Is it time to kill the calculus curriculum? | Hacker News Reader

Is it time to kill the calculus curriculum?

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17 pointspseudolus61 comments

I've taught calculus in college, and currently work in tech. I think the point of calculus in college is to give new minds a vocabulary and intuition for processes involving rate of change. I've never had to solve an integral symbolically at work, but I have had to write code to implement variations of gradient descent, which utilizes derivatives, and I've written code to sum different sensor measurements to estimate spatial location, which is basically integration. Long story short, I don't use calculus "out of the box", but it gives me a framework for thinking about things.

The bigger issue in general is that college curriculum in general needs to be realigned to fit the needs of the current marketplace. I'm personally an accounting major, took business calculus in college and currently work in the tax industry. Five years after graduation and four years working professionally, I have never used anything remotely related to calculus. Statistics and data analytics, on the other hand, I use all the time. The vast majority of my peers also say the same thing - they never use calculus.

So I would say the statements in the article are true. Colleges these days are dinosaurs at changing and keeping up with the times. The reality is most college majors probably need to be shifting more heavily towards computer related skills in general. The whole idea that you need a CS degree to learn programming skills is an obsolete idea as well. Computer programming is a general-purpose skill as far as I am concerned. Anyone studying a STEM major needs to know how to write computer programs, at least at a basic level.

Rather we need to realign expectations of what college means. College as a means of preparing students for grad school accomplish those means perfectly. College as a means to train folks for the workforce, that's less perfect.

I'd argue that we _shouldn't_ alter the purpose of college, but find new ways to fill the gap in the market for professional jobs that aren't research-focused (i.e. academia) or vocational. There's a very real middle-of-the-market segment of education/job training that's missing.

Programming bootcamps are a good example of filling the middle-of-the-market, but they're probably too short and too simplistic to bring a graduate up to the real entry-level, junior developer. It illustrates, in my opinion, that something needs to exist between vocational schools and colleges to fill professional needs.

Sounds like a job for community colleges.

That is true but employers insist on people having bachelor's degrees. That's the problem so you have lots of people going to college that really only want to focus on career growth.

Also these same employers are always complaining about how the new grads don't have the "skills" they want.

Sounds like we need to figure out why employers want things that are not necessary for excelling at positions.

Because they've externalized training costs, and the closest thing to what they want (without training people themselves) are people with BA/BS degrees. The best I've seen with an employer focusing on employee education to a non-BS/BA target was a USAF base that partnered with a nearby technical school to get a lot of mechanical and electronic technicians. But that's not the norm, and I suspect politics were involved to set up the program in the first place.

EDIT: The other positive case I know of was NC partnering with the pharmaceutical (drug manufacturing) industry in the late '00s, but I have no idea how that turned out. They were partnering with community colleges and universities throughout the state to develop a targeted non-BS program for the drug manufacturers to pull from.

Employers, in general, just want to hire "smart" people and the BA degree has become symbolic of something that "smart" people have. So every employer uses it as a way to just screen out the "dumb" people. At the same time, employers increasingly want new employees to have some sort of skill set that can be applied to the job.

If you listen to complaints from new grads you can see a common trend - "college did not prepare me for the real world", "college did not give me the skills I need to succeed" and so on.

This is why I say we need to move away from the one size fits all view of college. We need BA degrees that are "career focused" and we need BA degrees that are more academic focused. It may also be wise to have a hybrid version as well.

> Employers, in general, just want to hire "smart" people and the BA degree has become symbolic of something that "smart" people have. So every employer uses it as a way to just screen out the "dumb" people. At the same time, employers increasingly want new employees to have some sort of skill set that can be applied to the job.

Definitely this is the case. A degree is merely a signal. Eployers want the smartest 10% of the population. If they were left handed, employers would require left-handedness.

What I find discouraging is how routine and repetitive most work is. It's like you are the paramedic at the county fair and you're job is bandaids on elbows, but you need to be an expert brain surgeon in case that comes up.

