When I took calculus in high school, I didn’t understand a single concept. By the grace of an extremely generous teacher, I marginally passed the class. In college, I got through three levels of calculus, but I didn’t understand anything.

During my second attempt at learning Calculus III, I listened as the professor described missile trajectories and satellite positioning, and I asked myself: “I’m a bio major, when am I going to launch a missile!?”

Today I teach biology at a private high school in New York City; I’ve also taught math for the past six years.

I no longer struggle to understand the fundamental concepts of calculus, but I’ve chosen not to teach the course. Instead, I developed a “math applications” class specifically for high school students who are not “calculus bound.”

In my class, students analyze real-world data and share what they’ve learned visually. Many discover that math isn’t only an esoteric language, it is a way to make sense of the world and share that understanding with others.

I believe that deprioritizing abstract math like calculus in favor of practical math, with a focus on statistical literacy, reduces barriers to entry and will help increase diversity in the STEM fields.

Before taking math applications, many of my students, like many Americans, had significant levels of math anxiety. All joked that they were the “dumb kids” because they didn’t understand algebra or trigonometry. Now they tell me that, as one student beautifully expressed it, “Math isn’t meant to be a trap, it’s like a puzzle that allows us to discover an interesting hidden picture.”

This is the class that I should have taken in high school. Unfortunately, my class is an anomaly.

Valorizing calculus as a proxy for intelligence and potential for succeeding in the STEM fields is nearly universal, has negative consequences for education and has kept many students from exploring STEM majors in college.

Despite all this time and effort to teach kids calculus, very few students even consider majoring in math. In fact, only about 1.3 percent, or 31,000, of the over 2 million annual college graduates major in math. Most students who take calculus in high school are doing so to “look good for college.” Approximately 80 percent of these students retake the course in college.

I’ve done some simple back-of-the-envelope calculations regarding the amount of time spent learning calculus to determine whether it is time well spent. If you assume that one semester of classes takes about 100 hours to complete, a student will spend a minimum of 200 hours of time in calculus class for a given year.

If 400,000 students — a conservative number — are taking calculus in high school, we are now talking about 80 million hours. Double that to include college students, and we are talking about 160 million collective hours of student life.

This equals more than 18,000 calendar years — all on a subject fewer than 5 percent of students will ever use in a professional setting, and likely never again.

For context, farming was developed about 12,000 years ago. That means that every year we are spending 1.5 times more time teaching calculus than it took for modern civilization to arise.

This is a terrible return on investment! What could those non-math-majors learn with all those collective years?

## I listened as the professor described missile trajectories and satellite positioning, and I asked myself: “I’m a bio major, when am I going to launch a missile!?”

This isn’t to say that calculus has zero value. Rocket scientists, physicists and civil engineers use calculus daily. And for students who don’t pursue those careers there is value in terms of accurately characterizing and solving problems that deal with variable rates of change. But will a million students a year need these skills? What is the opportunity cost of attempting to develop these skills?

We could ask those questions of every class a student takes in high school. The difference is that most courses in high school cultivate skills with broader applications. For example, even if a student never reads Shakespeare or writes another essay after graduating, literacy and writing fluency are still necessary in almost every single field.

An equally important dimension to consider is calculus’s effect on access to degrees and equity. We can’t ignore how calculus serves as a formidable gatekeeper. Of the 15 highest-paying undergraduate degrees, all but one require at least one semester of calculus at most colleges.

This means that students who struggle with math are effectively barred from pursuing the degrees that lead to the highest starting salaries. The calculus requirement also deters underrepresented students, many of whom have never received sufficiently rigorous math teaching, from pursuing STEM degrees.

It is one thing to say that someone shouldn’t major in aerospace engineering or computer science if they can’t handle calculus, but do we really need to dissuade them from pursuing a degree in finance or biology?

How many finance majors will become derivatives traders? How many biologists will pursue a career in modeling cell motion? Why do pre-med students have to take 2-3 semesters of calculus but zero semesters of statistics, the discipline that most informs best health practices?

**Related: ****PROOF POINTS: How a debate over the science of math could reignite the math wars**

The original impetus for promoting high school calculus in the 1960s was fear of the Russians winning the space race. That is *not *a good reason to continue to push calculus today.

I believe nearly all high school students will be best served by taking statistics instead. There are significantly more occasions, both inside and outside of a career, that require statistical literacy than require technical expertise in calculus.

Statistics are necessary to understand and navigate the barrage of data we now see daily. If we want students to successfully navigate digital misinformation and separate half-truths from lies, especially when most people get news via social media, which has a strong financial incentive to promote content that increases “engagement” at the cost of verifiable truth, they will need to have a solid sense of statistical literacy and validity.

