Math that Matters: The Case for Probability over Polynomials

When I was in high school, students divided into two camps: those who “got” math and those who believed they simply weren’t “math people.” 

I was one of the “got” math people who spent countless hours doing trigonometry and eventually doing AP Calculus where I was doing derivatives and all sorts of ‘fancy’ math. Deep down, I knew what this was really about – it wasn’t about practical skills but about signaling I was smart, just like the other high-achiever types. It wasn’t about learning. It was just another credential for the college application rat race.

Meanwhile, some of my friends struggled with math not because they lacked ability, but because the content was so disconnected from anything they cared about. When any of us asked the teacher when we’d ever use this stuff, she gave the standard response about college preparation and developing abstract thinking skills. 

But looking back now, I realize we were all learning the wrong math – both the students who excelled and those who gave up. It is yet another example of how schools fail teenagers.

The math most useful in real life isn’t calculus or advanced trigonometry – it’s probability and statistics. And yet our education system treats these subjects as afterthoughts, typically confined to a single elective course typically in senior year, if taught at all. 

This is backwards.

Consider what probability and statistics let you do: 

• understand risk in everyday decisions
• detect misleading claims in news articles
• make smarter choices about money; and
• grasp uncertainty in everything from weather forecasts to medical tests

A teenager who understands basic probability can immediately see through the false promises of gambling apps targeting their age group. One who grasps statistical significance can better interpret health studies they encounter about supplements making grand promises about physical health. 

These aren’t “someday you might need this” skills – they’re immediately useful.

The evidence and arguments for emphasizing probability and statistics is compelling:

• Daniel Kahneman’s Nobel Prize-winning research reveals how humans systematically misjudge probabilities in predictable ways. His work with Amos Tversky shows that even simple statistical concepts like base rates and regression to the mean are counterintuitive to most people, leading to poor decisions in everything from medical diagnoses to financial investments. Teaching probability early could help students avoid these cognitive traps.
• Jordan Ellenberg, in “How Not to Be Wrong,” demonstrates through dozens of examples how statistical thinking illuminates everything from lottery scams to political gerrymandering. He argues that the mathematics most useful for citizenship and everyday life isn’t calculus but the ability to reason about uncertainty and variation – skills that probability and statistics directly develop.
• Bryan Caplan explicitly argues in “The Case Against Education” that our math curriculum teaches skills with little real-world application for most students. He points out the mismatch between the predominantly algebraic-calculus track and the actual mathematical needs of most careers and life situations, which more often involve understanding data, risk, and basic statistical concepts.
• Arthur Benjamin, in his famous TED talk and subsequent writings, makes the case that statistics should replace calculus as the “summit” of high school mathematics. He argues that for most students, statistical literacy is far more valuable than calculus in a world increasingly driven by data and probability, yet our curriculum treats statistics as optional while pushing students toward calculus.
• Andrew Gelman, one of today’s leading statisticians, has written extensively about restructuring mathematical education around understanding uncertainty rather than abstract proofs. He advocates for teaching statistics through simulation and real problems, suggesting that even complex statistical concepts can be made intuitive when presented in contexts that matter to students.

To make room for more probability and statistics, we need to be willing to cut something. I’ve previously argued against Shakespeare and other subjects here.

But if we’re focused on what to downshift on within math, the obvious candidates are topics like advanced trigonometry, detailed polynomial factoring, and calculus for non-STEM students. 

These are precisely the topics that prompt eye rolls and “when will we use this?” questions from students – because they’re right. Most won’t use these skills unless they pursue specific technical careers.

But teaching probability and statistics well requires more than just changing the curriculum – it requires making it engaging. Instead of abstract problems about pulling colored balls from urns, we should use real-world applications that matter to students:

