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Because I’m an investor who also writes, I receive an inordinate number of pitches, some so standard they literally begin with “Hi [Reporter Name],” others surprising. Like a recent missive from Otter PR which asked the following question: “Are you interested in a guest post or op-ed opportunity from coach Rick Singer on whether college is only about the money and whether the admissions process has issues?” I nearly ate my hat. You’ll recall Rick Singer was the college admissions consultant who masterminded “Varsity Blues” bribes from wealthy parents to coaches at highly selective universities. Once caught by the FBI, Singer provided incriminating evidence that led to federal charges for 33 parents and prison sentences for 22 including celebrities Lori Loughlin and Felicity Huffman. Singer was released from prison last year and promptly hired a PR firm for his new admissions consulting business, which I will not name. Otter PR’s email didn’t reference Varsity Blues or scandal, although it did acknowledge “Rick has been featured in numerous publications recently.” Check.
The more important pitches are from companies seeking investment. Like CORPUS, the Netherlands-based 9-story, 135-foot human-shaped structure that offers an interactive “journey through the human body,” now seeking funding to build additional giants in China. Or less likely but potentially lucrative opportunities like a “poultry hotel” combining a 5-star hotel with an industrial-scale poultry farm (side benefit: guests get fresh eggs and chicken). Or a new fast-casual Asian brand that promises to revolutionize the U.S. dining scene. “Our strategy is simple,” says the pitch. “We aim to replicate the success of the other ‘John’ brands. Think Papa John’s, Jimmy John’s, and Taco John’s.” The investor presentation also mentions Johnny Rockets and Long John Silver’s. What’s missing? Asian John’s! The other Johns “have already helped build [the] Asian John’s [brand].” According to the founder (John), the key to success is locating “next to one of the other Johns. We put it next to a Jimmy John’s.” The marketing campaign writes itself: “There’s a new John in town.” Watch out Panda Express!
Last week I received a pitch from Apex Cybernetics, a Silicon Valley-based robotics company building “AI-powered Teacher Robots that teach children math and provide companionship.” I endeavored to learn more about the company, but there was no trace besides the fact that Apex Cybernetics was the multinational tech megacorporation in Godzilla vs. Kong. While the robots are undoubtedly coming, before we let them teach children math (and provide companionship), we ought to agree on what needs to be taught.
Because there’s some dispute, as seen in the calculus wars. The critique is that calculus is a complex, esoteric subject not utilized outside school, but helpful as a selection or weed-out mechanism for college admissions officers and STEM majors with limited capacity. And that calculus has become a nonsensical proxy for academic rigor – a college Squid Game, and one that became even more important post-Covid with the rise of test-optional admissions. One survey found 80% of calculus students admitting they took AP Calculus because it “looks good on college applications.”
Some belligerents in the calculus wars call it an artifact of an earlier war, the Cold War, when the priority was producing physicists and engineers to keep up with the Ivanovs. Most observers seem to think students would be better off studying statistics and data analysis. And speaking of data, to make matters worse, calculus magnifies inequities in terms of wealth and race even more so than standardized tests – in part because many low-income high schools don’t offer it. The nonprofit Just Equations calls calculus a “stumbling block rather than a stepping stone.” As such, calculus – and AP Calculus in particular – may be a better indication of privilege than rigor.
What's true of calculus is also true of trigonometry and, to a lesser extent, algebra. There’s too much focus on rote problem solving, prioritizing classification of problem type and knowledge of the one valid approach. High school and 100-level college math curriculum is full of formulas and processes developed long before current math teachers were born. For students, it’s far too much acontextual problem solving for no apparent reason. They don’t understand why the work is important and aren’t motivated to complete it let alone think deeply about it. It’s hard to argue there’s no causal link to declining performance on international assessments or a recent Gallup survey finding less than 40% of 18-24 year-olds believe math is very important to them. Both of which raise a large (prime) number of concerns around quantitative skills, data literacy, and preparation for work and citizenship.
This is the context for an important book out this fall. Ted Dintersmith is the author of What School Could Be and producer of the documentaries Most Likely to Succeed and Multiple Choice (also out this fall). He is also a physics PhD who built a successful first career as an investor and now a second as education reformer. And as his new book Aftermath demonstrates, he’s had it up to here with how we teach math.
Ted marshals an asymptotically large amount of evidence that adults use little to none of the math they learned in high school. Ted himself has “never used a smidge of the math formalism” he studied in high school, college, and grad school. To justify the status quo, educators (and some parents) argue that “this math serves a higher purpose: it teaches us how to think.”
Ted acknowledges that President Obama wasn’t wrong when he assured us that algebra, geometry, trigonometry, and calculus is for learning how to learn. Of course “rote math could foster a degree of critical thinking.” But this assumes gifted teachers and ample time, neither of which are typical conditions in math class.
