Draft California Math Framework

Although it was actually updated last year, the Draft California Math Framework has been making the rounds again recently because of a recent comment period and an upcoming meeting of the committee, as well of course a somewhat inflammatory tweet:

Background

First let’s establish that we want all students to succeed regardless of what income level they come from. Second let’s agree that what we’re doing now — even with massive improvements to how and what was taught with Common Core adoption — isn’t working.

I’ve argued many times before that standards frameworks need to be able to evolve faster to keep pace with what society and industry demand. This recommendation doesn’t recommend sizable changes in the course and structure of publicly funded mathematics instruction, but it does seem to impose new limits.

For the Framework Recommendations

The job of public education is to educate all students. Not just special education students, not just students from low incomes, not just students from high incomes. By removing the idea that math acceleration is normal, we can help all students achieve greater UNDERSTANDING as opposed to just a rite of passage/memorization. How? See the example below of a type of problem often called Low Floor High Ceiling from Dr Jo Boaler’s Mathematical Mindsets. The problem is accessible to anyone, but allows students in the same classroom to have varying degrees of understanding and more importantly, teaches while they figure it out.

I’ve given problems like this in both a challenging inner city high school and a magnet/GATE middle school, and more often than not students are engaged because it presents the issue as a puzzle to be solved, not something they can memorize a procedure (like FOIL).

But first we need to address the content of math classes. It’s often antiquated and if you need further evidence, I present to you the fact that big-button Texas Instruments calculators are both the same price as they were 20 years ago and required in many of our math classes. See desmos.com for what we should be having students use instead for engaging, meThis is ridiculous — despite our math teachers telling us we “wouldn’t have a calculator all the time” we actually do. Tellingly, the Framework encourages and gives examples of how students can use technology based tools to support their own inquiry such as Geogebra and Desmos!

Against The Framework

The premise FOR math acceleration is that if we don’t let kids get as far as they can in high school they will be disadvantaged in college/beyond. That we are holding kids back by not letting them take Algebra in 7th or 8th grade. That requiring all students to go the slower route will hold back kids who are ready for more advanced work.

Holding back from… what?

College enrollment is on the decline. Companies like Google don’t require a degree and are offering credential classes for careers that pay big money. Essentially, the concern is that by making math accessible to all, that the kids who would be top performers aren’t even able to be such; and that by trying to appease ‘all’ we appease none. That public mathematics instruction will be diluted in the name of equity and thus become inequitable to students who can do more. Here I’m going to break from the narrative a bit and say that for my own kids, I would have a hard time if they got to a place where their math or science classes were too easy — I want them to be pushed not necessarily to ‘get ahead’, but because I feel education should always be challenging.

It’s hard to see statements like those in the CA Framework like those expressed in chapter 8 and not feel like it’s the beginning of the end of public education. If students from higher socioeconomic situations aren’t able to be given challenging classes, their parents will just take them out and put them in private schools where they will be challenged — with or without justification. The primary argument against acceleration in middle school is here (highlights my own):

“Many students, parents, and teachers encourage acceleration in grade eight (or sooner in some cases) because of an incorrect conclusion that Calculus is an important high-school goal. This approach relies of the false belief that Algebra I must be taken in grade eight in order for the student to reach a calculus class in grade twelve. This framework clarifies these misunderstandings in three ways:

First, because of the rigorous nature of the CA CCSSM grade-eight standards, a three-year high-school pathway can be sufficient preparation for a calculus class in grade twelve, as outlined in the pathway graphic on page x (to be decided by formatting)

Second, the push to calculus in grade twelve is itself misguided. In Mathematical Association of America (MAA) and NCTM clarify that “…the ultimate goal of the K–12 mathematics curriculum should not be to get into and through a course of calculus by twelfth grade, but to have established the mathematical foundation that will enable students to pursue whatever course of study interests them when they get to college” (2012). The push to enroll more students in high-school calculus often leads to shortchanging important content that does not lead directly to success in the advanced placement calculus syllabus, which is significantly procedural. “In some sense, the worst preparation a student heading toward a career in science or engineering could receive is one that rushes toward accumulation of problem-solving abilities in calculus while short-changing the broader preparation needed for success beyond calculus” (Bressoud, Mesa, and Rasmussen 2015).

Finally, the results do not support the push for more and more students to take calculus in high school: About half of the students taking Calculus I in college are repeating their high school course, and many others place into a pre-calculus course when they enter college (Bressoud, Mesa, and Rasmussen 2015).”

My Suggestions

Parent education is key, as well as the ability of public education to accommodate the most motivated students and not give the impression (as this has) of slowing down the hardest working students. The traditional order of Algebra I/Geometry/Algebra II is broken but it’s such a cultural element it would be akin to police not reading Miranda rights. Having taught Algebra I, Geometry and Algebra II quite a few times in my day, as well as 7th grade math under Common Core, there are topics that can be combined or even mostly eliminated for the general student without harming future calculus aspirations. We should make the third year of mathematics data science/statistics focused because information literacy and interpreting data is probably the most important skill of our day; as is being able to communicate about that data effectively.

Conclusion

When the non-educator parent first hears, “California won’t let my kid take calculus in high school!” the initial reaction is panic and being upset that public school is holding them back from expectations and individual performance. As a former teacher of both underserved and GATE students, I understand not wanting to have my kids fall behind and hence less opportunity. But I don’t think that’s happening here. Instead, I think it’s more an indictment of higher education and the fact that colleges need to become more pragmatic and I’ve love to see more adopt ‘Credegrees’ — keeping the liberal arts focus but with clear paths to employment post graduation.

As the CA Dept of Education itself says here, the Framework doesn’t say you can’t take calculus, only that we should have less of a focus for all on it — and let them explore rich mathematical tasks across all grade levels. Read more about their position for Gifted and Talented students here.