From a podcast with Russ Roberts and Erik Brynjolfsson (the guest):
Guest: My pet little thing, I just wanted to mention, is I’m not as much of a fan of calculus as I once was, and I’m on a little push in my high school to replace calculus with statistics. In terms of what I think is practical for most people, with the possible exception of Ph.D. economists: calculus is just widely needed. But that’s sort of a tangent. Russ: Well, it’s interesting. My wife is a math teacher, and she is teaching a class of seniors this year, split between calculus and statistics, for one of the levels of the school. And statistics is–I agree with you. Statistics is in many ways much more useful for most students than calculus. The problem is, to teach it well is extraordinarily difficult. It’s very easy to teach a horrible statistics class where you spin back the definitions of mean and median. But you become dangerous because you think you know something about data when in fact it’s kind of subtle. Guest: Yeah. But you read newspapers saying–I just grimace because the journalists don’t understand basic statistics, and I don’t think the readers do either. And that’s something that appears almost daily in our lives. I’d love it if we upped our education in that area. As data and data science becomes more important, it’s going to be more important to do that.
Most of the discussion concerns the new book The Second Machine Age, or what I call “average is over and over.”
That this hasn’t already happened says everything we need to know about education. Is calculous even useful when you get past calculous? I don’t remember a lot of calculous proper when even working with differential equations? They will certainly find all the wrong ways to do statistics, but still.
I feel the need to add that for everyone whose first impulse is to dismiss will find it easy to dismiss my point. Sure, we do integrations and the occasional mathy boondoggle is fun and impressive. But how often do people really doing advanced work find the elegant analytic solution? And even then, why is the math path for everyone the same as what is not even required by the most advanced practitioners?
Have we not all encountered those who understand the mechanics of statistics, but have no grasp of the meaning of their application to particular circumstances, relationships, or functions?
Maybe, but the way I was taught calculous was almost as a way to say “Hey, look how non-applicable we can make math!”
I guess it’s possible I was just taught in a relatively horrible fashion, but a lot of us were.
I have heard this sentiment before, I think it’s misguided. And I say this as someone who uses statistics and predictive modeling daily for my job.
First, how many high school students actually take calculus? Most of my peers did, but I went to a very good high school where everyone went to college (and mostly top tier schools). Considering about half of Americans don’t even go to college, much less finish it, I’m guessing that it’s a safe bet that at least half of high school seniors don’t take calculus already. It’s far from a requirement to graduate for most students. So to suggest that by replacing calculus with statistics will lead to a statistically literate society seems way off.
Secondly, mathematical statistics uses calculus. Sure, there are ways to learn statistics without calculus, but anyone who wants to seriously learn the subject needs to understand calculus. In other words, if some of the students are moving on to college and want to learn statistics in depth, they’ll need calculus anyway.
Also, I thought “we” all wanted more STEM majors in this country. Well, calculus is certainly pre-requisite for most engineering, even more so than statistics (stats are helpful too, but I know of engineers who didn’t take any stats). You need it for physics. I’m sure it’s required for other sciences as well, and certainly for math majors.
I’m actually not sure that treating statistics as solely a mathematics course makes sense either. If you wanted it to be taken by more high school students, I think it would be nice if it were flexible and counted as either a math or a science class. Or just let it be a total wild card elective. I think it’s much easier to make a case that a fourth year of history or English is more useless than calculus for many kids (certainly no one is talking about the great shortage of history or English majors).
Saying statistics requires calculus both is and isn’t correct. The calculus doesn’t make anything more clear compared to, say, knowing linear algebra. (Linear regression and correlated random variables are a mess otherwise.) Calculus in and of itself doesn’t really matter, the comfort and familiarity with mathematical notation that typically accompanies calculus is much, much more important.
A bigger issue, in my mind, is trying to make the learning more useful. When I’m doing statistics-y stuff I’ll often open up, say, R and do some quick examples. You can go pretty far playing around with R. And it makes it substantially easier for students to experiment. But at that point you’ve massively complicated the course from “intro stats” to “intro programming + intro stats”.
But on the other hand, an intro stats course without at least some programming seems rather odd to me. Find the mean and variance with a calculator? Rely on only statistical estimators with closed form solutions? Sounds as primitive as teaching with a slide rule and abacus.
” Yeah. But you read newspapers saying–I just grimace because the journalists don’t understand basic statistics…”
I’m not opposed to more statistics and less calculus in high school, but I think there are better solutions for this specific problem.
