6 ms·

Is programming the new math?

78 points by pankratiev 16y ago

yaks_hairbrush 16y ago
I had a rather bruising experience last fall "teaching" precalculus to a lecture of 180 students. Although I'd try to engage the students and explain how the stuff is useful, the students would have none of it. I got scathing reviews about how I was teaching stuff that wouldn't be useful until calculus 2 (which is, of course, a feature and not a bug). We're fundamentally talking about 18-year-olds with bad attitudes here. If we can engage them with programming as opposed to further disengage them with math, I'm all for it. Anything that hastens the realization that learning is your own responsibility would pay great dividends to the students.
- chopsueyar 16y ago
  Teaching 180 18 year olds math in the same room, at the same time? How much does that cost?
  - yaks_hairbrush 16y ago
    Let's see... in tuition, the students paid collectively over $300,000. Between me and the two TAs who were grading and doing discussion sessions under me, about $60,000 was spent on teaching for the class (the $60,000 figure includes the graduate student tuition waivers and our health benefits).
    - barry-cotter 16y ago
      Is that $300K their collective annual tuition or the amount paid for the credit hours for the course?
      - yaks_hairbrush 16y ago
        Just for the precalculus course.
      - burgerbrain 16y ago
        180 students for a single term can get over 5 million USD pretty easily in the US.
- eru 16y ago
  Perhaps an apprenticeship-system might be worth a try? Let them work together with adults---that might put some sense into them.
  - evanhanson 16y ago
    I've long believed the master-apprentice system to be the most effective type of teaching system. Unfortunately, it doesn't scale.
    - eru 16y ago
      You just need more masters. It works fairly well in Germany.
    - cynicalkane 16y ago
      It scales, but only in a massively parallel way.
- deleted 16y ago
  [deleted]
- calibraxis 16y ago
  I think your employers set you up for failure. Nearly all educational institutions make math seem like something only weirdos could enjoy, for their later employment as tools of industry. I say that as someone who was once so motivated to learn math, I lied to a highschool precalculus teacher in order to take proof-oriented calculus at a university. (Though she thought she forebade me, I gained prerequisites in a summer-school, running as fast through the material as I was allowed, passing the maximum 3 tests per day — one test per chapter — once I hit my stride. This allowed me to take classes at a university with a highly regarded undergrad math program). Yet... the university class was boring. Producing "rigorous" epsilon-delta proofs (and whatever else we did) was a tedious exercise which improved my abilities in no significant way. Probably made me dumber. I took only one more math class after that. All of it was a waste of time. Didn't "teach me how to think better" or any of that paternalistic claptrap. I wish you did not blame your students for their "bad attitude." I sincerely don't mean to be rude, but maybe your attitude could also use some modification. In a better world, you might have been teaching an intro to enjoying one's inborn mathematical abilities, with a crack team of TAs from the psychology dept undoing everyone's damage from earlier schooling.
  - cynicalkane 16y ago
    I can't figure out what your hatred of epsilon-delta proofs has to do with employers setting up a pre-calculus teacher "for failure" and the indoctrination of students as "tools of industry". I'm sorry that your introduction to real math left you sour, but I assure you that epsilon-delta proofs are not a conspiracy by the industrialist class to brainwash kids away from critical thinking--or whatever you are alleging.
    - calibraxis 16y ago
