Teach programming, statistics — not calculus

Get rid of high school calculus to make way for computer programming and statistics, writes Steven Salzberg in Forbes.

With computers controlling so much of their lives, from their phones to their cars to the online existence, we ought to teach our kids what’s going on under the hood. And programming will teach them a form of logical reasoning that is missing from the standard math curriculum.

With data science emerging as one of the hottest new scientific areas, a basic understanding of statistics will provide the foundation for a wide range of 21st century career paths.

Most students won’t need calculus, Salzberg writes. Those who do can take it in college.

If a few top universities announced they value programming and statistics as highly as calculus,  “our high schools would sit up and take notice,” he writes.

I’m not sure everyone needs computer science, but I would like to see non-calculus alternatives for non-STEM students.

When my daughter was entering 12th grade, I suggested she take AP Statistics, which I thought she might be able to use in the future.  The college counselor said AP Statistics was considered second rate. Elite colleges demanded AP Calculus.

My daughter earned a C in calculus her first semester. The counselor said she’d doomed her college chances. So Allison dropped the course to do an independent study on American poetry, was rejected by Yale, Brown, Penn, etc. and went to UCLA, where she earned an A+ in statistics. After two years, she transferred to Stanford, where she dabbled in programming. (“Everyone knows Java,” she said.)

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Comments

  1. I keep seeing “They need Calculus on their transcripts or colleges won’t think they’re serious students” as a valid reason for curriculum choices. Sounds like the kind of thinking people do if they didn’t actually learn anything in advanced courses except how to cram for a test and get something that looked competitive on the transcript/resume.

  2. Logically it would seem that a course in linear algebra would make more sense that a high school course in calculus inasmuch as linear algebra is useful in a large number of fields incuding calculus itself.

  3. Mark Roulo says:

    Most students won’t need calculus, Salzberg writes. Those who do can take it in college.

    The same can be said for programming.

    If a few top universities announced they value programming and statistics as highly as calculus, “our high schools would sit up and take notice,” he writes.

    Calculus is used by colleges as a way to *stack* applicants. Programming is easy compared to calculus and thus less useful to the colleges. The same is true for discrete probability and statistics (I think that continuous probability requires calculus …).
     
    Calculus is valued by the top universities because it is difficult! I don’t see top universities changing over to using easier high school classes as the filter for the college incoming freshmen.

    • Probability (discrete or continuous) is a fascinating as well as highly useful branch of mathematics. i wouldn’t call either probability or statistics particularly easy. However more significant than their technical difficulty is the highly unintuitive nature of these subjects.

  4. If a student doesn’t have the chops for calculus, he’s probably not a good fit for university in the first place. Statistics *might* be interesting for some, but in my opinion it’s not necessarily more practical for daily life. People are just as bamboozled by stats after they’ve taken a stats class as they were before.

    • J.D. Salinger says:

      “If a student doesn’t have the chops for calculus, he’s probably not a good fit for university in the first place”

      There used to be plenty of students who got into good schools in previous eras who didn’t have calculus. And there are still schools today that don’t use calculus as a filter–particularly for those students who are not going into STEM majors.

  5. Any ASCB program in computer science is going to require calculus plus a boatload of advanced math.

    If you want to program, you can pretty much get by with a CIT/CIS degree (associates), or learn stuff on your own.

    A serious CS program will include:

    Engineering Physics I/II
    Calculus I/II
    Linear Algebra
    Diff Eqns
    Applied Stats
    Abstract Algebra
    Numerical Analysis
    Intro to Philosophy/Symbolic Logic
    Digital Logic

    Calculus isn’t a weed course, per se, it’s just the requirement for a ‘real’ computer science degree. There are plenty of universities which will grant IT degrees which don’t require calculus, but they aren’t degrees in Computer Science.

    • Calculus does not seem very relevant to most of Computer Science. Why is it important for Computer Scientists?

  6. Eric Fleming says:

    While I will not question that statistics and computer programming are better uses of a high school students’ time, I will defend highly selective colleges and support that they are right for placing a high premium on calculus.

    Its less about the contents of calculus and more about what it means to be successful in calculus. It means that your ability to abstract information and carry out precise algorithms is not hindered by the vocabulary intensive language of calculus. Calculus is the perfect tool to test the history of a students analytic capacities literally through k-12. As someone who has tutored over a hundred students in calculus in college, the most unprepared students had almost no understanding of algebra, geometry or trigonometry. They always got lost in the problem, forgot the large picture, and made arithmetic mistakes in half of their problems. Calculus is the last leg of the K-12 marathon and selective colleges want to know who is still going strong.

