This is a blog post written by me (Boaz) with Edith Cohen. It is cross posted on Scott Aaronson’s blog. See also a thread on Twitter.
See also the open letter, and fuller analysis of the CMF proposed revisions.
Mathematical education at the K-12 level is critical for preparation for STEM careers. An ongoing challenge to the US K-12 system is to improve the preparation of students for advanced mathematics courses and expand access and enrollment in these courses. As stated by a Department of Education report “taking Algebra I before high school … can set students up for a strong foundation of STEM education and open the door for various college and career options.” The report states that while 80% of all students have access to Algebra I in middle school, only 24% enroll. This is also why the goal of Bob Moses’ Algebra Project is to ensure that “every child must master algebra, preferably by eighth grade, for algebra is the gateway to the college-prep curriculum, which in turn is the path to higher education.”
The most significant potential for growth is among African American or Latino students, among whom only 12% enroll in Algebra before high school. This untapped potential has longer-term implications for both society and individuals. For example, although African Americans and Latinos comprise 13% and 18% (respectively) of the overall US population, they only account for 4% and 11% of engineering degrees. There is also a gap in access by income: Calculus is offered in 92% of schools serving the top income quartile but only in 77% of schools serving the bottom quartile (as measured by the share of students eligible for free or reduced-price lunch). Thus minority and low income students have less access to STEM jobs, which yield more than double the median salary of non-STEM jobs, and are projected to grow at a 50% higher rate over the next decade.
Given these disparities, we applaud efforts such as the Algebra Project, the Calculus Project, and Bridge to Enter Advanced Mathematics that increase access to advanced mathematical education to underserved students (in Bob Moses’ words “raise the floor”). However, we are concerned by recent approaches, such as the proposed California Math Framework (CMF) revisions, that take the opposite direction.
See this document for a detailed analysis and critique of the CMF, but the bottom line is that rather than trying to elevate under-served students, such “reforms” reduce access and options for all students. In particular, the CMF encourages schools to stop offering Algebra I in middle school, while placing obstacles (such as doubling-up, compressed courses, or outside-of-school private courses) in the way of those who want to take advanced math in higher grades. When similar reforms were implemented in San Francisco, they resulted in an “inequitable patchwork scheme” of workarounds that affluent students could access but that their less privileged counterparts could not. The CMF also promotes trendy and shallow courses (such as a nearly math-free version of “data science”) as recommended alternatives to foundational mathematical courses such as Algebra and Calculus. These courses do not prepare students even for careers in data science itself!
As educators and practitioners, we have seen first-hand the value of solid foundations in mathematics for pursuing college-level STEM education and a productive STEM career.
While well-intentioned, we believe that many of the changes proposed by the CMF are deeply misguided and will disproportionately harm under-resourced students. Adopting them would result in a student population that is less prepared to succeed in STEM and other 4-year quantitative degrees in college. The CMF states that “many students, parents, and teachers encourage acceleration beginning in grade eight (or sooner) because of mistaken beliefs that Calculus is an important high school goal.” Students, parents, and teachers are not mistaken. Neither is the National Society of Black Engineers (NSBE), which set in 2015 a goal to double the number of African American students taking calculus by 2025. Calculus is not the only goal of K-12 math education, but it is important for students who wish to prepare for STEM in college and beyond.
We agree that calculus is not the “be-all and end-all” of high-school mathematics education. In particular, we encourage introducing options such as logic, probability, discrete mathematics, and algorithms design in the K-12 curriculum, as they can be valuable foundations for STEM education in college. However, when taught beyond a superficial level (which unfortunately is not the case in the CMF “data science” proposals), these topics are not any easier than calculus. They require the same foundations of logic, algebra, and functions, and fluency with numbers and calculations. Indeed, the career paths with the highest potential for growth require more and deeper mathematical preparation than ever before. Calculus and other mathematical foundations are not important because they are admission requirements for colleges, or because they are relics of the “Sputnik era”. They are important because they provide fundamental knowledge and ways of thinking that are necessary for success in these fast growing and in-demand fields.
We also fully support incorporating introductory data analysis and coding skills in the K-12 curriculum (and there are some good approaches for doing so). But we strongly disagree with marketing such skills as replacing foundational skills in algebra and calculus when preparing for 4-year college degrees in STEM and other quantitative fields. These topics are important and build on basic math foundations but are not a replacement for such foundations any more than social media skills can replace reading and writing foundations.
