Yet More on the California Framework (Part 1)

There is a new open letter by STEM practitioners who oppose the California Math Framework revision (CMFR). The same group also published an Analysis and Critique of the proposed changes, and a blog post by Boaz Barak and Edith Cohen. I’ll use the latter’s initials (BB/EC) to refer to them and the set of three documents (no offense intended for the other authors; it’s just that Boaz and Cohen are the sole signatories of the blog post, and I’m trying to keep it simple.)

I could and will quibble with some of what they say, but basically, they are correct and express similar concerns to the ones I raised in three previous posts. (The California Math Framework Revision, More on the California Framework, and Detracking, How To.)

Like everyone in this conversation, BB/EC tell us about their interest in equity and in reducing achievement gaps. They concede that the CMFR is well-intentioned, but they fear it will only make things worse. I believe they are right, but because they do not propose a way forward, and because of the usual polarization in the math wars, this will be seen by many to imply an endorsement of the status quo.  Essential reminder: the status quo cheats many students of a decent math education, in part by keeping them separate and not equal.

Here are some of the key points BB/EC make, with my comments. (Disclaimer: I have only read a little bit of the CMFR. If you think that disqualifies me from the conversation, you can stop reading. However I am confident that everything I say in this post is valid.)

1. 8th grade Algebra 1 and 12th grade Calculus should not be eliminated

I agree with that.

This does not mean that the traditional Algebra 1 course deserves to continue unchanged for yet more decades. I have spent much of my career arguing for a transformation of the course, and I stand by what I’ve written about this. (See for example my article on the Common Core and/or the approach I take in this Algebra textbook.) Nor does it mean that all who take Calculus as seniors actually learn Calculus. (See for example Robin Pemantle’s guest post on this blog.) There are things we can do to improve those courses, and we should absolutely pursue those, but abolishing them altogether will not do it.

To those who fear that allowing the mere existence of such classes will harm those students who do not qualify for them, I’ll point to a simple solution, the one I described in Detracking, How To. It is entirely possible to have (e.g.) a Geometry class with the ninth graders who took Algebra 1 successfully in 8th grade, and tenth graders who took Algebra 1 successfully in 9th grade. This is not tracking: everyone takes the same Geometry class. Under this system, not everyone takes Calculus in high school, but it is still available to all in college.

My guess is that somewhere between one quarter and one half of students can successfully take Algebra 1 in eighth grade. This in turn makes it possible for them to take Calculus as seniors, which makes it easier for them to pursue STEM majors in college. Nothing is gained by preventing them from doing that.

2. “Data science” cannot and should not replace algebra

I agree with that.

I wrote about data science here, and in defense of Algebra 2 here. In a nutshell: actual data science is built on a foundation of statistics and computer science. Those disciplines cannot be taken up without a grounding in at least Algebra 2 and Precalculus. The true and unfortunate fact that so many people had bad experiences in Algebra 2 does not change the fact that it is a necessary foundation for any quantitative discipline, including data science. (Note that the writers of this open letter are themselves data scientists.) Our energy needs to go to teaching that content better, not diluting or eliminating it.

3. If implemented in its present form, the CMFR will likely increase inequality

I agree with that.

First: wealthy school districts and private schools will continue to offer 8th grade Algebra 1 and 12th grade Calculus. Whether we agree with this or not, that will work to their students’ advantage in college applications, college majors, and careers — thus increasing the gap between the privileged, who will not be subjected to the new Framework, and the students in districts that do implement it.

Second: within districts that implement the CMFR, there will be students who will still try to take Calculus in 12th grade. That will only be possible via expensive tutoring, or through compressing Algebra 2 and Precalculus into a single year, which is not likely to go well. (At my school, we managed to squeeze them into a year and a half. I don’t think any more than that is realistic, especially under Common Core.)

Third: another possible problem along these lines is that students who follow the data path will probably be offered a superficial approach to data science, which is all one could address without a solid Algebra 2 / Precalculus foundation. Don’t get me wrong: a visual and qualitative approach to data is not a bad thing. I designed and taught such a course for many years. But it does not provide a solid foundation for STEM majors, including Statistics and Computer Science. Also note that NCTM correctly warns that offering different paths in the same institution prior to the last year or two of high school will very likely lead to de facto tracking.

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If I agree with their main points, why do I not sign the BB/EC open letter? I’ll explain that in my next post.

— Henri

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