Risk management. When every entry level position has 1000 bachelor's degree grad applicants to them why would you consider hiring someone without one? Then they build a resume and you only hire from junior pool when filling senior positions.

Undergrad is 100% signaling if you're not STEM. Employers just want people who have what it takes to succeed in a difficult environment.

True but the reality is there are a lot of people going to college purely for career growth. Accounting is a good example. People studying accounting want to be accountants, more or less.

Right now college is a one-size fits all shoe and has only be slighting molded to fit both objectives. I would argue that we need to make a hard slip. The obvious career majors (accounting, business, marketing etc.) should become more career focused while the more traditional majors should focus on the traditional vision of college.

The "what college is really for" line hasn't been true in a long time.

Most if not all colleges programs advertise job placement rates for graduates, earning potential, and host career fairs, all aimed at undergraduate students (in addition to what the graduate schools offer of course).

The end result is a mish-mash of idealism meets reality, and a lot of students take out loans to practice learning things that they'll not use again, all in the hoped of getting a job.

The perception that college is about getting a job is what allows many colleges to charge very high prices. If everyone were clear that it is not about getting a job, how many would be willing to take out student loans to do it?

I'm surprised you haven't needed calculus. Simple questions like "If my savings are X dollars, and I expect to live until age Y, and earn Z% on my money, how much can I spend per year in retirement without going broke before I die?" are differential equations, requiring the concepts taught in calculus to solve. I find knowing how to solve such questions to be very useful.

Many of these scenarios are practically solved by either known formulas (plug and chug) or tools that assist with the modeling. Likely both.

In practice, most professionals just don't need anything more than algebra and basic statistics. If they're numerate, they can get the job done because their industry already has a collection of mathematical tools that have been developed to solve the problem. It's only the ones making new tools that really need more advanced math.

This is exactly the situation for most business professionals. We don't need to know how the software works behind the scenes, we simply need to know how to use the software and understand the bigger picture - what does the data mean and so on.

If the only thing you do is plug numbers into code you don’t understand can you be replaced by a data entry clerk or an interface other software would call?

How can you truly grok statistics without calculus?

Statistics is completely different and personally I like it way better than calc. Most of the statistical analysis I do these days is all software based.

Statistics is not even close to completely different than calculus. In fact I'd say it's the opposite, statistics is completely derived from calculus. You can't even derive a PDF or moment or mle without calculus, literally the most basic aspects of stats. Sure you can study applied and not know how any of the software you use works but I'd say you're missing something if you do that.

It's not an either/or thing. Statistical methods use calculus as a tool.

Let's say someone handed you a pile of data on some event that fires after some random time (earthquakes, light bulbs burning out, bacteria lifetime, etc). You're tasked with figuring out the probability that event is going to happen whenever.

How would you do that? You would probably say, oh that's easy! Add up each lifetime of each event that happens before whatever time, and divide by total number of events.

Congratulations, you just did calculus.

> I have never used anything remotely related to calculus.

Really, you've never had to calculate an amortization schedule or the time value of money ?

We use excel to calculate these types of things now.

One of the reasons for studying math is so that your tools, whether it's software today or formulas or tables in the past, aren't just mysterious black boxes to you but something you can understand and figure out from first principles if the need arises.

Discussions over what math is worth teaching often focuses on what specific skills end up being used in some practical context.

But my feeling is that the real value of teaching math is how it introduces whole categories of abstract thinking. I've probably never actually used calculus practically, but in school it opened up a whole new world of practical analytical thinking to me, which, in itself, had very little to do with math or numbers.

I learned more about how to think from studying Euclid's Elements than I did from most of my other college classes. The professor was very up-front that it is a model for how our notion of the world can be built up from some basic assumptions. It actually made me much better at everything else, more so than explicitly studying higher-level calculus would have.

It also helps drive home the idea that what a thing is is not the same as our conceptual model.

