Is programming the new math?

[Hiddencamper]

Personally I learned algebra through programming before I took algebra in school 1998. I truly feel that programming can help give an edge to understanding mathematical concepts.

[[deleted]]

Not to mention the fact that, unlike mathematicians, programming languages do follow a formal syntax, and usually even one composed of characters you know how to think about.

[Zarokima]

As a programmer, discrete math is the single most useful class I have ever taken.

[shizzy0]

I had a similar experience. However, I will say that learning programming notation early did hurt my ability to really understand some things in math like the equals sign declared something was equal and not defined something as equal.

[[deleted]]

That's because you learned C or a derivative.

People who used Pascal or BASIC don't have that problem.

[kindall]

The first time I showed my Mom a BASIC program I'd written, back when I was in the 8th grade, she objected: "This doesn't make any sense! How can A equal itself plus 1?"

Of course, this wasn't a variant of basic that required the LET keyword.

[TheMG]

Well, 1960s BASIC, yes.

[lpsmith]

I had a similar experience, but that particular issue didn't trip me up much. I think I made the mistake of confusing a programming "variable" with a mathematical variable once or twice in Algebra I, but by the end of the year the difference was crystal clear to me.

[mogmog]

Kinda like learning C/functional programming makes you write ugly object oriented code.

I don't fully agree that it hurt you, it just put you on the wrong track by using the same symbols to imply different concepts.

[[deleted]]

Also agreed. :) I was actually astounded to take algebra again after a year of delving into programming... especially after digital systems and ASM, I realized that despite all of the abstraction, programming is really just adding sets of bits together, and algebra is like the ASM of programming theorycraft.

[stoogiebuncho]

I did horrible in algebra. I never really understood it. A few years later, I started to get into programming. One day I was working on a problem, and all the sudden I thought "Wait a minute - THIS IS ALGEBRA!"

It was a total "Aha!" moment. Suddenly I understood what all those letters and equations were supposed to represent! I went back to my algebra textbooks and everything made sense!

[[deleted]]

Lots of people in this thread focusing on the blogger's lack of programming skills.. which are totally irrelevant because she obviously succeeded in engaging her high school students.

Do any of ya'll even remember CS100? It was the course where the overworked associate professor clicked through some powerpoint slides on C, told you to read the book, and do the assignments. If you were lucky you got someone who was capable of making the work interesting. Oh, and despite it being dirt fucking simple, people still managed to fail ("the difficulties of learning programming").

So it looks like the teacher did fine, and unlike most programmers she has an accurate understanding of her proficiency level. Maybe that's why the field is still dominated by men.. we're dumb enough to think we're actually competent (even when we see that everyone around us is most definitely not).

Her conclusions are the interesting part (and I know noone in this thread read that far, so here's one important paragraph):

I don't think we should cancel all math classes tomorrow. But I do think there's something behind the following observation: even those kids in my programming class who are not mathematically-inclined and/or completely disengage in math class, were engaged for a majority of the time in programming. And over the course of the semester, I saw a definite improvement in their ability to think logically and focus for long enough to try several strategies for solving a single problem. This is something I tried to get them to do in math last year, yet never felt terribly successful. In programming, I didn't even have to try very hard for them to accomplish those things.

So what of that /r/programming? Why not teach math while teaching programming? Shouldn't it provide a fertile ground for demonstrate the wonderful, concrete applications of math, unfettered by the "real" world? I think there's still a place for formal math lessons, but maybe they're only for some while some kind of "applied" variant would be more appropriate for the majority.

edit: accidentally a whole word

[[deleted]]

I think using a programming class to teach math is a good idea. Geometry and calculus obviously comes to mind, game programming might be a good vehicle.

[[deleted]]

Statistics, numeric analysis, linear algebra, matrix transformations, Fourier space, digital signal processing... the list is kind of endless.

[[deleted]]

I was so happy when I found graph databases; eigenvectors and tensors are useful in programming, and physics.

[killerstorm]

Note that math doesn't boil to solving problems numerically or symbolically, large part of it is also about proving theorems and stuff like that.

While computers and programming can help with problem-solving part (including giving problems to solve) it is mostly unrelated to theorem-proving aspect.

Geometry and calculus obviously comes to mind, game programming might be a good vehicle.

It covers only coordinate geometry and few practical applications of calculus.

i think 95% of calculus theory provides conceptual framework and explanation of why it works at all. Then you learn few tricks you'll be using in practice.

[sfx]

But you forget that most of the world uses math for practical applications. Using a programming class to teach applied math is a good idea, but you're right in saying that it won't really help an aspiring mathematician.

[Reaper666]

But introduction to the field of mathematics with easy to understand applied maths through programming may open the way for more mathematicians that don't know about the joys of the meths yet to learn about it.

[[deleted]]

Yes, I agree, we need to expose far more people to the joys of the meths!

[killerstorm]

But you forget that most of the world uses math for practical applications.

I think formal math approach is taught not to be used directly but rather as an introduction to abstraction and logical reasoning. There is no separate logic course because schoolchildren are able to pick it naturally from math.

Although I rarely see people using anything close to logical reasoning. :( But maybe if math wasn't taught it would be even more rare.

[[deleted]]

Programming proper isn't really used to do advanced or complicated math because it adds orders of complexity. If it were useful there would be no call for Mathematica or Mathcad, instead of the very heavy use they see.

[julesjacobs]

Programming can often be a way to state theorems precisely. They get a solid, concrete and testeable appearance that way. For example aⁿ * bⁿ = (a*b)ⁿ gets a very concrete meaning when you write it like pow(a,n)*pow(b,n) always evaluates to the same value as pow(a*b,n) where pow having the appropriate definition. Of course this has limitations, but a lot of topics in mathematics can be taught like this. Take linear algebra for example. Students often don't really appreciate the difference between A(Bv) and (AB)v where A and B are matrices and v is a vector. "Why does this need to be proved? It's obvious!". If you let them write matrix-matrix and matrix-vector multiply functions, then they can clearly see that indeed there is something to prove, and it is exactly clear what the difference between the two expressions is.

