Every now and then, an academic decides they’re qualified to fundamentally rethink math education, and to share their brilliant solution with the world. That is already problematic when the academic is a mathematician or a math education researcher, but it is even worse when it is someone whose only connection to K-12 math education is that they were once a student, or that they are the parent of a student.
Reflecting the Broader Culture
Steven Levitt’s contribution to this genre, in the Freakonomics Radio episode on math education is not as bad as what we usually get from these self-appointed saviors, but it does have some glaring weaknesses.
– He did not consult a single math teacher. This is typical. It reflects the arrogance of so many academics, and the general societal disrespect for our profession. Perhaps more important, Levitt is unaware of the fact that the National Council of Teachers of Math has launched an in-depth reevaluation of the high school math curriculum, based on massive input from the math education community. Anyone seriously interested in the topic should take a look at Catalyzing Change as the starting place for an informed discussion.
– Complaining about bad Algebra 2 classes is the standard opening of a certain style of anti-math opinion pieces, and this podcast is no exception.The episode starts with Levitt’s daughter sharing some opaque and unmotivated Algebra 2 material she has to grapple with. I wrote about this line of argument here. To quote from that post: “I do not intend to defend poorly taught, boring, meaningless memorization of highly technical topics.” Yes, this approach to Algebra 2 is both deadly and widespread, but it does not change the reality that a well thought-out and well taught Algebra 2 can be a great course, and is necessary for further work in any quantitative disciplines, including statistics.
– The episode assumes that the purpose of math education is the teaching of skills that would be “useful” in daily life and in professional work. That is a narrow lens, which is only applied to math education. When is the last time you used what you learned about electricity, or dinosaurs, or pH, or Hamlet in daily life or on the job? Very few of us become scientists or playwrights. Is Levitt going to embark on a campaign to reduce all science and humanities education to strictly topics that have practical applications? Not likely, but this utilitarian framework would be consistent with his interest in researching financial rewards for students to motivate better grades.
In the end, these weaknesses merely reflect the broader culture, which of course affects people with PhD’s no less than anyone else. Fortunately, when Levitt digs a little deeper, he makes many points that deserve discussion.
We Need Change!
His first three points are largely correct:
– We need not stick to the traditional Algebra 1 / Geometry / Algebra 2 sequence.
– Teaching the most important things in depth is preferable to broad but superficial coverage. The most important areas are arithmetic, data analysis, problem solving, functions, and linear equations.
– Change is difficult because of teacher resistance and other pushback, but this can be overcome by changing standardized tests.
It is not easy to change a complicated, interlocking system. For example, some schools and districts have adopted a Common Core sequence that is supposedly integrated (as opposed to the back-and-forth between algebra and geometry.) But the high school standards are so numerous that there is no way to teach them well, even within the integrated curricula. (See my in-depth analysis of the Common Core State Standards for high school math.) This is in spite of the fact that we have known for decades that the math curriculum is “a mile wide and an inch deep”, as compared to countries with better results in math education.
I once organized a round table at a conference where high school math teachers would tell their middle school counterparts what they value, and what should be emphasized in 7th and 8th grade. Surprisingly, there was near-unanimity: middle schools should teach the most important basics of pre-algebra and basic algebra, and not stretch themselves thin by teaching end-of-the-book hyper-technical topics which are in any case developmentally inappropriate. However, the very same high school teachers used placement tests based on those end-of-the-book topics!
This is exactly parallel to what the College Board research showed: college faculty want a few important topics taught well, but high school teachers feel that every topic needs to be covered, even at the cost of a breakneck pace and little understanding on the part of students. And the reason high school teachers have this belief is that college admissions officers prefer to admit students who have had calculus in high school, and even more so students who took that course before their senior year. Thus, parents continue to pressure schools to accelerate students across mountains of arcane and boring materials, at younger and younger ages, often against teachers’ best judgment, and usually against students’ best interest. (Read more about this in my article on hyper-acceleration.) We are trapped in a deeply rooted system, which is unlikely to evolve until some attitudes and policies change not just in schools, but also at universities.
There is some truth to the idea that progress can be made by changing the standardized tests. We’ve seen this, for example, with the use of graphing technology. There was huge resistance to it, which magically melted away once graphing calculators were allowed on the SAT and AP tests. Alas, there’s a price to pay for the wielding of that tool: Levitt defends “teaching to the test”, evidently unaware of the resulting harm it can do to the quality of education. (Read more on this in my article on The Assessment Trap.)
Yes to Data, But How?
In any case, Levitt’s main message is:
– We should spend less time preparing students for calculus, and teach more about data, for example linear regression and correlation vs. causation.
– Data analysis should be taught in several disciplines, starting with math. This includes using spreadsheets and presumably other technology.
