I recently came across this defense of Common Core by two Berkeley mathematicians, Edward Frenkel and Hung-Hsi Wu. Both are sharp and highly respected and when you hear about serious mathematicians supporting the initiative, there's a good chance these two names will be on the list that follows.
Except they don't support it. They support something they call Common Core, but what they describe is radically different than what the people behind the program are talking about. The disconnect is truly amazing. Wu and Frenkel's description of common core doesn't just disagree with that used by David Coleman and pretty much everyone else involved with the enterprise; it openly contradicts it.
The case that Coleman made to Bill Gates and stuck with since then is that "academic standards varied so wildly between states that high school diplomas had lost all meaning". Furthermore, Coleman argued that having a uniform set of national standards would allow us to use a powerful set of administrative tools. We could create metrics, track progress, set up incentive systems, and generally tackle the problem like management consultants.
Compare that to this excerpt from Wu and Frenkel's essay [emphasis added]:
Before the CCSSM were adopted, we already had a de facto national curriculum in math because the same collection of textbooks was (and still is) widely used across the country. The deficiencies of this de facto national curriculum of "Textbook School Mathematics" are staggering. The CCSSM were developed precisely to eliminate those deficiencies, but for CCSSM to come to life we must have new textbooks written in accordance with CCSSM. So far, this has not happened and, unfortunately, the system is set up in such a way that the private companies writing textbooks have more incentive to preserve the existing status quo maximizing their market share than to get their math right. The big elephant in the room is that as of today, less than a year before the CCSSM are to be fully implemented, we still have no viable textbooks to use for teaching mathematics according to CCSSM!
The situation is further aggravated by the rush to implement CCSSM in student assessment. A case in point is the recent fiasco in New York State, which does not yet have a solid program for teaching CCSSM, but decided to test students according to CCSSM anyway. The result: students failed miserably. One of the teachers wrote to us about her regrets that "the kids were not taught Common Core" and that it was "tragic" how low their scores were. How could it be otherwise? Why are we testing students on material they haven't been taught? Of course, it is much easier and more fun, in lieu of writing good CCSSM textbooks, to make up CCSSM tests and then pat each other on the back and wave a big banner: "We have implemented Common Core -- Mission accomplished." But no one benefits from this. Are we competing to create a Potemkin village, or do we actually care about the welfare of the next generation? What happened in New York State will happen next year across the country if we don't get our act together.
[As a side remark, we note that even in the best of circumstances, it's a big question how to effectively test students in math on a large scale. Developing such tests is an art form still waiting to be perfected, and in any case, it's not clear how accurately students' scores on these tests can reflect students' learning. Unfortunately, our national obsession with the test scores has forced teachers to teach to the test rather than teach the material for learning. While we consider some form of standardized assessment to be necessary (just as driver's license tests are necessary), we deplore this obsession. It is time to put the emphasis back on student learning inside the classroom.]
These misguided practices give a bad name to CCSSM, which is being exploited by the standards' opponents. They misinform the public by equating CCSSM with ill-fated assessments, such as the one in New York State, when in fact the problem is caused mostly by the disconnect between the current Textbook School Mathematics and CCSSM. It is for this reason that having the CCSSM is crucial, because this is what will ensure that students are taught correct mathematics rather than the deficient and obsolete Textbook School Mathematics.
It is possible and necessary to create mathematics textbooks that do better than Textbook School Mathematics. One such effort by commoncore.org holds promise: its Eureka Math series will make online courses in K-12 math available at a modest cost. The series will be completed sometime in 2014. [Full disclosure: one of us is an author of the 8th grade textbook in that series.]
How can proponents of common core hold such mutually exclusive use and yet be largely unaware of the contradictions?
I suspect it is some combination of poor communication and wishful thinking on both sides. As spelled out in this essay by Wu, the authors desperately want to see mathematics education returned to some kind of Euclidean ideal. A rigorous axiomatic approach where all lessons start with precise definitions and proceed through a series of logical deductions. They have convinced themselves that the rest of the Common Core establishment is in sympathy with them just as they have convinced themselves that the lessons being produced by Eureka math are rigorous and accurate.
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