New York State Math Exams Baffle Teachers and Students Facing the Tradeoff Between Breadth and Depth

Ambushed by the Exam
original artwork by Tavet Rubel, created for Dewey to Delpit

Last week, New York City public school students sat for the state math exams. The scores won’t be announced until the summer, but there is reason to expect a dip. State exams are not typically available for public viewing until a month or two after the exam is administered, but the board of ed took special precautions this year to ensure that every copy of the test-booklets were returned to their offices and that no information about the exam leaked. What I hear from teachers who administered the exam, however, is that the 5^th and 8^th grade tests were completely unprecedented, both in their content and in their difficulty.

The transition to the national Common Core Standards is not slated to begin until 2014, so educators I’ve spoken to are struggling to understand why this year's 5^th grade exam abandoned topics like decimals and percents that have traditionally been the meat and potatoes of that exam, and focused instead on difficult pattern and area problems, some of which lie outside the stated 5^th grade curriculum altogether.

When teachers at an inner-city charter first told me about the changes in the test, I thought this might be what I’ve been waiting for—a move towards more rigorous exams. In a post that I wrote back in December, I predicted that more rigorous exams of the sort that education policymakers have been promising would bring to light very disturbing realities about the shallowness of student understanding in today’s inner-city schools. No one is less to blame for that situation than the teachers themselves—indeed, they are the only ones who really understand it and the only ones directly working to fix it. Nonetheless, it will fall to the teachers to teach differently, and under prevailing conditions, that will be impossible. I welcome more rigorous tests, not because they will force teachers to teach differently—I know plenty of teachers in the inner-city who already teach as rigorously as they possibly can—but because it will force the society to face the broader structural and curricular problems that, despite what you’ll hear from politicos and documentarians, stand in the way of serious academic achievement.

To put a slightly finer point on it, the schools that are passing the existing tests are, by and large, already committed to teaching for high rigor and deep understanding, as much as the strictures of the current system allow. (See my post on teaching to the test.) The schools in which rigor and depth are ignored are already failing the exams, so making the exams harder isn’t going to light any hotter a fire under their asses. The problem is not the incentives.

As far as math is concerned, one of the major impediments to depth and rigor is actually the breadth of the state curriculum: there are too many topics taught per year, so they all get treated cursorily. New York State uses what’s called a “spiraled math curriculum,” which means that each year contains over a hundred individual topics, organized into ten nebulous “strands;” these same topics—or ones very much like them—reappear, year after year, with slightly more depth and rigor. It’s a terrible way to organize a math curriculum.

The rhetoric of high expectations makes it hard to trim back curricula. The list of topics taught in a given year is the clearest and seemingly the most concrete measure of how challenging a curriculum is, so policymakers are reluctant to shorten it—unfortunately, a list of topics is a bad measure of a curriculum. Much more telling are the specific questions by which each topic is assessed on the exams; only when you look at the actual questions can you see what students really need to know, how comfortable they must be with the topics, how flexible they must be in adapting their knowledge to new situations—but, in order to glean this information, you have to know a lot more about math and spend a lot more time reading exams, and who bothers? Not voters, of course, and not politicians either. These are the guys who don’t even read the bills that they’re signing into law—you can bet they don’t read the exams that their boards of ed come up with.

The result is that changes in the exams tend to bring more, not fewer, topics. The current round looks to be headed in the same direction. I was talking to my friend Matt Kelly, who teaches 5^th grade math in inner-city Brooklyn, about this year’s exams and the Common Core Standards that will be phased in over the next few years. “If the problem with American math curricula is that it’s a mile wide and an inch deep,” he said, “they’ve just made it two miles wide, with the expectation that it’s going to be a mile deep—but it’s impossible. It’s not going to happen—especially when kids are coming in behind grade-level, not knowing how to multiply, how to divide.”

Matt is one of those teachers who works hard to teach math concepts. He is always searching for ways to build deeper understanding, but he worries that the new tests will make that kind of instruction impossible. “I’m not going to be able to do as much with fractions,” he says, “I’m not going to have time to use fraction tiles and shade in squares and all that stuff, if I have to teach operations with unlike denominators and fraction division and multiplication. I’m going to have to do it all procedurally.”

Of course, if the exams are hard enough, superficial procedural understanding won't be enough, and what'll happen then? Maybe they'll quietly reduce the rigor until students begin passing—but that'll be a lot harder on the nationally-normed assessments that are coming than it was on the old state-by-state exams. And if the rules of the Common Core Standards prevent them from dumbing down the test, well, then there might be a reckoning.