A wholesale abolition of Algebra 2 / Precalculus / Calculus would seriously undermine the pipeline to the hard sciences and engineering, and in fact to college-level statistics. Moreover, replacing it exclusively with data analysis would not help (for example) students who want to pursue computer science. Fortunately, we have an eminently practical solution, which is spelled out in NCTM’s Catalyzing Change. The idea is to spend two years on core content that all educated adults should know (such as the list proposed by College Board CEO David Coleman on the podcast.) And then students would choose different courses for their last two years. That could be calculus, statistics, discrete math, “pure math”, or who knows what else. I would not be surprised if the “data” stream ends up being the largest: as Levitt points out, it is the most readily applicable to the “real world”. (For example, at my school, the modeling and statistics class had two to four times the enrollment of our other post-Algebra 2 electives.)
I love the idea of data analysis becoming part of the science and social studies programs, as suggested by Coleman in the podcast. Statistics comes to life when it is about something, and even more so when it is about something students are interested in and care about. But, you say, science and social studies teachers would need to learn something! That is true, of course, and that would be great. That is also true of math teachers, who are no more prepared to teach statistics than their colleagues in these other departments.
A key difference is that 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. This is not unlike logarithms: in science classes, they are seen as a tool, and students need only understand how to use them. But in math class, we want to look “under the hood” and understand what logs are, their relationship to exponents, the properties of the function, the use of different bases, and so on.
Yes, that means that we need to develop a math curriculum for data analysis that is developmentally appropriate (avoiding college-level techniques) and intellectually honest (laying the mathematical groundwork for those techniques, including basic probability, in a way that high schoolers can understand.) This was attempted a few decades ago, in the Quantitative Literacy series, by Landwehr et al. Unfortunately that curriculum cannot really be used as is nowadays, as it dates from a time before the availability of computers. A 21st-century version should be developed by statisticians, epidemiologists, demographers, etc. And, of course, math teachers!
3 thoughts on “Freakonomics Radio on Math Curriculum”
I think I agree for the most part with everything you wrote. My last stab at this: blog.mathoffthegrid.com/2019/09/fantasy-high-school-part-3-statways.html (The video is really interesting if you have time to watch) Overall a much better starting point for the podcast would have been an interview with Uri Treisman over at the Dana Center around their ongoing pathways work. (And Levitt never really described what his work with the Schmidt Futures around the area really involved. My first thought was please don’t reinvent the wheel)
One more very anecdotal data point about deferring stats to Science teachers. My son is a month or so into Biology and they went over SD, SE, etc in the very beginning. However, the treatment was pretty much here are some formulas, hand-waving that they do something and go memorize them. I ended up having a followup discussion at home around basic questions like: why n vs n -1 or square rooted here? What underpins this formula? etc. All of which drove home how complex statistics really is and how its model sits on top of a complex Algebra 2 and Calculus foundation. Its my own preference but I find the discrete math pathway an easier (and more interesting) pathway.
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🙂 I like the anecdote. And yes, the assumptions and calculations that support statistics are not appropriate to high school. Let’s keep the hand-waving out of math class!
Thank you for this important blogpost, Henri, and please pardon my late reply. I could not agree more! As one with a background in statistics, I have always wondered why data analysis has been delegated to secondary math teachers as opposed to science teachers (including social sciences). First, we have to understand that while probability theory and mathematical statistics are subsets of mathematics (since these disciplines involve proving theorems), confusingly, statistics (descriptive and inferential, which are not about proving theorems but rather exploiting them to understand the observable world) is not mathematics. Certainly, probability and mathematical statistics belong in a mathematics classroom, but the practice of statistics is fundamentally science rather than math. Yes, of course the lines are beautifully blurred, as every human endeavor contains an inductive reasoning component. But math uses experimentation to develop conjectures to be proved, whereas science/statistics uses experimentation to develop hypotheses to be tested with uncertainty quantified. That latter is science, y’all. That’s right folx: It’s science that is undergoing the big transformation we’re justifiably worried about, more visibly than math is. We’re just all so mathematically illiterate that we’re like, “Ooh this is numbery so it must be math!” (Where does modeling live, you ask? That’s for another time.) Has anyone met a science graduate student who is about to complete their PhD and panics at the last minute because they never learned any statistics? Yep, statistics should have resided in science class all along. (This does not happen to math PhD students.)
I of course agree with Levitt that the math we teach in schools needs to be reformed; math educators have been preaching this for ages. But the way to go about this reform is to re-prioritize standards (e.g., depth over breadth), change standardized tests to reflect what we value, and adopt an integrated model that emphasizes connections between algebra, geometry, and probability. I believe it’s the artificial compartmentalization of mathematics that makes school-math in the US so often inane, such as the examples to which Levitt refers. Utah (where I live) has adopted integrated math standards, and while it was a big adjustment for teachers, and while Henri is correct that it’s still a pseudo-implementation at this point, it is a step in the right direction for empowering students as well-rounded problem solvers. After all, the term “integrated math” is redundant in countries that out-perform the US, no? And that folx in the US are notoriously poor geometers is an artifact of our compartmentalized model, methinks.
I hope that school-math reform strives to push for a set of integrated core standards that are more reasonable than the current laundry list of isolated topics, and I hope that school-science reform picks up the statistics that are so crucial to existence today. But math should still be math; it would be wrong to mis-advertise mathematics as data science to young people in schools.