      My "hatred of epsilon-delta proofs"? Boy, your little put-down is not only insulting, it's even absurd that I have feelings one way or another about simple mathematical techniques. Unless 'boredom' = 'hate' in your world. Sorry to even mention this and get your blood pressure up. (Didn't mean to scratch a sore spot by simply criticizing an educational system that I certainly paid my dues in.) And BTW, in addition to your other unsupported inferences (ironic given the subject matter), I wouldn't confuse not taking further math classes with stopping one's mathematical education. If you insist on reading things that don't exist in someone's words, how do your proofs turn out well? You must be constantly assuming things which aren't given, and even changing "equals" to "not equals" in a problem to turn it to one you have a textbook solution for. [Edit: Ahh... Not to sound at all stalker-y, but I looked at your public account info to understand your perspective better. I see that not only you studied at UChicago — which probably means Spivak's Calculus and learning epsilon-delta proofs might be a matter of pride with you — you work at a financial market. My comment does contain a criticism of the status quo, which you may have strong ideological feelings about and therefore respond with a bit less rationality than otherwise. And... maybe I did come across as calling a subset of people here 'tools'.]
- mcn 16y ago
  If my junior high and high school curriculum didn't even make it through precalculus after the typical six years of dedicated math courses, often featuring nightly homework, I would probably wretch at the mention of math too. I suspect that your students had already learned that they weren't going to use the covered material, even within subsequent math classes -- by being taught the same material year after year.
klochner 16y ago
A common gripe from young students when learning math is "I'm never going to use this!" With programming, it's much easier to motivate the subject matter - students want to learn the math so they can improve their projects. Similarly, I found linear algebra and linear programming much more interesting when I was studying economics, and classical physics much more fun when writing little javascript animations. So maybe applied math is a better approach at the intro levels. I'm just not sure how we get there from existing math-centric teachers and curricula.
- mcdaid 16y ago
  Spot on, "I'm never going to use this!" can be dismissed straight away as student use and see the results in their programs. My own maths ability increased dramatically when I got interested in astronomy, likewise trying to write games in basic.
- zeteo 16y ago
  Good point, but in any case "I'm never going to use this" is hardly ever a valid excuse. Its consistent application would rule out almost everything we call education, save the narrowest vocational training. It's also self-defeating: if you don't learn it, then indeed you'll never have the opportunity to get a STEM-related, well-paying job for using it. I could never understand some people's obsession with only learning things of immediate and obvious use. You should study math for much the same reason you study Shakespeare: to learn to think about things you had never thought about before, in ways that you had never imagined to exist.
  - ippisl 16y ago
    Education should not be about immediate and obvious use, true.but at least it should be about long term use. So when people learn history, for example, they should get some stories that help them define their national identity, in the long term. but if they just learn a bunch of dates that they forget a short time after the test, they just wasted their time. Does math, as taught today, have long term value? for non technical people, i'm not really sure.
georgieporgie 16y ago
I always found math to be problematic because it builds on itself, yet math classes vary so much by school and teacher. I ran into difficulty in a graduate level course simply because I had never once been shown algebra with inequalities. Also, you don't get instant, positive feedback, and immediate indication of whether your solution is correct as you do when programming.
- dkokelley 16y ago
  I think there is a limit to the positive feedback programming presents as well. Sure, a program may run as intended, but what if there are bugs that need to be worked out? What if there was a cleaner, faster way to perform the operations that version 1 did? This is what I truly enjoy about programming. Not that there is "instant, positive feedback," but that there are so many approaches to a solution, and room for refinement to make the program faster and cleaner.
noblethrasher 16y ago
