I’m confused about math

I was interested in this map that purports to rate the quality of math teaching. It’s from the National Council on Teaching Quality, and at first I thought it explained a phenomenon I’ve noticed.

Minnesota grade schools aren’t doing a good job preparing students with math skills. It’s the #1 obstacle to young people coming into science and math majors, especially biology (if they aren’t strong in math in the first place, they aren’t going to even try physics; everyone wrongly thinks you don’t need math to do biology.) We get students who fail the algebra requirement*, which surprises me every time. What are the schools doing? Back in my day, the high schools had a college prep track which told you that you at least needed pre-calc (trigonometry, etc.) to get into a good college. How do you get through middle school without algebra and geometry?

They have a state-by-state breakdown of their evaluation. I looked at Minnesota’s. It expresses a lot of sentiments I agree with: we should “require districts to adopt and implement high quality math curricula,” but they say we fail on that. We should “require elementary programs to address math specific pedagogy,” and again they say we don’t, but I don’t have any experience working directly with grade school math programs, so I’m taking their word on it. Then I notice that the way NCTQ assesses schools is with checklists of various aspects of teaching, and it’s all yes/no stuff. What are “high quality math curricula”? It seems to me that there ought to be something a little more quantitative about that.

Then I looked at their evaluation of our universities’ math teacher prep, and we get low marks, but again there’s a lack of specificity. All they score is how many hours of instruction math education students get in 4 areas, and the only evaluations are “does not meet” or “fully meets” their quota for instruction hours. And the variation is wild! On “Numbers & Operations+Algebraic Thinking,” for instance, some of our colleges provide 0 hours of instruction, while others provide 100 hours. I think the assessment is a bit inconsistent, and maybe not aligned with the goals of the specific programs.

I’m not trying to make excuses for the schools. I’ve been looking at their products, the students, for years and have been unsatisfied with their end result.

They declare that “13% of Minnesota programs earn an A or A+ by dedicating adequate instructional time to both math content and pedagogy” where again, they’re scoring them by this single metric. 26% of our colleges fail by that metric. Also, to get an A, the “program requires at least 135 instructional hours across the five topics and at least 90% of the recommended target hours for each topic,” but there are only four topics listed. I guess someone failed arithmetic, or copy editing.

I had to look at Alabama‘s evaluation. The South in general is scoring very well on math education, so good for them. They get lots of checkmarks in the binary metrics, for instance Alabama does “require elementary programs to address math specific pedagogy” where Minnesota doesn’t, but now I’m wondering what that means. “16% of Alabama programs earn an A or A+ by dedicating adequate instructional time to both math content and pedagogy,” but 24% fail.

I think we could all improve the quality of math education, but I didn’t find any of their reports particularly useful, and they seemed almost arbitrary. So I looked up the NCTQ, and discovered that it was the product of a conservative think-tank, and was associated with the US News & World Report, the magazine that publishes scores for colleges every year (I do not like them, even if my university scores well in their assessments). Then I read this review:

Now, to be candid, I am fed up with our nation’s obsession with data-driven instruction, so I don’t share the premises of the report. The authors of this report have more respect for standardized tests than I do. I fear that they are pushing data-worship and data-mania of a sort that will cause teaching to the test, narrowing of the curriculum, and other negative behaviors (like cheating). I don’t think any of this will lead to the improvement of education. It might promote higher test scores, but it will undermine genuine education. By genuine education, I refer to a love of learning, a readiness to immerse oneself in study of a subject, an engagement with ideas, a willingness to ask questions and to take risks. I don’t know how to assess the qualities I respect, but I feel certain that there is no standardized, data-driven instruction that will produce what I respect.

And then there is the question that is the title of this blog: What is NCTQ?

NCTQ was created by the Thomas B. Fordham Foundation in 2000. I was on the board of TBF at the time. Conservatives, and I was one, did not like teacher training institutions. We thought they were too touchy-feely, too concerned about self-esteem and social justice and not concerned enough with basic skills and academics. In 1997, we had commissioned a Public Agenda study called “Different Drummers”; this study chided professors of education because they didn’t care much about discipline and safety and were more concerned with how children learn rather than what they learned. TBF established NCTQ as a new entity to promote alternative certification and to break the power of the hated ed schools.

I should have read that before wasting all that time trying to interpret the data in the report. And now I understand how Texas and Florida did so well in the NCTQ evaluations.

We still have a problem in poor math preparation. I don’t think turning a bunch of conservative ideologues loose on the schools will solve it.

*I should mention that my university invests a lot of effort in remedial instruction to bring students’ math skills up to the level they need to succeed in our majors.