I've been slaving over this long enough—I'm just going to post it. More on this to come.

In my last post I outlined the trap in which American education reform is mired: our best hope for improving education—tying incentives to outcomes—has reduced inner-city education to a massive, year-round test-prep regimen. I want to talk about how we could improve the situation, but first we need to look more closely at the phenomenon of test-driven education.

The phrase "teaching to the test" gets thrown around a lot, and I don't want to write facilely about the ills of No Child Left Behind, because that leads to the kind of simplistic ideology I'm trying to avoid. I think that there are serious downsides to NCLB, and I'd like to discuss those in detail, but I'm hindered by the narrowness of my experience. I can talk with great specificity about the impact of NCLB on New York State middle-school mathematics education; but it's hard to be sure how generalizable that analysis would be. At some point, I'd like to conduct a qualitative study of state exams and curricula in a variety of subject-areas, at a variety of grade-levels, from a wide selection of states—but that study will require months of research. Anecdotal evidence from teachers in other states and subject areas, however, suggests that New York State middle-school math is not some wild aberration. What follows, therefore, in lieu of more definitive conclusions, is my analysis-by-extrapolation of the specific mechanisms by which NCLB is undermining education in America.

**Outcomes and Assessments
**

First of all, let's talk about the relationship between outcomes and assessments. The principle insight behind high-stakes testing and No Child Left Behind is that we should hold educators accountable not for what they do with their time but for the results they produce. That's a good idea (see my last post). The problem comes from the difficulty of determining what educators have produced. To do that, we introduce assessments, i.e. state exams— but our assessments are lousy. They don't really tell us much about the depth of student understanding; they tell us only about students' surface knowledge of a subject: whether they can apply the Pythagorean theorem, find the indirect object of a sentence, name three causes of the First World War.

As has been well publicized, under NCLB many schools, especially those in poor districts or districts with high percentages of at-risk students^{[1]}, have come to align most or all of their curriculum and instruction to these same shallow state tests. Some probably do this because they really are motivated only by the exam^{[2]}, but most do it despite the best intentions of their administration and faculty and in contradiction to their own stated aims— because, when it comes down to it, they often have no choice.

When I talk about how shallow state tests are, people tend to assume that means they're easy—that they test only the simplest mathematical procedures and concepts. If that were true, it would easy for a dedicated teacher or school to go above and beyond test-prep, teaching students about the deep structures and beauties of mathematics, literature, etc. In fact, though, state tests—even at the primary school level—cover a daunting array of information, much of which will be unfamiliar to your average adult.

See, for example, Appendix A, a list of New York State's procedural standards for 6^{th} grade math. Most adults, even those with a good understanding of mathematics, cannot tell the difference between a bar-graph and a histogram (standard 6.S.4) or "Determine the number of possible outcomes for a compound event by using the fundamental counting principle and use this to determine the probabilities of events when the outcomes have equal probability" (standard 6.S.11). Yet, under NCLB, a teacher with a classroom full of 6^{th} graders who can't perform multi-digit subtraction or tell with any certainty whether 1/5 is larger or smaller than 1/6, will be forced, if they want to keep their jobs, to ignore such gaping conceptual holes and power through a unit on data representation and compound probability.

Advocates of high-stakes testing are often the same people who argue for "back to basics" education. That viewpoint critiques progressive educators for focusing on abstract ideas of curiosity, creativity, and deep understanding, when students lack the basic skills and knowledge necessary to write a complete sentence or perform long-division. That critique may be apt, but basic skills and conceptual depth are not natural enemies: a strong foundation in the former is the quickest route to the latter. The attempt to create rigorous curricula in the absence of conceptual depth has led to the very opposite: a system in which there's no time for the basics or concepts.

This all adds up to the Heisenberg Principle of Education: we create assessments to measure student outcomes; but the assessments come, instead, to determine the outcomes. Viewed in the most extreme terms, this alters the entire project of education.