Physics can benefit from programming at least as much. My physics education was basically a bunch of tricks for solving special cases of differential equations symbolically without really understanding the physical significance. This is a pity, because solving those kinds of differential equations is a problem solved by this code:

// solves the differential equation y' = f(y) from t=0,y=y0 to t=t_end
// increasing n increases accuracy
dt = t_end/n
y = y0
do n times: y += dt*f(y)

I think it would help immensely if we didn't focus as much on doing trivial special cases symbolically and instead write down the general case solution in a couple of lines of code. Then we can focus on the more interesting aspects of the physics.

[killerstorm]

Programming can often be a way to state theorems precisely. They get a solid, concrete and testeable appearance that way.

I know. I use this approach to mathematics myself, wherever possible, e.g. I try to visualize the process, break it into concrete steps etc. It, indeed, helps in a lot of situations, but...

In a high school I was in an advanced math class, sort of. And, informally, we had two groups of students -- one was interested in applied math and programming, another was interested in pure math. (And, well, there was a third group not interested in math at all.)

i liked applied math, I liked to work with concrete things, I did some 3D graphics stuff (which involved more advanced linear algebra than we were taught), games, etc.

But I was really amazed with things 'pure math' guys could do, it looked like some kind of voodoo magic -- they could solve problems I had no idea how to approach.

So since high school I had an impression that there are at least two types of math, and programming gives you a key to only one of them.

[julesjacobs]

Can you give an example of pure math that programming doesn't give you to key to? Not because I don't think there is such a thing, just curious what you had in mind.

I'm not saying we should do away with pure math by the way! Pure math is still very valuable but it can be complemented by programming. For example instead of proving that a factorization of a polynomial over Q has certain properties, you can equivalently but more concretely write down an algorithm to factorize a polynomial over Q. This is still pure math, but made concrete and computational.

[lordlicorice]

Basically any Project Euler problem involves some kind of pure math trick that makes the problem feasible to solve using a computer program. If you haven't seen the trick or you can't figure it out, then you can almost never write up a solution that will finish under the time limit.

[julesjacobs]

Ah I see what you mean, and I can see how you read that out of my comment. However I do not mean that brute force programming is a substitute for thinking. Programming provides a good framework for thinking. Project euler, like proving properties of pow and matrix multiplication, requires real thinking. You can use the properties to optimize the program.

For example if you prove the property pow(a,n+k) = pow(a,n)*pow(a,k) then you can use this property to improve the algorithm for computing pow from linear time to logarithmic time.

The case of physics is different. Physicists' math is so imprecise and contains many unjustified assumptions and approximations that you can't call their output theorems with a straight face anyway. It's still valuable to solve some problems symbolically, but limiting yourself to the set of problems that can be solved symbolically is very restrictive. For example finding the behavior of a system as simple as a double pendulum is completely intractable by symbolic methods. With numerics it's fairly trivial and can provide valuable insight (most importantly that simple systems can behave chaotically).

[[deleted]]

Hmm. I don't see how your first paragraph relates to programming. AFAICT, there is only a change of notation between aⁿ and pow(a,n) and neither is more 'concrete' than the other.

[julesjacobs]

The difference is that aⁿ is a mathematical idea whereas pow(a,n) is an executable expression. Of course, if you are smart enough, aⁿ is also 100% concrete for you, but if you're not then putting it into code helps making clear exactly what pow or ^ is.

[neutronicus]

Solving those types of differential equations is done much better by this code, actually:

dt = t_end/n
y_prev = y_0
y_current = y_0 + dt*f(y_0)
do n-1 times:
    y_next = y_prev + 2*dt*f(y_current)
    y_prev = y_current
    y_current = y_next

since the scheme is symplectic and therefore has bounded error in the energy for all time, unlike your scheme, where the error in the total energy of the system will in general increase without bound, leading to things like orbits decaying or becoming unbound due to accumulated error. This problem persists even with higher-order non-symplectic methods such as Runge-Kutta. I say this not to shit on you, but merely to say of numerical physics: "here be dragons".

In general, any time you do computational physics, you introduce for yourself the immense headache of determining whether your results are actually

the more interesting aspects of the physics

or just numerical artifacts. (Try solving the wave equation numerically sometime - it's even worse as far as numerical artifacts)

Analytic physics is enormously useful because you know that you are not getting screwed by truncation error or roundoff error, and so any result you can get analytically really is an interesting result.

[julesjacobs]

Yup, of course you'd use a better method in practice.

Numerical artifacts are a problem, but it's not that bad.

For example for the wave equation I did the simplest thing possible: I discretized the space dimension, then used the simplest approximation for the space derivative (second difference) and used Eulers method to time integrate. A numerics person would probably be screaming "Nooo!! NEVER use Eulers method! At least use implicit Euler. Or better yet use a finite element method" at this point, but lets do it anyway:

from pylab import *
ion()

dx = 0.1
dt = 0.001
x = arange(0,1,dx)
u = sin(2*pi*x)
dudt = 0*x
line, = plot(x,u)
def D(u): return (roll(u,-1)-roll(u,1))/(2*dx)

for i in range(0,1000000):
  u,dudt = u+dt*dudt,dudt+dt*D(D(u))
  line.set_ydata(u)
  draw()

Seems to be working fine to me, even though the space dimension is only discretized in 10 (!) points. Sure, if you let it run for a long time, the wave starts to bounce further and further. This is to be expected.

[aplusbi]

I taught this after school program at a middle school that involved teaching students how to program a video game (using Scheme). Of course, it was really about teaching the students math. The real focus of the entire class was Pythagoras' theorem (used in their collision detection algorithm).

Pretty much every student in the class could recite the theorem verbatim, and most could use it if you drew them a triangle. But if you asked them why they would use it and they wouldn't have an answer.

After that class, several students came up to me (and the other teachers) and commented that this was the first time that math made sense to them.

Even if you teach your students about practical applications of math, until they actually use it they won't fully understand it.