Title is clickbait, the piece has nothing about killing calculus in any sense, but is instead about adding “data science” or some math more applicable in that domain as an alternative, coexisting terminal point as a target of secondary math education, with most of the groundwork already happening in pre-AP curriculum.

the problem is a lot of the math curriculum is designed to teach engineering computations that were only useful in the slide rule era.

nobody nowadays needs to know how to hand-calculate gnarly trigonometric integrals, or solve systems using Cramer's rule. it is just pointless hoop jumping as far as I can tell.

at the same time, avoiding teaching calculus in high school still seems like a disaster to me. people are saying "teach statistics and data instead of calculus" -- but how can you hope to understand statistics if you can't compute an expected value, which is defined as an integral? if you don't know how a PDF and CDF relate to each other? calculus is just very important, there's no way around it.

you could have a calculus class with much less mindless computation though -- it would probably be both easier for students challenged by this and more useful for all students.

> "how can you hope to understand statistics if you can't compute an expected value, which is defined as an integral?"

99% of humans would benefit greatly from studying statistics without the calculus underpinnings that greatly complicate the education for marginal added understanding, particularly as they relate to probabilities and risk. the more mathematically inclined can study the calculus in more advanced classes.

one of the great barriers to sociopolitical advancement is the gross misunderstanding of risk (covid being a good example) and basic statistical education can help ameliorate that.

teaching basic probability and statistics to everyone would be great. basic statistical education seems to me like you can get it done at middle school level -- all you need is addition and multiplication, fundamentally. i'm not an expert in pedagogy though so i might be overestimating things.

but the idea being proposed is that one can get rid of the calculus class in the high school curriculum, and fill its role (of advanced math target/preparation for quantitative college majors) instead with some kind of data/statistics class. I don't think this is going to be possible unless the data/statistics class ends up teaching calculus -- otherwise it would have to be way too watered down.

it'd be hard to get rid of calculus as a high school elective though, even if it were removed as a requirement, because most (competitive) colleges would still see it as a (small) differentiator.

but it's still not necessary to learn calculus for data science in high school. you can piece-wise your way to a lot of practical understanding, learning useful building blocks like bayes and monte carlo methods along the way. all you need is excel (with the analysis toolpak) for that. that would set up the more interested to have a solid foundation for a deeper, more theoretically rigorous dive into it in college.

i think a course like that could be really good, but I don’t think you could avoid telling people about the concept of derivatives or integrals. If you tried I think it would just make things seem more confusing and arbitrary. and you might as well introduce the notation and definitions at that point, it’s pretty simple.

you wouldn’t need most of the material in a current calculus class (who cares about the volume of a weird surface) but i still believe you would need calculus.

i'd analogize with basic physics. you can get pretty far using newtonian formulas and the like without ever delving into the calculus underpinnings. same in economics. calc gives you a deeper understanding, but only adds utility at the margins (which is helpful in academics or r&d, but not so much in high school). you can have the computer do curve-fitting and finding optima for you and still learn a lot about how to tease out useful information from an otherwise amorphous mound of data.

Judging by Eureka Math, 10% of a 6-8 Common Core math curriculum (by hours) is rudimentary probability/statistics.

There's a lot of math that _everyone_ needs to learn, even if not college bound. Those who are college bound and interested in any quantitative major can certainly learn advanced versions of all of these.

People need to understand basic probability and statistics. (This would be useful to teach in a civics class too, if we still had them!). Calculus isn't needed for the basics.

Basic financial mathematical literacy. "How to balance your checkbook^Waccounts, now that we barely use checks any more". What do interest rates mean in the context of Credit Cards, mortgages, savings accounts, etc...

Understanding what the numbers really mean. People use numbers a lot, but what are they really saying? Are people using numbers to lie?