Colleges are risk-averse, move slowly and are unlikely to spearhead change. High schools could change how they emphasize certain courses, but pressure on students to get into selective colleges, along with long-held perceptions that having calculus on their transcripts will help them achieve that goal, makes change difficult.

So, it’s time for parents to strongly encourage their children to take statistics instead of calculus in high school. Statistical literacy is potentially as important as traditional literacy, regardless of the path a student chooses.

If we are serious about increasing academic equity and improving the educational experience and outcomes for all, it’s time de-emphasize calculus.

*Selim Tlili is a high school science teacher at The Ramaz School in New York City. He earned his bachelor’s in biology from SUNY Geneseo and his master’s in public health from Hunter College. Follow his writing at selim.digital.*

*This story about statistical literacy was produced by **The Hechinger Report**,* *a nonprofit, independent news organization focused on inequality and innovation in education. Sign up for** Hechinger’s newsletter**.*

This kid is but one person. I teach calculus and I make it interesting including using problems from other subjects. The idea of a limit, 0 and infinity are fascinating. If I hear the word “barrier” once more I could switch to teaching English.

What about calculus based statistics. The only time I used a lot of calculus in my undergraduate studies was in advance statistics courses. I don’t see how the watered down statistics curriculum can take the place of a calculus course. It would be better to offer a business or social sciences calculus course in place of regular AP calculus class.

I wholeheartedly agree with this assessment. Statistics is a much more valuable math course than Calculus for the vast majority of the population and career fields. For years, majors in the business fields didn’t even require Calculus, only Prob & Stats. Now they require it, but call it “Business Calculus” whatever the heck that is”. The author is correct, with so much misinformation on social media we need a population educated in statistics to recognize bogus studies, sample sizes, etc.

This is such a bad take. The problem isn’t just the students, it’s teachers like yourself that never enjoyed calculus in the first place. How can teachers who don’t understand or enjoy the material themselves be expected to properly pass on that curiosity and sense of wonder about the mathematical world onto their students? I’ve been tutoring since I was 13. I’m nearly 30 now, and I guarantee that the problem lies not with calculus itself, but in the way math in general is taught from a very early age to kids, period. We need to change that and remove anti-intellectualism from our schools – but that’s a completely different conversation altogether.

That’s the solution-dumb it down so everyone can succeed, temporarily. Keep standards high so that the world will be led by people who understand it not by those who couldn’t do.

Statistics is the poster child for an area of study where knowing a little bit just makes you dangerous, and actually understanding any of the basic techniques people use to actually do anything meaningful with statistics requires understanding a fair amount of calculus.

And, by the way I’d like to see everyone take statistics in high school. Just after they’ve taken a year of calculus. Instead of cutting subjects that are mandatory to understand the modern world, let’s cut cursive writing, memorizing state capitals, “sig fig” rules, and the sort of history class where you’re told the story of the first Thanksgiving and that Columbus proved the world was round.

My Ph.D. is in Statistics, and although I tended to do well in math, including calculus, I never found a love for STEM until I took my required stats course for an undergraduate Psychology major. The applied aspect was the key.

It’s not dumbing it down – it’s making real life clearer. If you know how to interpret statistics, you can get a better understanding of what are good conclusions, and what is a stretch.

For example, I have taught psychology students to read the statistics in manuals of standardized tests that they are learning to administer. Some are being used for purposes that were never validated, or the items have questionable differential item functioning (i.e., may be biased). This includes some IQ tests and gifted indicators.

Calculus has its own uses, including to derive much of the statistics that are able to be applied. As a stats person, I do think that the glorification of Calculus over Statistics is unfortunate. They should be on more equal footing – with the potential for statistics to apply to more day-to-day life being emphasized.

When I taught Calculus, my students who had difficulties had weaknesses in Algebra, Geometry, or Trig., not Calculus concepts. Focus on weaknesses and don’t abandon them.

I guess it is like understanding the difference between reflexive and object pronouns (Sai). Seems important that some folks should know where the top is.

I agree whole heartedly with this article. As a teacher in multiple grades from 2nd through high school I have seen the struggle some students have with math itself. Far too much emphasis on math for college students. We need to honor multiple intelligences in college enrollment. There are many ways to be smart. How many jobs require calculus or even algebra for that matter? Let’s stop this bias in favor of math intelligence. An understanding of statistics has a greater benefit and is used in multiple disciplines. There is also good evidence now that male and female brains differ. Read Stanislaus Dehanae, the French cognitive neurologist.