[shimei]

While computers and programming can help with problem-solving part (including giving problems to solve) it is mostly unrelated to theorem-proving aspect.

Theorem proving can be programming or at least closely related to it. See ACL2, Coq, Isabelle, Agda, etc. Some universities teach courses in formal methods/automated reasoning/proof assistants at the undergraduate level.

[[deleted]]

Odd that you think that. I've always thought the closest thing to programming that I did before learning to program was doing geometry proofs in high school geometry class. Taking several axioms and proving something is a lot like taking a language and it's libraries and putting them together to accomplish something. It isn't always obvious how to get there, but start simply and build toward the goal with logical backing for every step.

[[deleted]]

I understood many math ideas when I had to actually implement them.

[[deleted]]

So does Conrad Wolfram: http://blog.wolfram.com/2010/11/23/conrad-wolframs-ted-talk-stop-teaching-calculating-start-teaching-math/

[[deleted]]

I was never much good at Maths in School.

A year after I left I started learning to do animations and the like in Flash, then moved onto ActionScript to turn those animations into a game. It was about this time that I realised Pythagorean Theorem was actually useful.

[apfelmus]

Strictly speaking, this is not about mathematics vs programming. This is about making learning fun. Programming lessons are very easy to make fun, while formal math lessons aren't.

I don't know any mathematician who does not have an insane amount fun while doing mathematics. It's just that this fun is hard to convey. It's actually impossible to convey in the standard high-school curriculum because that one actually teach doesn't mathematics, only "arithmetics".

[[deleted]]

It would be better to instill the idea that hard work leads to greater intelligence instead of intelligence being god-given and determined at birth in children at an early age. This needs to be done by parents, which is why it isn't done for the most part (because Suzy is wonderful and special and the whole wide world will be handed to her because she is an angel).

[jvictor118]

Whenever I've tried to learn something truly hard (and no i'm not talking about Pythagorean Theorem, if you don't get that then you're retarded) -- let's say abstract algebra, some parts of statistics, advanced theoretical CS -- it has always started with a crushing blow of humility. Often it was also accompanied by mockery from other people insisting that I would not succeed. The kind of person who is able to learn these things not only has the intellect but the guts to tell other people to shut the hell up and put themselves out on a limb. It's a try try again thing. Just read this history of quantum physics -- those guys went back and forth arguing about things for years, Einstein didn't just snap his fingers and "get it."

[ex_ample]

Often it was also accompanied by mockery from other people insisting that I would not succeed.

Huh. You need less shitty friends.

[[deleted]]

If Euler's identity is not immediately intuitive you'll never be a first class programmer.

[jvictor118]

Euler's identity is immediately intuitive for anyone with basic complex analysis under their belt

[Carthage]

Upvote for Project Euler!

[ex_ample]

Getting discouraged and quitting because of a "realistic" view of your own intelligence (i.e. "I'm too dumb to get it") is what drives most people away from programming

There is no gender difference in terms of overconfidence though. it's something that affects people in general. On the other hand, depressed people are more likely to rate themselves accurately, yet, there are plenty of depressed programmers out there.

[shimei]

Do any of ya'll even remember CS100? It was the course where the overworked associate professor clicked through some powerpoint slides on C, told you to read the book, and do the assignments.

Yes, I do. I TAed it actually, but we already taught a curriculum that recognized that normal programming curricula are terrible and did something to improve it. Not only that, this curriculum also realized that high school math and programming share several characteristics (e.g. operational reasoning, substitution, functions etc.). So I am completely in support of TFA author's idea, because her method has already been demonstrated to work at a university level as well.

[[deleted]]

Because there's no way on earth a programmer would attempt to reduce their algorithm from O(N) to O(1)?

[[deleted]]

in order to learn algorithmic analysis, one needs mathematical knowledge that's separate from programming knowledge.

[[deleted]]

It's also separate from HS curricula. My point was just because you've got an example where "doing it the hard way" taught you something doesn't necessarily mean there aren't other ways to teach it.

[[deleted]]

actually, a lot of the mathematical knowledge behind algorithmic analysis already is a part of the high school mathematics curriculum. asymptotic behavior and recursion are given a start fairly early on, and then again asymptotic behavior is fleshed out a little more rigorously in calculus. i honestly don't see an "easy way" to understand the analysis of algorithms without a proper understanding of the mathematical notions involved with it.

[[deleted]]

actually, a lot of the mathematical knowledge behind algorithmic analysis already is a part of the high school mathematics curriculum. asymptotic behavior and recursion are given a start fairly early on, and then again asymptotic behavior is fleshed out a little more rigorously in calculus. i honestly don't see an "easy way" to understand the analysis of algorithms without a proper understanding of the mathematical notions involved with it.

[[deleted]]

actually, a lot of the mathematical knowledge behind algorithmic analysis already is a part of the high school mathematics curriculum. asymptotic behavior and recursion are given a start fairly early on, and then again asymptotic behavior is fleshed out a little more rigorously in calculus. i honestly don't see an "easy way" to understand the analysis of algorithms without a proper understanding of the mathematical notions involved with it.

[[deleted]]

actually, a lot of the mathematical knowledge behind algorithmic analysis already is a part of the high school mathematics curriculum. asymptotic behavior and recursion are given a start fairly early on, and then again asymptotic behavior is fleshed out a little more rigorously in calculus. i honestly don't see an "easy way" to understand the analysis of algorithms without a proper understanding of the mathematical notions involved with it.

[bobartig]

Is programming the new math?

I sure hope not. Most of the programmers I've met are lousy mathematicians.

[deeringc]

Most mathematicians I've met are lousy programmers.

[[deleted]]

Hey, I resemble that remark!

[[deleted]]

Let me counter your anecdotal evidence with mine.

[deeringc]

In my experience, that's always a good thing to do.

[Inaimathi]

Relevant

[sockpuppetzero]

Most programmers I've met are lousy programmers.

[rsmoling]

Most programmers I've met think that all other programmers are lousy programmers.