You won’t need to teach people reading or writing either soon as voice interfaces get good enough. Still have no idea how The problem of automating away most of the jobs will be solved. A hope of lowering brith rates to compensate for it is about as optimistic as nuclear winter fixing global warming. Maybe I’m too idealistic, but with the best minds applied to the right problems fusion reactors and deep space travel would have been possible decades ago. Instead we have targeted ads and videochat filters.

(Somewhat tangential to the article since its main point of advocacy was adding data science courses, but I've been thinking about math reform and wanted to expand on the New Math).

It appears that the New Math failed to catch on as a math reform because:

1) Starting with formal system and building from axioms on up is appealing to mathematicians but doesn't match children's psychology, which requires concretions rather than abstractions in the early years.

2) There wasn't a good enough plan to get parents on board with the reform. Mathematics was highly regarded yet poorly understood in U.S. culture, leading to pushback from parents (and teachers) when they saw a different mathematics curricula then what they had ("You can't change math! Math is Math!").

Math reforms will need to avoid these two snares. Perhaps a data science class at middle school and up would work well since it would avoid concerns about radical changes to the curricula.

One approach I'm considering is doing a history-based approach to mathematics. I don't have anything shippable yet, but explaining the history of the integral calculus has helped my students understand the difference between Leibniz's and Newton's notations, as well as provide motivation for why we're studying limits.

Calculus is wonderful but the way it's taught is abysmal.

Calculus should be taught by teaching professors, not research professors. It needs to be taught by someone who is focused full time on teaching. But wait, there's more..

There should be two levels of Calculus 1: long-term, or short-term. Short-term calculus is a regular class, taught by whomever is available and qualified.

Long term classes are smaller, meet more frequently (how about four times a week), and taught by a professor whose focus is teaching, not research.

To understand calculus IMHO (full disclosure I failed it three times. Fourth time was a charm) you need a mastery of algebra and trigonometry. I didn't get that, and I think less and less kids are getting that kind of mastery. Hence, a longer term of smaller classes focused on the premise that not everyone in the room has mastered algebra or trig, and teach from that perspective.

Thank you for coming to my Ted talk..

The current approach to deal with the remedial situation you describe is “corequisite support.” In the case where the placement test says you’re not up-to-speed, you get assigned to extra sections of prep/tutoring rather than being told to stop your college progress and retake the prerequisite(s).

More linear algebra should arguably be taught earlier. Of course it could be used to do calculus as well.

Are they teaching basic financial math in school these days? Based on my interactions with the under 30 crowd, I'd say important topics like interest rates on borrowed money and tax fundamentals are completely absent.

Well, does school education always has to align with current professional trends? There are professional degrees and colleges for that purpose.

Today trend is data science, it was car and motors in 50s, electronics in 90s. Should you change school education just for that?

I believe school education should tell us more about world around us. That includes science, art, languages, history, geography.

Why do we have this notion that having school education should always help us in our career in some way (money, progression etc).

Why not just learn about the world around us? Being all-round human being is also a good.

Working professionals don't use calculus. It's a dinosaur subject that's taught out of habit by school systems that aren't accountable for student outcomes!

Students would be much better served by learning the foundations of probability and statistics.

For example, they might learn that the probability of some value less than or equal to x is the integral of a CDF from negative infinity to x, or that the normal equation for linear regression minimizes a multivariable loss function by computing a vector of partial derivatives.

Calculus is absolutely essential for most science. However I think Calculus in High School is a bit ridiculous. If a student has reached that point they should be transitioning to a middle college program where they can spend more time on the subject without burning out dealing with the High School hoop jumping.

> However I think Calculus in High School is a bit ridiculous. If a student has reached that point they should be transitioning to a middle college program where they can spend more time on the subject without burning out dealing with the High School hoop jumping.

It's possible for a student to be advanced in math but not equally advanced in other fields; it's also possible for a student to be academically but not emotionally advanced; both of these may make it better for a student who is academically prepared for calculus to pursue it in high school rather than a post-secondary environment.

