A personal FAQ on the math education controversies

I was a contact person for the open letter on K-12 math education, and am in strong support of the recent letter on the role of data science in math education (and would encourage readers that are faculty members in California to sign it). Since I tend to see the same questions and objections arise time and again, I thought it would be useful to write my responses to these. The following is my own opinions only, and does not reflect the views of any other contact person or signer of these letters. I also apologize in advance for the lack of links and references below. However, if you ask questions in the comments, I’d be happy to give more sources.

Q: The status quo in US math education is terrible and doesn’t work for many children, especially students of color and low income students. Aren’t these letter writers just trying to protect a flawed system that worked well for them?

A: The US math education system is very complex, but I agree that it is largely failing a large chunk of our students. But that doesn’t mean that any change will necessarily be for the better. Just because a system is bad, doesn’t mean you can’t make it worse. We have a responsibility to “first do no harm” when we experiment on millions of children of our largest state, and the proposed changes are not based on any solid evidence, and in my opinion (and the opinion of many other experts) will make things worse. Indeed, there is no shortage of experiments in mathematics education that yielded no or even negative progress in terms of equity.

Also, not all change needs to be curricular change. The inequalities in the system were not created because of the math curriculum, and will not be fixed by it. Many top-performing countries use a fairly traditional math curriculum, some strongly influenced by the Soviet system.  The inequalities in the US arise from huge disparities in the resources at school, and a highly unequal society at large. I personally think that improving education is much more about support for students, resources, tutoring, teacher training, etc, than whether we teach logarithms using method X or method Y.

Q: Shouldn’t CS and STEM faculty stay out of this debate, and leave it to the math education faculty that are the true subject matter experts?

A: The education system has many stakeholders, including students, parents, teachers, citizens, employers, and post-secondary educators, and they all should be heard. STEM careers and other quantitative fields are the fastest growing in opportunities and student interest in college. As such, one of the goals (though not the only one) of K-12 math education is to prepare students to have the option to major in STEM in college, if that is what they want to do. STEM faculty are the best equipped to say what is needed for success in their field, and what they see is the impact of K-12 preparation. Math Ed and STEM faculty can and should be working together on the  K-12 curriculum. 

Q: But not all students will go to STEM in college. Shouldn’t the K-12 math education system also offer something for the students that are not interested in STEM?

A: I agree that not all students will go to STEM and that (for example) not all high-school students should be forced to take calculus. However, if we are offering an option that is designed for students that are not interested in STEM then we should be honest about it. At the moment high-school data science courses are marketed as a way to “have your cake and eat it too” – courses that are on one hand easier than algebra and calculus and on the other hand give just as good or maybe even better preparation for a career in tech or data science. This is misinformation, and the students most likely to fall for it are the ones with the least resources. In addition, the type of thinking developed by rigorous math courses can benefit students throughout their lives and careers, regardless of the path they take.

Q: Isn’t equity more important than giving students opportunities to advance in math? Shouldn’t mathematical education policy be focused on the kids that are struggling the most and facing most challenges, in particular students of color?

A: I personally think equity and expanding access to mathematical education is absolutely crucial. This is why I was and am involved in initiatives including AddisCoder, JamCoders, Women In Theory, and New Horizons in TCS. But true equity is about actually educating students more, not about moving the goalposts and claiming success. This is doubly true in the context of the US education system. There will be many routes open to well-resourced students to bypass any limitations of the public system. These include private tutoring, courses such as Russian School of Math, Art of Problem Solving, or simply opting out of the public system altogether. Also, due to local control, wealthier districts are likely to opt out of any reforms that they perceive (correctly) as giving worse preparation for post-secondary success. 

Hence changes such as the CMF will disproportionately harm low-income students and students of color, and make it less likely for them to succeed in STEM. Not coincidentally, many educators, researchers, and practitioners of color have signed both letters, while the CMF itself has no Black authors. There are efforts that actually do work to decrease educational gaps: these include Bob Moses’ Algebra Project, Adrian Mims’ (contact person for one of the letters) Calculus Project,  Jaime Escalante  (from “stand and deliver”) math program, and the Harlem Children’s Zone. Notably, none of these projects involve lowering the bar. 