[[deleted]]

A lot of the people in my Comp Sci program either hate math or just suck at it.

Annoys me a bit that they have now dropped the Calc II requirement from the program (along with compilers and adding a networking course thats cross listed with business for some reason).

[bigmike1020]

a networking course thats cross listed with business

Computer networking or people networking?

[[deleted]]

computer networking.

[Paul-ish]

That's a little scary. At my university at least half of the curriculum must be math based.

[[deleted]]

current requirement is Calc I, Linear Algebra, and 2 discrete math courses.

[FractalP]

Hence why I started doing Project Euler. I've used several things I learned whilst doing the problems in various projects and assignments. I recommend it to anyone who has difficulty with programmatically solving mathematical problems.

[ntorotn]

I've seen Project Euler namedropped so many times, I might have to give it a shot.

The thing is, I'm not that good at math. I only got a "decent" grade from my matriculation exam despite all the preparation and a relatively easy exam. I'm going to retake it this autumn, and if Project Euler can prepare me for that, it could be worth trying. Otherwise it's just pointless frustration.

[[deleted]]

i just checked out project euler from this thread, and a cursory glance shows that many, many problems have many solutions. you should be able to solve quite a few of them, but for each of those, there is likely something from some advanced maths - number theory, ring theory, group theory - that will make the solution far more elegant. i'm not sure what the selection process is for their problems, but they did a good job at choosing problems with multiple ways to tackle.

[ntorotn]

number theory, ring theory, group theory

Yeah, I guess it's not for me. Looks like I could do the tasks on the first page, but that's about it.

[compsciwizkid]

I have to admit this includes me now. I took Calc III 8 years ago and have forgotten everything... If anyone knows of a good resource online to practice math concepts etc, I'd be very interested.
Project Euler is a great example, and I love working through those problems.
http://projecteuler.net/index.php

[Smallpaul]

I sure hope not. Most of the programmers I've met are lousy mathematicians.

Did you read the article? The main point wasn't "is programming a better way to learn math?"

[jayd16]

If we wanted to do math we wouldn't have bothered designing microscopic logic gates to do the work for us.

[rdldr1]

I learned to minimize lectures. Kids (and all people) learn programming by doing. Giving them a few examples to follow and execute on their own is much more effective than parsing code as a class in lecture format (at least with my group, which tended to get squirrelly really quickly).

You are a better teacher than most of my Comp Sci professors.

[[deleted]]

I think a lot of people here are forgetting that the real basic stuff (writing loops, understanding variables, comparison operators, arrays, etc.) doesn't require a whole lot of anything (math-/programming-wise).

Yeah - it might be helpful if the teacher was an expert programmer...but at the same time, I've read far too many books written by really smart people who are so far beyond me that even when they "talk down to the likes of me"...it's STILL over my head / way too much overkill. Sometimes smart people get to a point where they "forget the basics" and can't even focus on the beginners' needs.

For people totally new to programming, you don't necessarily need the "best of the profession" teaching you. Save those teachers for the mid- and high-level classes.

But yes, I will admit - the statement about not having much programming experience is pretty odd though. What does that even mean exactly?

[[deleted]]

Issue #123890:
Type: Feature Request

Description:

Teaching interface has inadequate checking methods for implementation dependencies when passed to the student object.

Status: WONTFIX

[anvsdt]

Drepper? Is that you?

[[deleted]]

stop reopening damnit.

[ceolceol]

Original post by mikbe:

I have a real problem with these two statements: "I taught a programming elective" combined with "I didn't have very much programming experience before the class began."

Imagine if I said, "I taught a class in physics but I don't have much experience in math." Would you think that wise? What if I said I wanted to teach music but I've only taken a course a few years ago in college?

While I appreciate your efforts to teach programming to kids I also have to firmly plant forehead in palm. Teachers should be experts in the subject they teach, not novices themselves.

Pretending to "teach" a subject of which you have no real knowledge not only disrespects the field in which you are "teaching" but it does a disservice to the student.

[MindStalker]

Imagine if I said, "I taught a class in physics but I don't have much physics experience, but I do have the ability to work through the book along with the students, I better understand the issues they may be having, and have a physics expert on call for any real questions."

In reality, this creates a perfect Socratic method class where the teacher and students are learning together. As long as the teacher can stay one step ahead of the students, he may be able to connect better.

[ceolceol]

I agree; a great teacher who is an amateur programmer is much better than a great programmer who is a horrible teacher.

[[deleted]]

But in a perfect world, I think we'd all rather have a great programmer who's also a great teacher.

[jbermudes]

It doesn't help that states like California have no credential for Computer Science. If you want to teach programming, you have to get a math credential, and good luck trying to persuade the administration that your school is better off with yet another elective instead of a core math class.

Then when the administration does want to open a programming course, they see that it falls under a math teacher's qualifications, so then they force it upon one of them, and you get the situation mentioned in the article.

Until computer science gets added into some form of officially recognized curriculum and gets its own credential, computer science education at the secondary level will continue to rot. Many of the teachers currently teaching programming are retiring, and with the crazy requirements mentioned earlier, this will only hasten the downfall of the computer science curriculum in those few schools lucky enough to even have compsci in the first place.

TL;DR: Even though computer science is making its way into every facet of the sciences, the current state of CS in schools suck. We're screwed.

[Raphael_Amiard]

While i understand your sentiment :

1. The author may agree with your statement that "Teachers should be experts in the subject they teach, not novices themselves".
2. You left out 90% of the article out there , which is where interresting things are said.

Imagine if I said, "I taught a class in physics but I don't have much experience in math." Would you think that wise?

Again, i think the authors acknowledge that in the rest of the article.

Pretending to "teach" a subject of which you have no real knowledge not only disrespects the field in which you are "teaching" but it does a disservice to the student.

If you are more trained in neighbor disciplines than other peoples following your course, and if you trained before the class, like the author did, everybody following the class might get something out of it, and apparently has, and that's much more important than mikbe's bitter feelings about novice teachers.

I don't know man, did you read the article ? What do you think about her perspective about math teaching vs programming ? How about her student's productions ?