For example, statisticians could make an effort to correct such misunderstandings by getting in touch with those journalists and offering to help edit such pieces in the future for statistical accuracy and clarity.
Also, statisticians could form a Snopes-like group that actively seeks out such misunderstandings and corrects them for all to see on the Internet.
I would agree that statistics is more widely useful than calculus. Even though I’ve spent my career in math-related stuff and majored in math, I’ve probably used actual calculus in work maybe a dozen times, primarily when I was doing scientific programming and was writing orbit sim software or when I was doing hardcore graphics programming (that was the only time I used differential equations for pay).
OTOH, I use statistics every day. I may not be doing markov chains or whatever, but knowing about averages, means, modes, stddevs, percentiles, and other stuff is hugely important for my work in data mining and keeping a large production dataworld up. I took a fairly good “business statistics” course in college (in addition to more beefy courses later) which would make a decent high school senior level statistics course.
Sadly, any teacher competent to teach it would likely have a good job in industry…
You mainly need the math to prove you are better than the next guy who can’t quite hack the math.
Why is it most people never know what I’m talking about with the zero-sum dimension of education?
Do they just ignore it, not believe it, have already discounted it and I’m just whistling in the wind?
Do I just give up or do I double-down?
I was replying to the main post, but didn’t notice any reference to “zero sum of education” in the comment list for this post. (and I don’t keep a database of all blog comments in my head grouped by commenter – sorry – I can barely remember what I’ve posted 🙂
Anyway, for HS kids, the question is what makes one a more informed citizen: a terminal course (one that is the last class of this sort ever taken), or a terminal course in statistics. If you’re a math type, you may take both (and neither will be “terminal”), but if you’re going to college and will be majoring in English or something else that isn’t technical, what is more useful to you? Also, statistics is useful as a citizen, since so many political arguments are based on interpretation (and misrepresentation) of statistical arguments, while a terminal course in calculus will be forgotten and never used again by most such kids.
Yeah, I know, but it’s built into every education discussion. What is it for?
The question is why do people take Calculus? My answer to that it is to get to higher math. But why do people need higher math?
Because they are in some super-specialty and my suspicion is that it is entirely because academic papers require higher math to be accepted into the most prestigious journals.
That is to say, the math isn’t even necessary except to look super advanced.
As in, how much do we actually need another mathematical model in economics or biology or anything else. There was that recent discussion over how people in industry don’t use the IS/LM or whatever.
So, the question I think is why are we teaching math courses that are mostly so that the top 0.1% can compete with each other when we could teach other math that the 99.9% would find useful?
I think it’s because of the trickle-down nature of education from the Tenure system. But nobody buys that.
As an advanced math student, I was required to take calculus in high school; statistics was not offered. In retrospect, that was a waste. Calculus is required for physics, but social sciences need statistics, as do many specialties within the life sciences. I’ve never used calculus after passing the SAT, but wish I knew statistics better.
I blame it on the Russians. After Sputnik, American education was re-tooled to make every smart kid a rocket scientist.
A really good college-prep school would offer both.
I don’t know nuttin’ ’bout statistics, but I used to enjoy Carl Bialik’s column in the WSJ, where he’d closely examine a statistic and/or bit of data mentioned by a journalist or politician or ?, and using everyday language he’d explain why it was insufficient to support the premise, or in some cases, a completely incorrect conclusion was drawn. Unfortunately, I now read that he’s been hired away from WSJ to Silver’s 538 place.
Can you teach useful statistics to people who cannot master basic calculus? Isn’t that the question that should be asked first?
But even before that what is calculus useful for with regards to most people?
Even engineers I know (me included) wish they had a lot more statistics.
I guess it doesn’t have to be at the expense of calculus, but I’d make that trade.
I think that the simple principles of calculus (limits) and statistics are both great and can be useful in life but the way there are taught is as an intellectual excise/contest. IMHO the signaling function of schooling squeezes out useful practical education.
Addendum: Apart from the signalling value, the way they are taught now neither is very useful for 95% of students.
High schools offer calculus to those in the college technical track. Not having exposure to calculus is going to be a real detriment to those students in freshman physics and calculus.
On the other hand social science programs don’t presume that students arrive knowing stats. They generally put a class in the requirements for the program as appropriate.
The high school precursor to calculus is trigonometry and analytic geometry. Analytic geometry may be useful to those who take calculus in high school, but it’s not useful otherwise.
What would be a better solution is to retain calculus for those in the math/science/engineering track. For other students offer a semester each of trigonometry and probability and statistics.