• Sports Analytics: Students could analyze their fantasy sports team performance using probability distributions, calculate the true value of different player stats, or determine whether a winning streak is skill or random chance. A basketball fan might learn expected value by calculating whether a player should shoot a 3-pointer or drive for a 2 based on their shooting percentages – mathematics that suddenly matters when applied to their favorite team.
• Social Media Content Creation: For aspiring YouTubers or TikTok creators, statistical thinking offers immediate value. Students could analyze video performance data to determine what factors correlate with higher engagement, use A/B testing to compare different title formats, or apply probability to predict which content categories have the best chance of going viral based on platform algorithm patterns.
• Gaming Strategy: Video games provide a perfect laboratory for probability concepts. Students could calculate drop rates for rare items, optimize resource allocation in strategy games, or analyze win rates with different character builds. The mathematics of expected value directly translates to better gaming decisions, creating an immediate connection between abstract concepts and personal interests.
• Music and Streaming Analytics: Students could examine the probability distributions of streams across different artists, analyze what makes songs trend on platforms like Spotify, or calculate the expected payout from streaming versus other revenue sources – connecting statistical thinking to their passion for music.
• Understanding Social Dynamics: Probability helps make sense of social phenomena students experience daily. What are the chances of two people in their class sharing a birthday? How can they understand selection bias in social circles? Why do certain rumors spread faster than others? These questions make statistical concepts relevant to their immediate social world.
• Consumer Decision-Making: Students regularly make purchasing decisions. Statistical literacy helps them analyze whether a sale is actually a good deal, understand the risk/reward of extended warranties, or calculate the expected lifetime cost of different electronics – skills they can apply immediately at the mall or online.

When students see immediate and useful applications, the dreaded “when will we use this?” question disappears.

The benefits of this shift would be profound. We’d graduate students better equipped to:

• Make informed personal decisions about money, health, and risk
• Understand scientific claims and evaluate evidence
• Navigate an increasingly data-driven world
• Think probabilistically about complex problems
• Detect misleading statistics and flawed studies

I will digress and offer one more slightly detailed and pressing reason to prioritize probability education: the explosion of sports betting among young people, particularly young men. 

As states legalize gambling and betting apps target younger audiences, many students will encounter these platforms and never truly understand the mathematics behind them. A strong foundation in probability & mathematical reasoning would help them see through the carefully crafted illusion of easy money, understand concepts like house edge and expected value, and recognize how betting odds are strategically designed to favor the house.

Rather than simply telling students to avoid sports gambling (a strategy with limited effectiveness akin to abstinence-only sex education), we could equip them with the mathematical tools to understand why the vast majority of bettors lose money over time. This is mathematics as a form of protection against predatory industries and companies.

Even for STEM-bound students, stronger foundations in probability and statistics would be valuable. Many cutting-edge fields like AI, genomics, and climate science rely heavily on statistical methods. A student heading into computer science is more likely to need knowledge of probabilistic algorithms than advanced calculus.

Some will object that reducing traditional mathematics could harm students’ abstract reasoning abilities. But probability and statistics develop these same skills while being more practical. TBH, “abstract reasoning” is often the catch-all reason given when teachers can’t really answer a student’s “when will I use this?” question. It’s a thoughtful sounding way of saying “Because, I told you so”. Understanding confidence intervals requires just as much abstract thinking as understanding the quadratic formula – but one has far more real-world applications than the other.

Here’s what a reformed curriculum might look like:

• Middle School: Basic probability concepts, data literacy, and simple statistical measures
• 9th Grade: Core algebra with probability applications
• 10th Grade: Geometry with data visualization and spatial statistics
• 11th Grade: Advanced algebra with statistical inference and modeling
• 12th Grade: Advanced statistics and data analysis (with calculus as an optional track for STEM-focused students)

This isn’t about making math easier or less rigorous – it’s about making it more relevant. 

The mathematical challenges of understanding probability and working with statistics are just as rigorous as traditional topics. The difference is that students can see why these challenges matter.

The world is becoming more complex and data-driven. The ability to think probabilistically and understand statistics isn’t just useful – it’s becoming essential. We owe it to our students to teach them the mathematical tools and associated reasoning they’ll actually need to navigate this world. The sooner we make this shift, the better equipped the next generation will be to face the challenges ahead.

Some of the brightest minds in mathematics education – from Kahneman to Gelman – have been pointing us in this direction. It’s time we listened.

The real opportunity here isn’t just better preparing students for some abstract future. It’s about making mathematics immediately relevant to their lives today. When students analyze the statistics of their favorite games, calculate the real odds of social phenomena they care about, or use probability to understand the news they consume, math transforms from a chore into a powerful lens for seeing their world more clearly.

A shift toward probability and statistics could make math more democratic too. Traditional math curricula often function as sorting mechanisms, separating “math people” from everyone else. Statistical thinking, with its blend of quantitative skills and real-world contexts, can be more approachable and engaging for a broader range of students. Done right, it could help more students discover that they are “math people” after all.

Building an education system around what’s relevant now, rather than around outdated notions of what might be useful someday, isn’t lowering our standards. It’s raising them by demanding that what we teach actually matters. The cost of continuing to teach the wrong math isn’t just wasted time—it’s a missed opportunity to give students tools they could be using every day.