    • SC Math Teacher says:

      “…and made arithmetic mistakes in half of their problems.”

      B-b-b-but…calculators!

      How is that even possible?

  7. twitter_TheRandomTexan says:

    Any statistics beyond the plug and chug stuff taught in the basic course requires a heavy dose of calculus AND programming. Followed by linear algebra, set theory, and numerical analysis. Anything less is just Cargo Cult Math.

    • I don’t see why one would need much in the way of programming to study statistics. The most important prerequisite would seem to be harmonic analysis.

  8. Calculus, statistics, and programming are all good things to do in high school. But it does not make sense to suggest swapping out senior calculus for programming, because then students are only taking 3 years of math. Surely there is a good alternative for calculus. Maybe it could be statistics, or some kind of discrete math. I like the linear algebra idea too. But programming is not math. It makes as much sense to say that students won’t need calculus so have them take another writing course. I would like to see student do more (real) writing. But not at the expense of math in their senior year.

  9. “There used to be plenty of students who got into good schools in previous eras who didn’t have calculus”

    While that’s technically true, it’s only true because they took incredibly difficult high school courses that demonstrated they had the ability for calculus. Calculus was then required for a college degree.

    Today, that’s flipped. Since colleges can’t require certain courses or flunk out large portions of kids, they “require” high level math in high school as a way of keeping out kids who aren’t smart enough to do the work. Of course, all URM schools can get around this gate by simply putting the classes on the transcripts, but I’m not sure colleges didn’t plan on this in the first place.

    At a certain point, it becomes obvious that college admissions is just a corrupt game.

  10. “What math courses do young people really need?”

    Education is not about the generic needs of “young people.” It’s about the best individual educational opportunities. Most high schools, after algebra II, allow students to substitute programming or statistics for any math requirement.

    “So here’s a simple fix: get rid of high school calculus to make way for computer programming and statistics.”

    Calculus does not stop high schools from offering programming and statistics.

    “Convincing schools to give up calculus won’t be easy.”

    Why should anyone read further?

    “In their never-ending competition to look good on a blizzard of standardized tests, schools push students to accelerate in math starting in elementary school..”

    Standardized tests have nothing to do with STEM preparation. Look at the questions and the raw percent correct absolute scores.

    “Colleges need to adjust their standards too. They can start by announcing that high school programming and statistics courses will be just as important as calculus in admissions decisions. ”

    Once again, he is completely wrong. Admissions is it’s own world, and these people care much more about your CR score than your math score on the SAT. Most are NOT STEM graduates and high scores on Math 2 SAT II or AMC/12 don’t mean much. In fact there is little correlation between your SAT score (at the high end) and admittance. For the most elite colleges, having almost perfect SAT/ACT test scores might, at best, raise you probability of admittance to 20%. At best. After that, everything depends on the sensibilities of admissions people, not professors. Salzberg should spend some time looking at the statistics in common data sets. So much for statistics if you don’t go looking for them.

    Universities set distribution courses and departments define the courses needed for getting their degrees. I know of no college that requires calculus for graduation. In fact, during the many college tours and admissions’ info sessions we went to, all we ever got as feedback was a very negative view of math – how you can substitute other fuzzy classes for math, like “The Geometry of Nature” or “Great Ideas in Computer Science”. The admissions person at Tufts exclaimed how he was very happy he did not have to take any math past pre-calculus. Admittance to the very top colleges does not require calculus. Our gender and sexual studies tour guide at Yale was proof of that.

    “The college counselor said AP Statistics was considered second rate. Elite colleges demanded AP Calculus.”

    The counselor was wrong, and getting a 5 in AP Calc BC does not increase your chances. My son’s friend got rejected at 6 Ivy league colleges. Admission to a top college has little to do with academics at that level. Look at the scatter plots for SAT/GPA and admittance. In my son’s Princeton rejection letter (not even waitlisted), they said that “most” of their applicants were “admittable”. That would be about 20,000 out of 25,000 applicants. So admissions people (not professors) select about one-in-twenty of those admittable students, and they are NOT looking for AP calculus. My son had an 800 on the Math 2 SAT II, a 5 on AP Calc BC, and scored high on the AIME test. They could at least have put him on the waitlist to make him feel good. His AI was 236.

    “…was rejected by Yale, Brown, Penn, etc. and went to UCLA, where she earned an A+ in statistics.”