Q: Maybe the problem is with the STEM college curriculum as well? For example, why do students need calculus for a computer science degree when hardly any software engineer uses it? If colleges would make their curriculum more practically oriented then we wouldn’t need to teach high-school kids this hard math.

A: There is a narrow answer and a deeper answer to this question. The narrow answer is that the goal of K-12 education is to prepare students for success in the world as it exists now. If you want to fight these battles at the higher education level, then you should fight them and win them, and only later change the K-12 education to fit the new college curricula.

However, there is a deeper answer why university education has always been about more than just giving students the minimal vocational skills. We believe that our mission is not just to give students some tools that they’ll use in the first job out of school, but broader ways of thinking that will help them keep up with new developments throughout their careers. Computer Science is a great example of this. Fifteen years ago, most computer scientists didn’t need to know much about algebra, probability or calculus, but these days deep learning is fast expanding to every area of CS. The time between an academic paper to a real-world product is getting shorter and shorter, and one skill a computer scientist needs these days is the ability to read a complex technical text and not be afraid of learning new math. Foundational courses such as college calculus and linear algebra (which themselves build on high-school Algebra II and  pre-calculus) are crucial for this skill.

Q: Aren’t you devaluing data science and saying it’s less important than Algebra or Calculus?

A: Absolutely not. I think literacy with data is an essential skill for any citizen in our modern society, and strongly support it being taught for every K-12 student. This does not mean that it can or should replace the basic math foundational skills. Data science can and be included in variety of courses, ranging from the computational and natural sciences to the social sciences and even humanities. (For example see the courses satisfying Harvard’s quantitative reasoning with data requirement.)

“Data science” is an evolving field and at the moment not very well defined, and as such there are data science courses of vastly different types. A high-school course or module in data proficiency can be extremely beneficial for students, but without prerequisites such as algebra, probability, and programming, there is a severe limit to the depth that it can go to. For students who will not go into STEM or data science, such a data literacy course would be highly recommended. Students who will take a deeper course later on are better served by foundational courses such as Algebra, Pre-calculus, and Calculus. 

By the way, there is nothing about data science that makes it inherently easier than algebra or calculus. While (univariate) calculus is ultimately about functions you can draw on a paper and reason intuitively about their graphs, issues of correlations vs causation are highly subtle, and even experts could get it wrong. The skills and rigorous modes of thinking developed in courses such as Algebra II and beyond are required to develop a true understanding of data science. 

There is another reason why a prerequisite-free data literacy course should not be considered as part of the math curriculum, which was eloquently put by Henri Picciotto (see also this): “in math we should not teach black-box formulas and software packages that students cannot possibly understand thoroughly. We have been moving towards teaching math for understanding at all levels. There is no reason to use data analysis as an excuse to backtrack. Let science and social studies teachers use standard deviation, correlation coefficient, regression, confidence interval, and the like without understanding the underlying assumptions and the reasoning and calculations that lead to those. Math teachers should not. “

Q: Isn’t the CMF an evidence-based proposal that is backed by a huge number of citations?

A: The short answer to this question is “No”. The medium answer is that the CMF contains many citations but often the research cited is sloppy, or is cited incorrectly. (For example, they make plenty of unsupported claims on neuroscience ,whereas essentially all neuroscientists agree that our understanding of the brain is nowhere near the level that it could be used to guide curriculum development.) The long answer is out of scope for this blog post, but here are some links to analyses done by other people. I will update this blog as more are put out (this is a 900 page document after all), but some people that wrote about this include Michael Pershan and Beth Kelly (see also this). Brian Conrad has been working on fuller analysis of the CMF, and I will update this post (as well as tweet about it) as parts of it become available.