Some subjects just cannot be taught from authority. The problem with math education, as I see it, is that primary and secondary school math teachers really can't answer too many 'why' questions (for a variety of reasons such as lack of knowledge or lack of time). Teaching math from a programming perspective (or vice versa) should work since you must (as opposed to 'shall') model problems you care about in terms of math.
ahlatimer 16y ago
I had a short stint as a research assistant for a prof who's using programming to teach high school seniors and entering freshmen math skills [1]. I'd have to ask him how the research is going now, but the preliminary results were encouraging. [1]: http://sites.google.com/site/computationalsystems/ http://sites.google.com/site/computationalsystems/
fleitz 16y ago
Iterative programming is the new arithmetic, Functional programming is the new math.
mian2zi3 16y ago
Physical education is the new math. Students don't like to be trapped in stuffy classrooms. They want to be outside and run around in the fresh air and sunshine. Over the semester, not only have my students improved markedly in physical fitness, but they've learned critical problem solving skills. We're playing football. They've developed increasingly sophisticated plays, analyzed defenses and developed counter-strategies. They fluidly execute novel strategies informed by planning and an awareness of the evolving whole-field situation. Clearly, PE is the new math. WTF? Math has specific content and method. A proof is not a program. A for loop is not an integral. Your vaguely technical subject is not a substitute for math just because your students seem more engaged. Teaching people to think logically isn't the point of math, any more than it is the point of history, biology, literature or, yes, even programming. If your students have fuzzy feeling when problem solving, they probably have fuzzy ideas about math. They haven't been taught clearly. If they're uncomfortable with reasoning in math, they haven't been forced to develop intellectual independence. And foisting of "check the steps" on a computer won't help. And don't get me started on how naive an ideas of correctness that is.
- chad_oliver 16y ago
  I think the issue is not that mathematics is bad, but rather that it doesn't deserve the privileged place it has in the curriculum. Maths above pre-algebra is not generally useful, but instead it is only useful to those who go on to study the more technical subjects (e.g. engineering). Maths is maths, and will always be a powerful tool. But the author is saying that most people need to learn problem-solving and logic more than they need to learn maths; for most people maths is useful only in that it teaches problem-solving and logical thinking. Thus, replace it with programming. In my opinion, I think a far better idea would be to replace the 'computer studies' classes with programming. Most of these classes teach how to use Excel and Word, and if they do programming it's only a limited variety using Visual Basic. Modernise, guys!
- panic 16y ago
  A proof is not a program. The Curry–Howard isomorphism[1] would beg to differ. I think programming is much closer to math than this comment gives it credit for. In some sense, programming is even stricter than math. When doing math, you just have to satisfy your instructor or your reader. When programming, your program must run on a real computer -- there's no room for hand waving or imprecise arguments. [1] http://en.wikipedia.org/wiki/Curry–Howard_correspondence http://en.wikipedia.org/wiki/Curry–Howard_correspondence
candeira 16y ago
The problem with "I'm never going to use it" is that it's a self-fulfilling prophecy. Further down the line, this attitude excludes you from jobs and opportunities where you need to be able to use it. I say teach math (up to algebra and basic trig and calculus) and programming in every high school. Dropping out is so much easier than dropping in at a later age.
kylemaxwell 16y ago
As much as the discussion has focused on defending mathematics and the importance of teaching it, that's not to discount the value in teaching kids about coding. Whether or not they later become hackers, they'll have an appreciation for how things work and an interest in doing rather than simply watching.