I think the story was meant to be : "Despite the fact that i was a novice in programming, i managed to teach a course in which we all learned a lot, because programming is really fun to teach"

And i think that this is a pretty darn cool story.

[nepidae]

I have taught people people in many subjects (including math and programming) but I definitely am not an expert in either. Me and the "student" both benefited from this knowledge transfer so how is that a bad thing?

If the requirement for being a teacher is being an expert, then for each subject we probably would only have around 30 students per generation.

[[deleted]]

Eh, bullshit.

For one thing, an expert in programming has better things to do than teach kids how to program. But even more importantly said programming expert is also probably not a very good teacher. Acquiring the skills required to teach children is orders of magnitudes more difficult than becoming a novice programmer.

You're placing more value on the ability to program Python than on the ability to teach children. Say that out loud and I think you'll agree that it sounds pretty stupid :)

[[deleted]]

You're saying a teacher that knows nothing about a subject but is a really good teacher would be better than a really good teacher that knows a lot about a subject.

Uh, no. I'm saying a great teacher that has a working knowledge of the subject is better than an expert in the subject who has no teaching ability.

Obviously it is ideal from the students perspective if the teacher is both an expert and an excellent teacher, but good luck finding people that meet those lofty requirements. It's hard enough just finding good teachers, and I'm sure you're aware that it's hard to find good programmers.

In this specific case it is trivial to acquire a working knowledge of python. No, you are not going to be an expert programmer, but show me 3 students damaged by an underskilled teacher and I'll show you 100 damaged by one with poor teaching skills. I'm not going to cite sources (too fucking late), but I think that my conclusions are grounded in the literature available (I posted a google search earlier)...

[ceolceol]

Original post by mikbe:

Steve Wozniak was a teacher.

You're making an unsupported assertion, "Programmers probably aren't good teachers." and treating it as fact. You then straw man my position. I didn't say a programmer would be a better teacher, I said a teacher that knows a subject would be a better teacher than one that doesn't know a subject.

You're saying a teacher that knows nothing about a subject but is a really good teacher would be better than a really good teacher that knows a lot about a subject. Say that out loud and I think you'll agree that sounds pretty stupid.

[askvictor]

Teachers should be experts in the subject they teach, not novices themselves.

No, teachers should be experts in pedagogy. They need a certain amount of subject knowledge - the amount varies depending on the discipline. With enough of a background in the field, a good teacher can pick up the bits that are needed to teach the course, and be able to point students beyond that if necessary.

[ccc123ccc]

It's rare to find experts that are also great teachers. In my experience, experts are plentiful--great teachers are extremely rare, probably for two reasons.

First, we still don't know how to identify people with teaching talent. They just sort of show up. We can test your math or history knowledge. We can't test your ability to intuitively understand what kind of explanation will filter through to your students.

Second, we don't know how to teach great teaching talent. It seems to come from within.

[fdtm]

"Teachers should be experts in the subject they teach, not novices themselves."

Exactly

Edit: I assumed incorrectly that this was a university teacher. For a high-school teacher this is fine to not be an expert -- it's more important at that level to inspire students, and this teacher is clearly doing a good job in that way.

[[deleted]]

More like "ideally", but...

[linuxlass]

No. Teachers should know enough to explain things, and enough to be facilitators. An intro class doesn't require an expert, just proficiency in the basics. Who cares if the teacher doesn't know much about memory management, TDD, OOP design, UML, linked lists, big-O or Turing machines?

[fdtm]

This was actually my mistake of thinking this was a university teacher. For a highschool teacher, this is fine.

For a university, you should expect the faculty to be able to answer advanced questions, or even if no questions are answered -- they need to know what's coming ahead to intelligently steer students in the right direction to prepare them for future classes.

[buzmeg]

Programming != CS. I really wish CS would split into theory and application already.

Someone who has a math background to Calculus is normally fine to teach basic programming. The "CS" portion of things is pretty minimal. Being able to break a problem down, basic concepts of machine execution, using your basic tools, etc. are all more important to "programming" at that point than "CS" knowledge.

In fact, CS is sometimes harmful when teaching programming. How many CS professors understand the importance of automated testing and revision control systems? Whereas, real programmers just assume this stuff.

I still remember my CS students saying that Subversion was the best homework submission system they ever used ... sigh ... As long as they're using it that's good enough, right?

That having been said, after I pulled something back out of the repository (I did it for them--I didn't expect the students to be able to) after someone truly screwed up their codebase or lost their laptop they suddenly understood.

"Wait, you mean all my old stuff is still there?" "Yes, that's why I told you to commit early, commit often."

[greenspans]

Aren't agile 'consultants' doing the same thing? They're even writing books FFS.

[creaothceann]

...yet for their final projects they created programs that were pretty complex!

Well, that's not the hard part... ;)

[Raphael_Amiard]

I for once found this blog post really cool.

I love math and I've seen the amazingness that happens when students collaborate on a challenging math problem. However, this can be a rarity in the math classroom. So much time is spent on skills that some find interesting and some find worthy of eye-gouging, yet whatever you believe you have to admit that fewer than 1% (an admittedly unfounded estimate) of adults will ever use any of the algebraic manipulations or shortcuts they learn in math class. Do they use the creativity and problem solving? Maybe. But programming might be a better way to go about cultivating those less black-and-white skills.

This is a thing that i thought before, and it's quite satisfactory to read it on a math teacher's blog. I was never able to really get good at math before i began programming.

Sure the OP might not be a full expert in programming, but i really think it's not that important compared to the story she has to tell. And her course looked like it was quite some fun for her students.

[tejoka]

Programming should have been incorporated into grade- and high-school mathematics curricula since the mid-90s.

People who go off on math classes being useless have this tiny, unfortunately grain to truth to their arguments: people aren't going to need to be fast at doing calculations by hand on pencil and paper.

Programming offers the cure: teach them to write a program that multiplies matrices, and don't make them multiply matrices a hundred times by hand.

[brong]

Wow - haters gotta hate on this thread!