David H. Bressoud, Ph.D. has written extensively on the challenges, perils, and benefits of teaching Calculus in High School and College. Bressoud’s statistics are troubling regarding how few students actually continue in post-secondary mathematics after taking calculus in high school or who stumble through it in college to never take another math class again (Bressoud, 2021). Dr. Bressoud endorses the ideas that many of these students might be much better served learning data science and statistics rather than calculus as it is currently taught (Bressoud, 2017 & Bressoud 2021). As a math teacher since the turn of the century and administrator for the past decade, I agree with Dr. Bressoud’s call for America’s mathematics content and sequencing in high school and post-secondary to be re-examined with new and fresh perspectives of what maths are most relevant for today’s workplace and morally responsible for all high school students to learn, especially those not needing rigorous calculus study for their college majors and career pathways. There certainly are math access inequalities in public and post-secondary education alike. The scarcity of high quality teachers and well supported calculus instruction in particular and mathematics and science teaching in general has indeed contributed to this historical racial and socio-economic achievement gaps K-12 public education as well as in the United State’s admissions and financial aid awards disparities at all post-secondary institutions from the ivory elite towers to our backyard community colleges. The true damage, however, is not just quantitative but is also qualitative in the dashing of dreams and diminishing of hundreds of thousands of teenagers’ aspirations, undergraduate registrations, and overall reduction of career choices students make to not learn and/or work in the STEM fields. We are certainly heading into an American worker shortage in these fields that are so needed to help solve our biggest health care, energy, water, and food shortages, issues, and potential crises in the near future. If only our high schools, colleges, and universities would stop siphoning out the potential talent and creative souls that may just need a little more encouragement, meaningful lessons, better prepared teachers, and help in learning their maths and science as young adults to become future scientists, doctors, engineers, and most of all educated citizens.

Sources:

Bressoud, D.M. (2021). The strange role of calculus in the United States. ZDM Mathematics Education 53, 521–533.

Bressoud, D. (2017). Introduction, pp 1–8 in D. Bressoud (Ed.), The Role of Calculus in the Transition from High School to College Mathematics. Washington, DC: MAA Press.

Teach both….my high school does. Some understand and love the Calculus (me). Some don’t. No reason to not teach both. Those who need it and want it cannot be denied access.

I am thrilled that so many people feel strongly enough about what I wrote that they took the time to respond to the editor. I certainly didn’t think that I would have universal support for my ideas. Hearing people’s objections helps me to strengthen my arguments and create greater clarity.

I would like to respond by saying that my intention is not to reduce academic rigor or to water down high school math curriculum. I also don’t mean to suggest that calculus should not be offered at the high school level at all. If a student loves math and has significant talent for math then by all means lets encourage the student to take calculus. I never suggested, nor would I ever suggest, that students be “denied access” to any kind of learning. I specifically ended my essay by suggesting that parents encourage their students to make a choice that will be a better fit for most students.

The reality is that schools, like all institutions, face opportunity costs. If a high school math teacher is teaching calculus, pre-calculus, geometry and algebra every day (I’m sure it varies by need but most high school math teachers I know teach multiple subjects rather than teaching multiple sections of the same subject), then they have to make choices about how they are teaching.

The considerable time that calculus teachers must spend to ensure that they are effectively teaching calculus means that they have that much less time available to teach effectively teach their other core math subjects.

I’m glad that many of you have taught or experienced excellent calculus teaching in high school. I have nothing but the highest level of respect for math teachers. But most people struggle with the abstract nature algebra, trigonometry and calculus.

I don’t believe that statistics is less rigorous than calculus. It is more applicable than calculus in day to day life which is why I believe that time spent teaching statistics will pay higher collective dividends to students.

I am a strong proponent of rigorous education. I believe that rigor shouldn’t be a mile wide but an inch deep. The way math is taught in many high schools in America is fairly shallow – we rush students to get through curriculum and up the heirarchy of math. I see how student think that they are dumb if they don’t get into calculus in high school. I see how math anxiety has a life long impact on self esteem and allows students to self impose limits on areas of study.

Encouraging students to take more time to learn foundational math and to learn the skills that will most serve them throughout their life can create a more rigorous math education. Teaching students both economic and statistical principles will help them navigate the world more effectively. This is not a matter of “reducing rigor” so much as a matter of teaching the most valuable math to students, particularly those who might not ever take another math class again after graduating high school.

As far as teaching statistics after learning calculus goes – I think that is an interesting idea and I can see how that approach would help students really understand statistics. But the reality is that most of the things that we do in life do not require great depth of understanding in order for them to be useful.

I don’t need to understand the principles of thermodynamics or engine anatomy in order to drive a car. I’m sure having in depth understanding of those principles would enrich my driving experience and would help me understand the car with far greater nuance but I do not need those principles in order to safely drive my car.

Likewise with statistics, I don’t need to know how to integrate

probability distributions in order to read a newspaper article about a new “miracle” drug to say “the sample size in the study seems rather small given the claims they are making”.