78 points by pankratiev 16y ago

I had a rather bruising experience last fall "teaching" precalculus to a lecture of 180 students. Although I'd try to engage the students and explain how the stuff is useful, the students would have none of it. I got scathing reviews about how I was teaching stuff that wouldn't be useful until calculus 2 (which is, of course, a feature and not a bug). We're fundamentally talking about 18-year-olds with bad attitudes here. If we can engage them with programming as opposed to further disengage them with math, I'm all for it. Anything that hastens the realization that learning is your own responsibility would pay great dividends to the students.

chopsueyar 16y ago
Teaching 180 18 year olds math in the same room, at the same time? How much does that cost?
- yaks_hairbrush 16y ago
  Let's see... in tuition, the students paid collectively over $300,000. Between me and the two TAs who were grading and doing discussion sessions under me, about $60,000 was spent on teaching for the class (the $60,000 figure includes the graduate student tuition waivers and our health benefits).
  - barry-cotter 16y ago
    Is that $300K their collective annual tuition or the amount paid for the credit hours for the course?
    - yaks_hairbrush 16y ago
      Just for the precalculus course.
    - burgerbrain 16y ago
      180 students for a single term can get over 5 million USD pretty easily in the US.
eru 16y ago
Perhaps an apprenticeship-system might be worth a try? Let them work together with adults---that might put some sense into them.
- evanhanson 16y ago
  I've long believed the master-apprentice system to be the most effective type of teaching system. Unfortunately, it doesn't scale.
  - eru 16y ago
    You just need more masters. It works fairly well in Germany.
  - cynicalkane 16y ago
    It scales, but only in a massively parallel way.
deleted 16y ago
[deleted]
calibraxis 16y ago
I think your employers set you up for failure. Nearly all educational institutions make math seem like something only weirdos could enjoy, for their later employment as tools of industry. I say that as someone who was once so motivated to learn math, I lied to a highschool precalculus teacher in order to take proof-oriented calculus at a university. (Though she thought she forebade me, I gained prerequisites in a summer-school, running as fast through the material as I was allowed, passing the maximum 3 tests per day — one test per chapter — once I hit my stride. This allowed me to take classes at a university with a highly regarded undergrad math program). Yet... the university class was boring. Producing "rigorous" epsilon-delta proofs (and whatever else we did) was a tedious exercise which improved my abilities in no significant way. Probably made me dumber. I took only one more math class after that. All of it was a waste of time. Didn't "teach me how to think better" or any of that paternalistic claptrap. I wish you did not blame your students for their "bad attitude." I sincerely don't mean to be rude, but maybe your attitude could also use some modification. In a better world, you might have been teaching an intro to enjoying one's inborn mathematical abilities, with a crack team of TAs from the psychology dept undoing everyone's damage from earlier schooling.
- cynicalkane 16y ago
  I can't figure out what your hatred of epsilon-delta proofs has to do with employers setting up a pre-calculus teacher "for failure" and the indoctrination of students as "tools of industry". I'm sorry that your introduction to real math left you sour, but I assure you that epsilon-delta proofs are not a conspiracy by the industrialist class to brainwash kids away from critical thinking--or whatever you are alleging.
  - calibraxis 16y ago
    My "hatred of epsilon-delta proofs"? Boy, your little put-down is not only insulting, it's even absurd that I have feelings one way or another about simple mathematical techniques. Unless 'boredom' = 'hate' in your world. Sorry to even mention this and get your blood pressure up. (Didn't mean to scratch a sore spot by simply criticizing an educational system that I certainly paid my dues in.) And BTW, in addition to your other unsupported inferences (ironic given the subject matter), I wouldn't confuse not taking further math classes with stopping one's mathematical education. If you insist on reading things that don't exist in someone's words, how do your proofs turn out well? You must be constantly assuming things which aren't given, and even changing "equals" to "not equals" in a problem to turn it to one you have a textbook solution for. [Edit: Ahh... Not to sound at all stalker-y, but I looked at your public account info to understand your perspective better. I see that not only you studied at UChicago — which probably means Spivak's Calculus and learning epsilon-delta proofs might be a matter of pride with you — you work at a financial market. My comment does contain a criticism of the status quo, which you may have strong ideological feelings about and therefore respond with a bit less rationality than otherwise. And... maybe I did come across as calling a subset of people here 'tools'.]
mcn 16y ago
If my junior high and high school curriculum didn't even make it through precalculus after the typical six years of dedicated math courses, often featuring nightly homework, I would probably wretch at the mention of math too. I suspect that your students had already learned that they weren't going to use the covered material, even within subsequent math classes -- by being taught the same material year after year.

klochner 16y ago

A common gripe from young students when learning math is "I'm never going to use this!" With programming, it's much easier to motivate the subject matter - students want to learn the math so they can improve their projects. Similarly, I found linear algebra and linear programming much more interesting when I was studying economics, and classical physics much more fun when writing little javascript animations. So maybe applied math is a better approach at the intro levels. I'm just not sure how we get there from existing math-centric teachers and curricula.

mcdaid 16y ago
Spot on, "I'm never going to use this!" can be dismissed straight away as student use and see the results in their programs. My own maths ability increased dramatically when I got interested in astronomy, likewise trying to write games in basic.
zeteo 16y ago
Good point, but in any case "I'm never going to use this" is hardly ever a valid excuse. Its consistent application would rule out almost everything we call education, save the narrowest vocational training. It's also self-defeating: if you don't learn it, then indeed you'll never have the opportunity to get a STEM-related, well-paying job for using it. I could never understand some people's obsession with only learning things of immediate and obvious use. You should study math for much the same reason you study Shakespeare: to learn to think about things you had never thought about before, in ways that you had never imagined to exist.
- ippisl 16y ago
  Education should not be about immediate and obvious use, true.but at least it should be about long term use. So when people learn history, for example, they should get some stories that help them define their national identity, in the long term. but if they just learn a bunch of dates that they forget a short time after the test, they just wasted their time. Does math, as taught today, have long term value? for non technical people, i'm not really sure.