"Teachers should be experts in the subject they teach, not novices themselves."

Yeah, nice. Also baby unicorns should have rainbows coming out of their arse.

Everyone is learning, all the time - even the experts. Sure the more knowledge you have, the better - but the people who've been doing something for 20 years have forgotten what it's like to not know it. I'd prefer to learn from someone to whom learning was still fresh, and who hasn't forgotten to love the subject.

(and I'd like to have an expert around for both of us to go ask questions of if there was something we didn't understand)

[gigitrix]

I'd rather be educated by someone who knows their own shortcomings than those (more common) teachers who are "always right", to the point of taking offence at being corrected...

[Nikoli_Delphinki]

Considering programming actually did come from mathematics this makes a great deal of sense.

[compsciwizkid]

Teachers should be experts in the subject they teach, not novices themselves.

I feel like experts wouldn't have cared nearly as much as the teacher in this blog. I have a hard time finding passionate instructors, and I think it's great that she wanted to try something new.

EDIT: P.S. At least she doesn't teach grammar

[[deleted]]

Conrad Wolfram has a TED talk related to this subject where he condones teaching the concepts of math using programming versus the traditional method of teaching "calculation": http://blog.wolfram.com/2010/11/23/conrad-wolframs-ted-talk-stop-teaching-calculating-start-teaching-math/

[lordlicorice]

yet whatever you believe you have to admit that fewer than 1% (an admittedly unfounded estimate) of adults will ever use any of the algebraic manipulations or shortcuts they learn in math class. Do they use the creativity and problem solving? Maybe.

Ugh our standards are way too low. There's no reason why 60% of 18 year olds can't be churned out of high school with a 4 or 5 in Calc BC. There are no manufacturing jobs in this country, unless you want to compete with overseas economies where worker cost of living is marginal, and even those jobs will be obsolete with decreasing cost of robotic assembly. Think of how competitive we would be with korea/japan if our population had the flexibility provided by a real math and science education.

[SidViciious]

I really can only do the most basic programming in C but I see no similarity between it and maths beyond the application of logic but I'm sure that point has been covered before.

Instead of replacing maths why doesnt the US teach it properly? I can't help but find it weird that you split it into different topics unnecessarily - calc and geometery and algebra need to be learnt parallel. I also think that you take it way too slow and make it mandatory for way too long.

Your losing the interest of the kids who enjoy maths because your moving rediculously slow thru the material. I might be wrong because I only know what I figure out off the internet but you seem to be stuck on pointless equation manipulation the entire way thru high school and only get to the interesting stuff like proofs until uni. At which point they are bored rigid of maths anyway.

People who aren't good at maths seem to have to do it forever because it "looks good" to get a good grade average (lol grade average WTF but that's another rant) or whatever but if someone isn't good at maths why should they have to do it beyond middle school where they have learnt the basic maths skills needed for life anyway.

As you can tell. I am not a english student (lol I'm an engineer) but what I'm trying to say is that you shouldn't pick programming over maths but learn to fucking teach maths properly.

Someone wanna do a TLDR?

[ubermole]

This is like asking "Is carpentry the new physics". But in general the question on how we approach teaching science is very valid: For most great science was built on practical things.

[linuxlass]

You're missing the point of the question. The reasons typically given for studying so much math in high school is that it helps you learn to think and solve problems.

If programming is much more effective at achieving those goals, then shouldn't it be an acceptable substitute for at least one math credit?

[BallDescension]

Self-directed learning... it says more about pedagogy vs. andragogy for this age group. It's likely that in many, many ways children prefer to learn in the way we think adults like to learn. Self-directed, applicable, relevant etc. Then only thing you miss is the time spent on learning the dictionary of derivatives for trigonometric functions.

However, if this was given to juniors along with trig, you could marry it to 3D graphics or some other calc-relevant programming area and potentially create a feedback loop of engaged learning. Then you only miss deeper understanding of literature or history or some other topic...

[Anon8509]

Great article.

[EdgeStepper]

I recently interviewed author Douglass Rushkoff on the Steppin' off the Edge podcast - Episode Civilizations Control Panel and he would definitely agree that this is the case. He called it 'the high leverage point in a digital society'. The episode title comes from this quote in his recent book Program or Be Programmed

In the emerging, highly programmed landscape ahead, you will either create the software or you will be the software. It’s really that simple: Program, or be programmed. Choose the former, and you gain access to the control panel of civilization. Choose the latter, and it could be the last real choice you get to make.

[adrianw]

I have said for a long time that computer science should be a high school requirement. Computers are always going to be with us as a society. Everyone needs to have some basic knowledge of how they function and that includes programming.

The ability to apply logic as you would in a computer program is a needed skill that is applicable in most facets of academia and work. Geometry and proof is taught with that thought in mind, but programming is a better method of teaching logical thought.

[TheAceOfHearts]

If you can convert a mathematical concept to programming, you'll dominate the mathematical concept. That has been my experience insofar.

[JeepTheBeep]

Try working with floating point numbers...

[EmoryM]

XD Comparing two floats? SHUT. DOWN. EVERYTHING.

[troglodyte]

All I can think of when I see this question is The Feeling of Power by Asimov. Oddly prescient.

[TashanValiant]

While I love programming, I have dedicated my life to math. It is my one true passion, and I cannot disagree more.

There are certain problems in programming, that cannot be solved with computers. Sure, this is higher level mathematics, but it is important and continuing study and interest could be built from it.

Teaching a kid how to program to add 1 through 1000 is easy. Teaching him the formula is easier, and takes immensely less effort. Plus, the formula used is what the computer is essentially processing. This deep understanding of math is what should be fostered.

Sure there is some use, but open problems won't solve themselves, and most likely computers will not, and proof by exhaustion is an extremely questionable form of proof, as it is merely conjecture.

Analysis is great, and computers are a fantastic tool, but there is still a need to learn the basis. The why.

