bucks the chosen system, especially with students who are likely to do poorly due to factors outside of the school and thus who will test poorly, is putting her job at risk by defying the principal or central administration. Consider it the Iron Law of Reform Education: it is better to rise in an ideologically-driven and failing educational system than it is to subvert the system to improve ‘outputs.’ That is, make children smarter.

This is something to consider the next time you hear people arguing against teacher tenure (by the way, teacher tenure is not like collegiate tenure; it simply means a teacher can’t be fired at will. Probably a useful thing in creationist school districts too).

Pseudo-reformers still see the educational crisis (which exists largely among poor children–might want to do something about that) as one of personnel management. Never mind, that, in practice, they suck at management. Of course, this assumes their motives are genuine.

We’re screwed.

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2 Responses to Curriculum and Pedagogy Matter and ‘Reformers’ Suck at Those Things: The Math Edition

1. Scott E says:

They want mastery, but they hate “drill and kill”. So why does a football team practice all week? They want to evaluate teachers based on test results, but they don’t want them to “teach to the test”. So why does a football team rarely practice plays it’s unlikely to use (or see) during a game? Then again, they fire football coaches who don’t win even when their players are not the most talented. Maybe, it’s the system.

2. joemac53 says:

I have a strong problem with spiraling. I was able to avoid it during my 35 year career as a math/physics teacher. Now I get to tutor a little. I just finished with a kid going into AP physics B by trying to get through 60 sections of a Saxon book (the king of spirals) during the summer. The book was very derivative (I recognized problems stolen from other books), choppy, lacked good pedagogical order and, and, and……..Only the first two problems in each section referred to the subject of the section before the spiraling began!
I didn’t see any of the cool problems or questions that I used over the years to pique interest or stir imagination. A teacher using that book was getting no help from the book. A teacher using that book had better be an experienced expert in high school physics and high school students.
My classes knew there would be “bookies” and “Joe probs” on any quiz or test. We even spent time on “How to read a math/physics book”.
We are not all the same. I taught so long in one school that admissions officials and physics/calculus professors knew what to expect from my kids (good in mechanics, great in optics, suck at electromagnetism, can do really hard integrals etc.). I am certain other teachers were recognizable.
Tell the reformers to screw.