With far too many Americans capable of cranking through quadratic equations but unable to calculate compound credit card interest, Ted’s answer is to replace the lot with practical math: estimation, statistics, probability, prediction, optimization, algorithms, decision analysis and game theory. For each subject Aftermath offers a raft of examples begging to be built into lesson plans. He also argues that context alone isn’t sufficient and that we should aspire to learning-by-doing.
Sounds good, right? The challenge is that by dint of being more practical, at the introductory level these subjects are less inherently complex with fewer multi-step cognitive-skill-building puzzles to be solved. So we need to solve for a new approach without igniting the typical firestorm of educator criticism that we’re dumbing down math. This math problem requires a Goldilocks solution where relatable problems aren’t so simple that there’s no learning but not so complex and irrelevant that there’s no learning.
Ted signals a need to dive deeper, faster. A unit on probability can move from coin flips to Bayesian inference and expected value tradeoffs. Optimization can progress from linear tradeoffs to network flow, constraints, and multi-variable optimization. Game theory can get quickly to Nash equilibria and strategy modeling. The key is to develop progressively harder multi-step problems that build the same muscles as algebra, trig, or calculus problem sets but in highly relevant contexts. (Another is to sneak traditional math into these subjects; algebraic manipulation can be taught through optimization problems, geometry via network design, and functions in statistical models.)
But project-based learning is the apex. Why not have students build a fantasy business, then present them with a series of multi-step problems around demand estimation (probability), capacity checks (algorithms, optimization), inventory (decision analysis, optimization), pricing (game theory), and risk analysis?
Because this isn’t the way math instructors were taught, nor are these subjects as familiar as the algebra, trigonometry, and calculus textbooks that have calcified our quantitative skills. One survey of math teachers found that nearly two-thirds had less than a semester of coursework on probability and statistics. Plus, changing teacher behavior is a hard slog. Witness ample evidence of the increased efficacy of active learning (ensuring information transfer occurs ahead of class, then utilizing peer learning, group problem solving, and project-based learning to improve understanding of key concepts) coupled with few indications that the sage-on-the-stage lecture model has been dethroned.
Not to say there aren’t a few points of light. UCLA replaced its weed-out Calculus for Life Sciences course with Mathematics for Life Sciences, which is doing a much better job building quantitative skills in a large, diverse student population. UT Austin has developed a series of high school and college-level courses focused on quantitative reasoning, statistics, and modeling and produced strong outcomes at dozens of community colleges. And Utah is planning to implement new math standards with an emphasis on data science and relevance.
But these remain the exception. The aftermath of Aftermath is that schools and colleges are going to need new resources and leadership to traverse the line segment from point A(lgebra) to point B(ayesian).
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In a recent text exchange with another author and education leader, Joel Hernandez (not a physics PhD but a former Marine), Joel suggested a mandatory year of CTE before college. “There are a lot more benefits to people knowing how to do stuff than doing the stuff itself (which we also need),” wrote Joel. In Joel’s world, we’d all be better off if more Americans received experience building things, even if completely unrelated to the things they’ll build in the future. My response to Joel: we’ve gone too far into the symbolic.
In 1992, at the dawn of the Clinton era, future Secretary of Labor Robert Reich published The Work of Nations which introduced the term “symbolic analysts” into the labor lexicon. Symbolic analysts were elites of the digital age: professionals who process information and symbols for a living. As they operate solely in the realm of symbols, they can sell their services across borders. And they’re well paid. But first they need to earn degrees, which requires demonstrating proficiency in manipulating symbols according to prescribed rules in algebra, trigonometry, and calculus. And because Clinton-era demand for management consultants and software developers seemed limitless, and because the gulf between symbolic analysts and the rest of the workforce (production jobs, frontline service jobs) would widen, we doubled and tripled down on algebra, trig, calculus, and college. Reich wanted all Americans to have the opportunity to become symbolic analysts.
But concomitant with our overshooting on classroom-based, tuition-based, debt-based career launch infrastructure, we overshot on the producing symbolic analysts. The past 30 years have taught us that shuffling symbols won’t build high-speed rail, homes, the electrical grid to support the clean energy we need, or even poultry hotels. And we didn’t anticipate that AI would be a great leveler of symbolic proficiency. It’s now clear that, for most young Americans, socioeconomic mobility will be defined by applied problem solving requiring subject matter expertise and practical or technical experience, with the ability to tap AI tools for the requisite symbolic problem solving.
So Joel’s right about CTE. And Ted’s right about math. We need to reform both and restore some balance to our education system. We need more judgment, adaptability, and applied quantitative skills than symbolic manipulation. Because there are already far too many Rick Singers running around manipulating people and numbers. And not nearly enough people building useful things like math-teaching cyborg companions and Panda Express killers like Asian John’s.