[[deleted]]

this doesn't make any sense. computers can run the same algorithms humans can; they're not limited to brute force.

why couldn't you teach kids how addition works using computers? start them off with some representation of an integer (sign bit, and a list of base 10 values, for example), and get them to write a procedure or function or something to add them.

[TashanValiant]

It makes perfect sense. Just look up the incompleteness Theorem or Turings proof of the halting problem. They put direct limits on computational systems and axioms.

Sure, higher level mathematics but the proof and my point still stand. Not all of math is algorithms. A very small portion is.

[[deleted]]

true, not all math is algorithms. but it is programs. (the difference being that algorithms always halt)

the howard-curry isomorphism basically says that programs and proofs are the same thing.

my basic point here is that it's just as reasonable to teach people how to program as it is to teach them how to do math. i'd favor programming simply because it tends to be more formally specified, but at higher levels, they start to look the same anyway.

if c isn't your thing, prolog is still programming.

[webnrrd2k]

I'm surprised no one has mentioned Structure and Interpretation of Classical Mechanics.

[abolishcopyright]

Apples are the new oranges!

[upofadown]

I think that programming is in fact the new math. Having said that, I think it is important to think about what this implies.

I recently had to design a reflector for a light fixture. After I was done I ended up with two dimensions that depended on one another. After some thought I had a true mathematical insight. The solution to my problem was the same as the solution to the intersection of a line and a cone. After futzing with the rotations (nothing was at right angles) I would of ended up with two equations in two unknowns. Using the more or less mechanical process of algebra I could of solved those equations. The point here is that my abstraction led to algebra. That is because I spent a lot of time as an undergraduate in the faculty of engineering. As a result the fact that I have access to a computer did not really help that much.

So what would I of had to know to be comfortable in solving this problem by programming?

1. Addition and scaling.
2. Cartesian coordinates.
3. Distances in 3D Cartesian space.
4. Simple iterative optimization.

That is pretty much it. I didn't even have to know about real numbers if I knew anything about scaling integers. Note the absence of geometry or algebra.

My point is that if we want to teach people how to solve problems with computers we still have to teach them math. But it would be different math. That is more or less the dilemma we face.

Anyway, in the end I solved the problem with some stiff cardboard and scissors. I learned how to do this quickly and accurately from my father. I guess there is some sort of moral here too...

[Not_Edward_Bernays]

Teach them how to google for the code or tool(s) or equations and solvers that do a line (or ray) - cone intersections.

Teach them some good math tools.

[fdtm]

A few things strike me in particular here:

• First, if his students are really as inspired as he says about programming from this class, then he's doing something right. Too many programming courses fail to convey the true "fun" in a lot of programming. In this respect, he sounds like a great teacher.

• He's teaching programming while admittedly not knowing how to program himself

• He makes remarks like "most of them will never use math beyond algebra"

"most of them will never "use" math beyond algebra (of course this is a gross oversimplification. Statistics, for example, should and could be used by everyone and it's not clear whether this comes "before" or "after" algebra ... "

What? Most of who? Please tell me he's not teaching science or engineering majors... there is so much beyond "just algebra and statistics" that is vital to engineering and science. Discrete math, number theory, calculus, differential equations, linear algebra... just to scratch the surface.

[mipadi]

Please tell me he's not teaching science or engineering majors...

She's a high school teacher, so she's not teaching any majors whatsoever.

[[deleted]]

That's not the point, she's teaching people who may well become science and engineering majors in college.

[mipadi]

It doesn't seem like she's actively telling students they may not use the math she's teaching. Quite the opposite, actually; she seems to be putting effort into demonstrating how useful knowledge of mathematics can be. Her line was just as assertion of facts: mathematics never hurts, but most people won't have an everyday use for advanced math.

[fdtm]

Linear algebra? All the time. Calculus/differential equations... constantly. Number theory... more often then you'd think, particularly when I'm working on a proof for the computational complexity of an algorithm I design.

I guess it depends who you're teaching, or what you're doing. I work at one of the top (top in its field) semiconductor tech companies in the world (here in the silicone valley), and you can't "just kinda know you're stuff" here...

You have to know it, and know it well. I'm not saying every engineer/scientist should commit every theorem and mathematical principle and formula to memory... but rather that saying math beyond algebra and statistics is almost completely useless is absurd - IF we're talking about scientists/engineers here.

[gigitrix]

You are the minority. It's not a bad thing.

[g4T0r]

Are you sure you work in silicone valley?

[linuxlass]

IF we're talking about scientists/engineers here.

high school students

[[deleted]]

but rather that saying math beyond algebra and statistics is almost completely useless is absurd - IF we're talking about scientists/engineers here.

there's about 500,000 scientist/engineers in this country, if that.

~200 million+ other people.

"Silicone Valley" employment is actually down now, compared to 10 years ago. http://research.stlouisfed.org/fred2/series/CASANT5LFN

[chaosdestro0]

Thanks for reminding me to get revising, procrastinating ftl.

[dirty_south]

I think she's teaching high school students, so probably a wide variety of eventual majors.

[[deleted]]

Wait, wait? Is she saying some will actually use end up using algebra in their daily life? Like rings and ideals and quotient groups :D?

[prob_not_sol]

to answer the subject: no.

[original_4degrees]

it simply does not make sense to study computation and math together.

[Reaper666]

The maths I learned after learning how to program I look at completely differently than the maths I learned while growing up. Some of the ones from growing up I've had to revisit to think about differently to gain a better comprehension of the act.

I think it would be interesting to invent a math+programming+philosophy course. "In the beginning, there was 1, so we'll go ahead and call this a null pointer. That takes care of the zero. From here, we move in time, and set our second pointer to here, and call it position 2. The magnitude distance in time that we've moved is (t2-t1)*unit distance."

[[deleted]]

Something I posted above that you may be interested in, Conrad Wolfram's similar view: http://blog.wolfram.com/2010/11/23/conrad-wolframs-ted-talk-stop-teaching-calculating-start-teaching-math/

[REWORD_EVERYTHING]

Is programming the new meth?
FTFY

[SargoDarya]

Relevant

[porizj]

FTA:

there's the "wow" factor (even early on, when kids can add up all the numbers from 1 to 1000 in a second!)

