All right, how did we end up in this mess? For this entry I poked around quite a bit trying to figure out the history of the California math standards. As many stories in education go, it’s a tale of the swinging pendulum. Some of the details are fuzzy (and some are hotly contested), but this is what I’ve been able to figure out so far.
In the 1990’s California was going through what has been dubbed “The Math Wars”. This was basically a philosophical battle, which roughly divided along traditional progressive/conservative political lines. On the left were a group of educators calling for an approach to mathematics instruction that emphasized the importance of conceptual understanding. Many in this camp believed in the constructivist approach to teaching, basically the notion (radical to some) that kids develop as stronger mathematical thinkers if they actually have to think mathematically. Rather than being given formulas or algorithms that are then explained by a teacher, in this model the teacher’s role is to support students in figuring out mathematical principles and strategies themselves. Once an underlying concept is discovered, the teacher presents the standard formula or algorithm in order to formalize it.
On the right was a group advocating for a “back to basics” or a more mathematically “pure” instructional approach. They criticized the constructivist approach to mathematics instruction (and the curricula that sprung from that movement) as “fuzzy math”, and feared that students were allowed and even encouraged to learn mathematical concepts without the precision and rigor that necessarily defines mathematics as a discipline. They also felt that the curricula that were based on the constructivist approach failed to adequately develop basic math skills and computational fluency.
One of the key events in the California Math Wars was the release of the 1992 California Math Framework. This document was developed at a time when the constructivist, “conceptual understanding” camp held the reins. The National Council of Teachers of Mathematics had released their own fairly constructivist standards three years earlier, and the 1992 California state standards followed suit. When schools started adopting curriculum that aligned with the new standards, there was resistance by many students, parents and teachers. The textbooks looked dramatically different than the ones that parents had used in school, with far fewer pages covered with problems in tidy rows and columns. Instead, flipping through a textbook would reveal pages of word problems, often accompanied by diagrams and drawings. Teachers who did not fully understand or embrace the constructivist approach struggled with the curriculum, and their complaints spread among concerned parents. When test scores started to drop in many parts of the state, the tide against the “whole math” movement started to rise.
In response to increasing public pressure, in 1997 the California State Board of Education put together a committee to write a new set of state standards. The Academic Content and Performance Standards Commission worked on the math standards for most of the year, but the resulting draft was not well received. The document, produced by a committee of twenty-one, was bursting at the seams with content to be mastered. It also contained several mathematical errors and some ambiguous language. Even more disturbing to the Board, it reflected much of the same constructivist philosophy that had caused such an uproar following the 1992 framework it was meant to replace.
The board’s solution was to give the draft to four Stanford University mathematics professors. They were directed to correct the mathematical errors and purge the standards of any reference to teaching strategies. They were also directed not to remove any of the mathematical content of the original draft. They completed their rewrite in a matter of weeks, resulting in the standards currently in place in California.
The genesis of the California Math Standards explains a lot about the problems they have created. It’s not surprising that a committee of twenty-one people, working for several months, came up with a set of standards that is over-packed with content. It’s also not surprising that a group of university math professors produced a final document that totally ignores the developmental readiness of elementary school students. What is surprising is that there hasn’t been another groundswell of opposition to this burdensome and clumsy document. For thirteen years teachers have tried to squeeze their kids into the box mandated by the standards, to find ways around them, or just to fly under the radar. We should demand a real rework of the standards, one that recognizes the reality that kids are not empty vessels to be filled with knowledge, but that also respects the rules of formal mathematics. Is it too much to ask for a little balance?
The federal government’s new Common Core State Standards Initiative gives me some hope. The standards produced by this project appear much more streamlined than the California standards. If those standards were accompanied by an equally reasonable assessment tool to replace the current tests, it could pave the way for a new era of reform. Instead of playing the game of test preparation at the cost of meaningful learning, we could focus our efforts on developing instructional approaches that lead to both understanding and mastery of the basic skills and concepts that our students need to succeed at the next level.