Ultimately I want my students to be able to use the skills I try to help them develop to improve their lives in a concrete way. I believe that greater emphasis on statistics will serve most students far more than greater focus on calculus.

I write about these kinds of issues and others on my blog (https://www.selim.digital/) and would be happy if you subscribed and continued the conversation.

The problem is T-I-M-E. Given enough time the average student can learn Calculus. As I tutored Pre-calculus in a demanding high school in San Francisco, I woul look out into the distance towards a field with little rings attached to a post.

I would witness the quality and quantity of time dedicated to throw a ball through such rings which yielded as result a ball passing smoothly through such ring. I can never do that. It is too hard. I have tried about 2 or 3 times and no success. Yet many of my students were succesful at doing so after hour after hour of everyday practice after school to acquire such a skill. If, only I had the talent …sigh.

The problem isn’t that calculus is hard (though it is), but rather that kids don’t come into the class with strong fundamentals from algebra and even middle school math. I think that can be fixed with explicit teaching, careful curriculum choice, smaller class sizes, supportive school administration etc. The solution to “not enough minorities in STEM” should be to give minority groups better preparation for a rigorous course, not get rid of the tough course. It’s not even like I think everyone needs to take calculus; if you couldn’t eke out a B- or above in precalculus maybe you don’t need to be in calc. But I see no need to completely replace calc with stats at the high school level. Offer both and let kids pick with their academic counselor.

I’m a radio systems engineer who uses both calculus and statistics all the time. They are critical to solving real-world problems that would be impossible without understanding and applying both. You need both—stats without calculus is a watered down half-education. And the weaker half, mind you—calculus has many applications, of which statistics is only one.

I don’t think it’s a problem with smarts, and that people just can’t get the material. I have run into Russians at 14 that are learning advanced calculus concepts like convolution. I have run into Chinese students who similarly are miles beyond where our kids are in both calculus and statistics. Are US children stupid, and incapable ? No! They are unmotivated by the way these subjects are taught, and they have low social expectations around learning them. It’s a multigenerational problem that leads to US children falling further and further behind. The fact is, that the most readily accessible and desired highly paying jobs in STEM are largely going to would-be immigrants, because we don’t produce enough US born citizens with the right skills in this area.

I don’t think this is core curriculum material issue for either course. It’s a “who is teaching it”, and “how it’s taught” issue. The fact that anyone taking the course thinks “when am I ever going to use this?” shows the mindset problem that has to be overcome before teaching can really happen.

Primary and secondary teachers may just not have the right level of mastery of the subject, nor any connection to the many concrete uses for it to drive their own curiosity and make them more engaged in the material.

I am a 47 year old, retired military, currently in grad school for aerospace engineering with a BS in Physics in 2015. I wanted to be a math teacher back in the 90s. Life took me away but, I have often put myself in a teaching role, or similar. At the end of my career I was developing training for warrant officer school. One of the projects I have just started is to teach calculus to kindergarteners. I have a lesson plan that gauges success by the child’s ability to take the area of a square. Ten hours and less than $1/kid with groups larger than 20 (bigger=better).

I agree with everything you said. I’ve long hated how calculus was taught. I know it can be done better. I support the idea of a “field related” content study plan. You may be overgeneralizing that all math can come from statistics but, I can’t argue that everything involves calculus.

What I hope you can agree with is that if the stigma of calculus is removed (because ‘we learned that in kindergarten’) society as a whole would be better.

Statistics is worthwhile to learn, like calculus. Either statistics or calculus could be practical, depending on the questions posed. Concluding that you cannot use calculus because it is preoccupied with missile trajectories (something you don’t need to know about) seems like concluding that you cannot use statistics because it is preoccupied with card games (something that you don’t need to know about).

Another opinion piece in a long line of pieces with the same tired thesis. You can almost set your watch by them.

Statistics should definitely be presented as a second option for students, for sure. Statistics is important. But to say it’s more important than Calculus is a bridge too far.

Remember that mathematics is a discipline of its own and not just the servant of other disciplines.

Remember that mathematics is about abstract relationships, truth, and beauty, not just a tool to be used. (And as others have said, it’s not at all obvious that statistics is “more useful” than Calculus.)

Remember that high school is not trade school and the goal should be a liberal education (in the classical sense), not simply to learn things that are most useful or profitable. The goal is also, perhaps primarily, to train young minds to appreciate what is good and true.

Remember that when students are failing, the solution is not to lower our standards but to help students rise to them. Like other commenters, I am worried that “lowering the bar” is partly the motivation behind this movement.

More of my thoughts here:

https://mrchasemath.com/2014/08/29/in-defense-of-calculus/

https://mrchasemath.com/2012/12/20/why-calculus-still-belongs-at-the-top/