College/University is easier than high school, and high school is no emotional safety bubble. High school is probably the most emotionally intense and punishing period of one's life in my opinion. School gets increasingly worse and worse from the first year until the last year of HS, and college is a relief.

High School is a time waster. It's designed to waste as much time as possible so that parents don't have to pay for child care. At the same time it's putting kids into extreme stress situations. Sitting in a classroom for hour long stretches, overcrowding, bullying, authoritarian discipline and arbitrary rules. 5 hours of lectures per day, 5 days a week with a vaguely humiliating hour of physical education which involves stripping in front of other people.

If the kid is ready for college, then do it!

"Most science" meaning physics. Calculus is of little use to either chemistry or biology. I took three semesters of it, and used very little of since despite majoring in biochemistry and getting a doctorate in microbiology. On the other hand, I wish I had studied more statistics. That's what is actually useful.

Isn't calculus a prerequisite for statistics? Areas and density intuitions from calculus are very helpful.

the intuitions from calculus are helpful for both statistics and economics and bits of other sciences: derivatives, higher order derivatives, min/max, discontinuities, integrals, etc.

however, in my last 10 - 20 years I've never actually calculated an analytical derivative. I think there might be some economists somewhere who are doing so, but in my experience that's generally because they don't understand enough about computers or modelling, and they're just roting 30 year old techniques.

In curricula yes, you have to take calculus courses first. And yes, maybe in some esoteric proofs you need it. But in real, useful statistics, that is actually analyzing data to see if it is statistically significant, calculus plays no role at all.

Calculus is the underpinning of statistics and probability. So you don't get rid of calculus that way :-).

I think more discrete math - at least first-order predicate calculus - should be added to high school math. But that would not take a lot of extra time, you could sandwich that into other things.

Nonsense. Physical chemistry and thermodynamics are underpinned by calculus. Try studying engineering without calculus ...

Physical chemistry is a minor subfield of chemistry, one in which I have never had to cause to use, even though my field deals with the chemical byproducts of microbes.

Chemistry has a great deal to do with calculus. Reaction rates, statistical mechanics, and physical chemistry are a few off the top of my head. That's where all those equations we memorize come from. Sure we could just learn the equations, but then what happens when we run into something that doesn't fit the neat assumptions that were made for that particular equation?

Statistics uses calculus heavily as well. It's hard to determine the probability of something lying in a range of a standard distribution without integrals.

On the other hand, 90% of the people going through college that take calculus are there to get education to do a job that requires little to no calculus. The hard part is predicting which 10% we should educate. Teaching calculus leaves the option open for that 10% to do the jobs that need it.

Please don't keep pushing fundamental education to colleges to fix. It just makes everyone worse, and fundamentally changes the role of universities - they are not there for remedial learning!

Calculus is not remedial education. It is typically taught in the first 4 semesters of college. (Differential, Integral, Multivariable, DiffEq)

English composition, World History, US History, all are part of a BS program. Why make a kid sit through 4 years of remedial junk in High School when he is already at a college level?

But you are right, remedial stuff like grammar, writing, and Algebra should be taught at a Middle/High School. Kids shouldn't graduate until they are done with that. But keeping someone 4 years at a High School just to run out the clock on their DOE funding when they hit 18 is nuts when they are at a college level.

Data science is worth learning, but... drop geometry, not calculus. Geometry is little more than a history lesson about the Greeks, combined with a stilted proof formalism that no human being actually uses.

Calculus, on the other hand, teaches you how the world works.

Uh, no way. Geometry is an incredibly important piece of learning any kind of physics, not to mention engineering. And yes, it is beautiful in its own right (and I will argue that statement is both a) objectively true and b) is a good enough reason to teach or learn anything).

We're talking about a high-school curriculum. The vast majority of high schoolers do not wind up in physics or engineering, but those that do should learn some geometry.

Like... trigonometry is important. All the other nonsense I learned in geometry class was a waste of my time.

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