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 ProjectJaime 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.

11 thoughts on “A personal FAQ on the math education controversies

  1. Thanks for this post, Boaz. I am a student at Harvard Graduate School of Education (and have tutored 100+ students of color in math), and I wish we at HGSE had more opportunity to dive into these active and relevant curricular debates.

    I feel very clear on the value of rigorous math education for students who are prepared to engage with it productively, but I have felt conflicted about the value for students who generally struggle with it.

    With some of my students, I have seen their capacity for complex understandings deepen through their struggling with math. For other students, they really never got past a surface level of pattern recognition. I am curious about what forms of learning and study that are adjacent to math, or are subsets of math, might be more productive and capacity building for them.

    1. Thank you Ben for this thoughtful response! Indeed, as I wrote, I think that STEM faculty and Ed faculty should collaborate. I don’t think everyone should study the exact same math, but we should also be honest about what courses convey. It may well be that for some students, it’s better to go slower than just skim quickly through courses which they don’t understand. But we shouldn’t use the hype behind “data science” to fool these students that there is a magic shortcut to get to lucrative tech careers without getting past the struggles and engaging with rigorous math.

  2. As a HS math teacher and researcher, I believe we can achieve much better results through collaboration and vertical integration among ALL of the educational stakeholder groups.

    Shutting out front line teachers leads to gaps in understanding the current situations on the ground. Shutting out the mathematicians and math/CS/Stats/Data Science professors leads to misalignment in students’ preparation — and also, as we see in the CMF rev 2, dangerous misrepresentation sof what is needed for ACTUAL data science study. And so on.

    We need a broad and rigorous debate on a math framework, not more turf battles.

    California should shut down this current effort and start over.

  3. I graduated from high school in 1960 at age 17 and 5 months. Before that, I struggled with math and hated it. My 8th grade math teacher did me a favor by giving me a D-, which forced me to take remedial math in 9th grade (a combo of arithmetic review and basic algebra and geometry). That
    gave me the extra time and training that I needed to successfully complete 2 years of algebra and a year of geometry in succeeding grades. Then I managed to somehow navigate the higher education system and graduate from UC Berkeley without any other math courses. Following that, I obtained a n elementary teaching credential, during preparation for which, I discovered that I was much better at math than my fellow credential candidates in the Math for Educators class!
    Hmmm.
    Life is strange.
    My point is that everyone is different. Mandating that everyone take algebra in grade 8 is a result of an “assembly line” view of education – that students are all widgets on an academic assembly line.
    In my 35 years as a grade 4 – 6 teacher, I used a technique called “differentiated instruction” that gave extra help to those who needed it and extra challenges those that would otherwise have been bored stiff. And guess what? My kids got better math test scores than most CA students.
    Another problem with mandating algebra for all in grade 8 is that when that was briefly implemented, it became a very watered-down course because most kids just weren’t ready for it yet.
    “Checking off the boxes” like this is not the rigor we would prefer.
    If I were to worry about what we need more of in math instruction, I would suggest more mental math and quantitative reasoning in grades K-6. As it is, math tends to be taught as a series algorithms to memorize with little attention to the cross-relationships.
    And please, While everyone needs to know basic algebraic and geometrical relationships,
    advanced algebra, calculus, trig, etc. are not any more necessary to a well-rounded education than Latin was back when I was in school and it was still taught. I’d rather see more science taught than more math. I think everyone needs a really good grounding in all the sciences to make sense of our ever changing and confusing world.

    1. Thanks! However, note that the standards for graduation are only to finish Algebra II. There is no requirement that everyone takes calculus in high school.

  4. Thank you for your comments, as a parent (working full time) I am already having a hard time to fill the gaps from the current system. I couldn’t review everything, (again peak time at work right now), but I managed to read at least 2 chapters and not only the whole thing seems does not seem easy to implement but it is full of agendas, forgetting the very basic point that public schools is funded by all tax-payers.
    Public education should attend all and not cater to a sub-group of people or push specific ideologies. I think you are being very generous with the “data science”. For me it will be a generation of “correlation is causation” people…I actually pointed on my document “what exactly is data science? ”
    The crazy thing is that if we decided to do the CMF framework and apply in kids sports, well we know they wouldn’t dare… but because it is academics… they decided to come with this non-sense.

  5. Being able to integrate and differentiate is less important than understanding that P(B|A) does not, in general, equal P(A|B), and you can learn that latter fact without learning how a probability distribution is defined. Wikipedia has a proof of Bayes’ Theorem without calculus:

    https://en.wikipedia.org/wiki/Bayes%27_theorem

    Yes, it is ultimately founded on calculus. But we don’t teach numbers to kindergarteners starting from Peano’s axioms, and we don’t need to gate the essentials of conditional probability behind calculus. In fact, doing so is positively harmful to society at large.

    1. Conditional probability is much subtler than calculus, which is why many people get it wrong. The analogy for teaching probability before calculus would be to start students with quantum mechanics rather than Newtonian physics because the former describes the world more accurately.

      1. It is subtler, which is why we need to start teaching it earlier, and deemphasize less useful courses to do it.

Leave a Reply to Boaz Barak Cancel reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s