georgieporgie 16y ago

I always found math to be problematic because it builds on itself, yet math classes vary so much by school and teacher. I ran into difficulty in a graduate level course simply because I had never once been shown algebra with inequalities. Also, you don't get instant, positive feedback, and immediate indication of whether your solution is correct as you do when programming.

dkokelley 16y ago
I think there is a limit to the positive feedback programming presents as well. Sure, a program may run as intended, but what if there are bugs that need to be worked out? What if there was a cleaner, faster way to perform the operations that version 1 did? This is what I truly enjoy about programming. Not that there is "instant, positive feedback," but that there are so many approaches to a solution, and room for refinement to make the program faster and cleaner.

noblethrasher 16y ago

Some subjects just cannot be taught from authority. The problem with math education, as I see it, is that primary and secondary school math teachers really can't answer too many 'why' questions (for a variety of reasons such as lack of knowledge or lack of time). Teaching math from a programming perspective (or vice versa) should work since you must (as opposed to 'shall') model problems you care about in terms of math.

ahlatimer 16y ago

I had a short stint as a research assistant for a prof who's using programming to teach high school seniors and entering freshmen math skills [1]. I'd have to ask him how the research is going now, but the preliminary results were encouraging. [1]: http://sites.google.com/site/computationalsystems/ http://sites.google.com/site/computationalsystems/

fleitz 16y ago

Iterative programming is the new arithmetic, Functional programming is the new math.

mian2zi3 16y ago

Physical education is the new math. Students don't like to be trapped in stuffy classrooms. They want to be outside and run around in the fresh air and sunshine. Over the semester, not only have my students improved markedly in physical fitness, but they've learned critical problem solving skills. We're playing football. They've developed increasingly sophisticated plays, analyzed defenses and developed counter-strategies. They fluidly execute novel strategies informed by planning and an awareness of the evolving whole-field situation. Clearly, PE is the new math. WTF? Math has specific content and method. A proof is not a program. A for loop is not an integral. Your vaguely technical subject is not a substitute for math just because your students seem more engaged. Teaching people to think logically isn't the point of math, any more than it is the point of history, biology, literature or, yes, even programming. If your students have fuzzy feeling when problem solving, they probably have fuzzy ideas about math. They haven't been taught clearly. If they're uncomfortable with reasoning in math, they haven't been forced to develop intellectual independence. And foisting of "check the steps" on a computer won't help. And don't get me started on how naive an ideas of correctness that is.

chad_oliver 16y ago
I think the issue is not that mathematics is bad, but rather that it doesn't deserve the privileged place it has in the curriculum. Maths above pre-algebra is not generally useful, but instead it is only useful to those who go on to study the more technical subjects (e.g. engineering). Maths is maths, and will always be a powerful tool. But the author is saying that most people need to learn problem-solving and logic more than they need to learn maths; for most people maths is useful only in that it teaches problem-solving and logical thinking. Thus, replace it with programming. In my opinion, I think a far better idea would be to replace the 'computer studies' classes with programming. Most of these classes teach how to use Excel and Word, and if they do programming it's only a limited variety using Visual Basic. Modernise, guys!
panic 16y ago
A proof is not a program. The Curry–Howard isomorphism[1] would beg to differ. I think programming is much closer to math than this comment gives it credit for. In some sense, programming is even stricter than math. When doing math, you just have to satisfy your instructor or your reader. When programming, your program must run on a real computer -- there's no room for hand waving or imprecise arguments. [1] http://en.wikipedia.org/wiki/Curry–Howard_correspondence http://en.wikipedia.org/wiki/Curry–Howard_correspondence

candeira 16y ago

The problem with "I'm never going to use it" is that it's a self-fulfilling prophecy. Further down the line, this attitude excludes you from jobs and opportunities where you need to be able to use it. I say teach math (up to algebra and basic trig and calculus) and programming in every high school. Dropping out is so much easier than dropping in at a later age.

kylemaxwell 16y ago

As much as the discussion has focused on defending mathematics and the importance of teaching it, that's not to discount the value in teaching kids about coding. Whether or not they later become hackers, they'll have an appreciation for how things work and an interest in doing rather than simply watching.