    Don’t confuse admission with ability in academics. I called 5PM on Thursday, April 27, 2014 as Black Thursday for Ivy League and some other top colleges. An admissions officer at MIT told students to “enjoy the random walk.” That’s what a knowledge of statistics – assuming that you bother to do the research – will tell you about college admissions.

  11. Elizabeth says:

    Okay, so most students don’t need poetry, either. Good grief. No one is “forced” by a school district to take calculus. I say the more math the better.

  12. Roger Sweeny says:

    It is certainly true that people get bombarded by statistical claims, and it would be useful if they understood what was behind those claims. So requiring a half-year course in “Understanding Statistics” might be a good idea. But on one condition: it would have to be taught out of the social studies department rather than the math department.

  13. Calculus is indeed a screening device. It’s a reasonably effective one if what you’re looking for is ability in the realm of analytical thought. But it’s also fairly arbitrary. And plenty of high schools are now offering Calculus classes for students who are not particularly good at, or interested in, math just because they need it in order to compete for college admissions, and not just at elite colleges.

    It wasn’t required 50 years ago to get into Ivy League colleges partly because so few high schools offered it that it would have ruled out plenty of very talented students that the selective colleges wanted. It’s also fairly easy to test for — unlike, say, extremely good research/writing skills.

    Colleges could use other arbitrary screens — fluency in a foreign language, for example — but they don’t.

  14. This year at the AP Calculus grading in Kansas City, there were over 407,000 exams graded. This is more students than took calculus at all two-year and four-year institutions, nation-wide, combined. The students don’t want to take calculus in college, and they use AP calculus to get out of it. Some students take the calculus AB exam in 11th grade and then come back to take the BC exam in 12th grade, and place into calculus 3 as freshmen in college.

    While statistics may be a more useful field of study for more people (books like Innumeracy, by John Allen Paulos, have been pointing this out for years), I think it is not going to be pushed as hard until it is accepted in college for more than just a general elective or as the social science statistics course (because it isn’t calculus-based statistics).

    I think the same is true for the coding classes (AP computer science A is in Java), but I’m not a CS teacher – do universities take Java as a CS-1 level class?

  15. Calculus is not a screening device for college admission. Departments don’t admit students, admissions officers do. For top colleges, you have to show good scores and grades, and you have to show that you have taken rigorous classes, like honors and AP. They will also judge you by what the local rep knows of your high school. Taking AP Statistics or AP Computer Science rather than AP Calculus is common for many seniors. If calculus was so important, one would see that advantage in admissions. It doesn’t exist. If students think they would struggle in AP Calculus, then they should take another course – as rigorous as possible. It’s not calculus that is a problem for admissions, but showing any unexplained academic weakness.

    For top students, there is no such thing as a reach or even a likely school. They are all just low probability schools. Even safety schools are a problem because your application might not be believable. When colleges accept only 20 percent of the applicants with SAT scores above 2300, then something else is going on. College admissions is now all about appealing to the sensibilities of admissions officers. Colleges told us over and over again that they are NOT looking for well-rounded students. They are looking for oblong students who they fit into a well-rounded class.

    Having just gone through this process and after studying all of the numbers I could find, my conclusion is that above a certain level (which is pretty high, but not that high), admittance has little to do with academics. It has to do with your story – and luck. In a couple of my son’s admittance letters from colleges, the admissions officer made a comment about his essay, NOT how he was such a good scholar or musician. They claim that it is a holistic process, but that means that one-out-of ten or twenty applications is selected based on subjectivity, NOT strictly academics. You would think that subjectivity would be limited to one-in-three or so, but it isn’t. The loser is academics. Being a valedictorian or having a perfect 2400 SAT is a negative for some admissions people. Admissions officers almost gleefully tell parents and students about all of those people they reject.

  16. Most persons who want to major in computer science must be eligible to take calculus as a freshman (or have already taken it and passed with a grade of C or higher).

    Even harder is the fact that many schools will only allow so many attempts as CS core classes (usually 7 tries for the first 5 courses, so you either pass the classes, or you’re out).

    Though I have to say my first course in comp sci. was much harder than anything that students today have to handle in their freshmen year.

    We had 30 homework assignments (approximately), quizzes, four exams, and a final project, on top of having to learn the mainframe OS, the editor, and the compiler and linker, along with basic commands to make hard copy, etc (this was in 1981, mind you). This was a 3 credit hour course, btw.

  17. Richard Aubrey says:

    In life, outside the classroom, stat/probability is rarely useful. It pays to know when you’re being put on, but not many of us are going to be looking at the basic data and comparing it to the publicly-announced results. It would require looking for a constipated dog.