Given the above, we, together with more than 150 scientists, educators, and practitioners in STEM, have signed an open letter expressing our concerns with such trends. The signatories include STEM faculty in public and private universities and practitioners from industry. They include educators with decades of experience teaching students at all levels, as well as researchers that won the highest awards in their fields, including the Fields Medal, the Nobel Prize, and the Turing Award. Signers also include people vested in mathematical high-school education, such as Adrian Mims (founder of The Calculus Project) and Jelani Nelson (UC Berkeley EECS professor and founder of AddisCoder) who have spearheaded projects to increase access to underserved populations.
We encourage you to read the letter, and if you are a US-based STEM professional or educator, consider signing it as well: https://bit.ly/mathedletter
Unfortunately, in recent years, debates on US education have become politicized. The letter is not affiliated with any political organization, and we believe that the issues we highlight transcend current political debates. After all, expanding access to mathematical education is both socially just and economically wise.
Note: This blog post reflects our — Boaz & Edith’s — opinions; the text of the letter speaks for itself. Similarly, any comments below by us or other letter signers reflect their personal opinions.
Note 2: The “Bridge to Enter Advanced Mathematics” (BEAM) project is currently having a 10x match program for new donors (and πx match for returning donors). If you want to support projects that make a real difference in expanding access to math, take a look at https://www.beammath.org/donate . Another project worth supporting is (co signer) Adrian Mims’ calculus project https://secure.actblue.com/donate/thecalculusproject
Windows On Theory 
In addition, calculus is perhaps the (certainly, one of the) highest achievement of human thought, which made modern technological civilization and science possible.
If we do not teach calculus based on the idea that many students do not find it useful in their later career, why teach them art, literature, philosophy or any number of similarly “useless” subjects?
Hi Boaz, it is nice to see mathematicians getting involved in math education. Did you consult on the matter academic experts in mathematical education including some prominent mathematicians who moved to this area?
I do agree with Boaz that the letter itself is about curriculum, I (and others) do have issues with their pedagogy and justification thererof. For background, they very much push “in context learning” in my view (and my fairly extensive reading of education literature which comes in part from me teaching our pedagogy course) terribly distracts from the learning as it is; a combination of methods and concepts and arguments about their correctness and effectiveness. E.g., addition and the concept of place value, integrals as area and the height at the end giving the fundamental theorem of calculus. This mix has always been a bit confusing with respect to how to teach. The addition of application and even personal context is a lot of extra burden on students some of it emotional which is fraught for the most vulnerable where the classroom may well be a refuge.
In any case, several of the letter signatories did read the framework carefully including many of the references. The references themselves are mostly opinion or position papers, but those that are research either don’t support the corresponding statements well or even sometimes are against those statements. Do check out the linked in the article that discusses some specifics of the framework. Moreover, a significant motivator or example of the approach was San Francisco unified, but parents there looked into the claims of success and to say the least they are problematic. One link is here,
https://www.familiesforsanfrancisco.com/updates/inequity-in-numbers
but there are a number of criticisms of the research quoted by the authors of the framework that are serious and well reasoned.
For what its worth, I personally did reach out to a colleague in math education at Berkeley about one of the references and got more information; to be sure, that reference in fact considered early algebra to be a success metric. In any case, now that this letter is out I should circle back and talk with him more and I will. Other’s involved have been in discussions with education experts for some time and these discussions continue.
But, long story short, I think a straightforward answer to your question is there is some conversation with experts but we have read the framework and it’s scientific references don’t support the strategies well or perhaps even at all.
Gil, yes people involved did discuss this with education faculty and several signers have experience with K-12 ed. Moreover the focus of the letter is not on as much on the pedagogy but on the content.
Best of luck, Boaz, with this endeavor.
1. First they say everyone should do algebra in 8th grade. Then they say noody should. But the answer is (and always has been) tracking. Stronger students should accelerate.
2. Of course, facility with skills (especially accurate multi-step algebra) is critical. But it’s not even like the liberal reformers want to do more drill. Or even that they approve of algebraic skills (instead wanting to spend time on “concepts”) And for that matter, algebra 2, trig, analytic geometry, and calculus give plenty of practice in multi-step algebra. Just work through a rotation of axes problem!