**Why We Educate
**

Before I got involved in inner-city education, my vision of the ideal classroom was one in which students and teacher were deeply intellectually engaged with subject matter, and the primary source of student motivation was not grades or any other extrinsic element, but curiosity. Under the constraints of NCLB, such a model is a fantasy, and—considering the furious pace that must be maintained in order to meet state standards in many schools—a dangerous one.

In the most successful post-NCLB inner-city classrooms, teachers engage students through games, competition, challenges, and fast-paced drills, in order to push them through a curriculum that they don't well understand and for which they often lack the foundational skills and knowledge. A good teacher, in this context, can provide students who never really understood division with tricks and mnemonics that will get them through a unit on fractions. The resulting sense of competence and success will obscure students' underlying sense of confusion—indeed, these students will have come to see mathematics as an arbitrary language with no discernable logic, and will not even recognize that they do not comprehend it—after all, they passed the exam, didn't they?

I don't want to exaggerate the situation. At its best, the inner-city classroom described above can be an exciting, safe, positive space for students. Issues of comprehension are less severe in subjects other than mathematics and in schools with wealthy or ability-selected students. Still, the primary aim of these classrooms is not that students fully comprehend what they're learning, nor that they engage deeply with their subject matter; the primary aim is that they be able to perform a set of discrete tasks, in the exact contexts and formats that are presented on the state exam.

This can be seen most clearly in teachers' attitudes towards conceptual understanding. Progressive teachers tend to view deep understanding of subject-matter as their ultimate goal; they teach specific procedures, facts, and rules only as stepping stones towards this type of comprehension. Teachers in inner-city classrooms talk about comprehension a lot, too. To some degree, they talk about it as a goal in and of itself, but usually it's justified, or even brought up in the first place, as a way to improve retention: the better kids comprehend material, the better they'll be able to remember the things they learn. Higher retention means less class-time devoted to review and, ultimately, higher scores on the state exam. Thus, for progressive private-school teachers, procedures are a tool to achieve conceptual understanding, whereas for those subject to the constraints of NCLB, conceptual understanding is a tool to achieve better retention of procedures.

[1] I'd like to know just how many teachers that is, but I've had a surprisingly difficult time figuring out what percentage of teachers or schools serve poor or high-risk students. The department of ed has a nice little digest of education statistics, which I've referenced in a couple past posts, but it doesn't have data on number of schools or students by income level of district. More surprisingly, it doesn't have data on number of schools designated as underperforming according to NCLB; this seems like an intentional omission, but who knows. It does have data on number of schools and students by type of local: about 23% of public school students are in cities with populations over a hundred thousand; I think we can safely assume that most of these attend schools where passing state test is of paramount concern. Another 19% go to rural schools, many of which, I suspect, are poor and in danger of failing to make state standards under NCLB. My data here is very limited, unfortunately.>.

[2] For the most jaded, burnt-out, or lazy educators, this is only natural: their motivations were already self-interested and economic. For most others, and to varying degrees depending on the individual, the material rewards and punishments tied to the exam have probably displaced the intrinsic motivations that originally drove them to educate. There's plenty of psychological and economic research on the capacity of extrinsic motivators to drown out intrinsic ones and for economic incentives to eliminate considerations of personal responsibility or community-mindedness.

**Appendix A: New York State 6**(back to main text.)

^{th}Grade Procedural Math StandardsWhat follows is a list of the mathematical procedures that New York State 6^{th} graders are expected to be able to carry out. I'm glazing over a big issue here: the list of NYS 6^{th} grade math standards is actually much longer than this, but most of them are conceptual and not tested on the state exams. I have a lot to say about that, but I'm not going to say it now. The list below is broken into various "strands," under which are various sub- and sub-sub-headings. Each strand represents a different area of mathematics, and you may wonder why there are so many different mathematical fields covered in a single year; in fact, all of these same strands are covered year after year, so that students learn a little more about each one each year; this is called a spiraled curriculum. Again, I have a lot to say about that, but I'm not going to get into it right now.

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