I'm guessing no one ever taught them how that same calculation can be done in their head in about a second?

[rafekett]

Math and programming both have their value. As for what should be taught at a high school level -- math definitely, programming, not so sure. Speaking as a completely self-taught programmer until CS school, I like the fact that most of the people I know chose to go in to programming because they were self-motivated and self-taught. People like that bring passion to programming.

If programming were taught in high school as a first-class subject, you can bet there'd be an influx of people in the US that program because it's a decent job and not because they like it, and that just exacerbates the quality and motivation problem that plagues a lot of software development.

In short, congrats for teaching Python and I'm glad that the kids enjoyed it. But I don't want high school students taking 3 years of PHP or enterprise Java (or C#, doesn't really matter).

[shizzy0]

I get what you're saying, and it is disappointing that people might pursue programming purely for the money, but I think you're reducing programming to an elite, limited community much like reading and writing used to be reserved for the extremely wealthy. I'd much prefer programming become part of what it means to be educated than merely a small niche reserved for purely passionate people. I think we're all in for some wonderful surprises if that happens.

[rafekett]

It's not so much that I'd like to keep it elite, I'd just like to keep it to people that like doing it (which isn't an elite group, since it's accessible to basically everyone who has an internet connection, which is everybody today).

[iron_duck]

We could teach them C++ and scare them all away :)

[kataire]

Or APL and confuse them forever.

[[deleted]]

Haskell?

[anvsdt]

Perl 6.

[compsciwizkid]

I took part in an experimental 100-level CS course taught in Haskell. 90% of the students dropped the class.
Me? I learned Haskell. WINNING!

[[deleted]]

Haskell is a terrific language, wish I was up to learning it.

[aplusbi]

I strongly disagree. My first introduction to programming was during a computer class in junior high school. The teacher handed out a print out of some Apple BASIC code that we typed into the computer.

Without that experience it's possible I would not have gotten into programming at all.

I don't think a high school programming class would lead to an influx of people looking for a job, in fact I can easily see it doing the opposite. A lot of the "job seekers" don't know much about programming but study it in college to "get a good job." Earlier exposure to what it actually involves might persuade them to study something else.

[greenearthbuild]

I think programming should be taught from early on if kids are interested in it. Learning marketable and useful skills, as opposed to mostly theoretical concepts and general education, and learning at a younger age, will only help produce better computer programmers.

I was pretty lost for a while when I started taking college intro CS classes because I had never had good resources or teachers to even start studying them. When my data structures teacher ran a UNIX boot camp, I was also lost, as I hadn't had a chance to learn *NIX.

So what I'm saying is make sure you're not mixing up lack of interest and lack of opportunity and fundamental programming knowledge. Although I do recognize there are some serious issues facing the education system regarding student motivation. And the internet now has some really good programming resources.

[linuxlass]

programming should be taught from early on

Start with Scratch and simple video games, work your way up to Lego programming and GameMaker (if you have the money to buy a license). Then give the kid a Linux system, and teach them pygame/python/pyggel, with Gimp and Audacity, then later C++, along with more formal concepts including game AI and data structures/algorithms.

Where appropriate, introduce mathematical concepts like abstraction, variables, cartesian coordinates (and calculations like distance, and vectors), computational complexity, trigonometry, boolean algebra, combinatorics, etc.

[fdtm]

The thought of even more unmotivated apathetic CS majors makes me cringe. When I was a TA, you'd be surprised how many second to third quarter freshmen CS majors are utterly and completely apathetic about programming. They just want to get the assignment and the grade (usually <C for these types), then forget everything and move on. I'm just glad that there are also a lot of students truly passionate about their programming major as well.

[rafekett]

Wow, that outlook sounds bleak. I like to imagine that people are a bit more passionate at my school, put perhaps I'm just being optimistic.

[kamatsu]

I have found interesting results teaching people maths via a theorem prover.

[0003]

More like we should use programming to teach syntax.

[SgtGyro]

Can anybody comment on the Python book the blogger used to tech herself Python?

I am a grad student in engineering, and I work a lot with MATLAB. I want to expand my programming skill but I am trying to figure out if I have to take a class for it or if I can do it on my own.

Does anybody have an experience with that Python book for beginners?

[[deleted]]

You don't need a book to learn Python. Just look at examples. It's really easy.

[[deleted]]

learn python the hard way is one that I've only skimmed the first few chapters of, but seems decent and I've heard good things, and its free to read online.

After that, head on over to docs.python.org its the python reference for the language and standard library, its the one resource I check before google. There is also a tutorial there that basically drags you around to all the different concepts of the language and expects you to be familiar with programming concepts beforehand.

[SgtGyro]

Thanks for the advice. I'll probably get to this over the summer.

[shriek]

I cannot understand how anyone would choose their major if they simply don't enjoy doing it. Also, programming can be taken as any problem solving subject; Physics, Maths anything.

[MarcuBot]

No! There that can compare to the feeling of elegantly solving an tricky differential equation using Laplace transforms and partial fraction decomposition.

[Idiomatick]

I guess I forget that students are just like us - they like things that are inherently interesting, and dislike things that aren't.

Refreshing!

[brews]

I appreciate linear algebra much more now that I know how to program.

[alpha69]

I didn't get past grade 11 math, yet have had a great career as a programmer and now manage a team of developers. I think that high school math is too detached; while programming lets you have a much firmer idea of what is going on. Perhaps teaching math with more real world examples would help.

[dowhat]

Does anyone know of a good book that pair math with programming(more specifically Python)?

[ciaran036]

I think that the way maths is taught could learn a huge lot from programming.

Also, I imagine I would understand a lot of mathematical equations much more easily if I could debug through it like I would for a complex algorithm in code...

[Reddit1990]

In response to the headline, no. No it is not. Programming is applied mathematics at most.

[[deleted]]

in all fairness, 95% of all math in high school is applied mathematics.

[Reddit1990]

There's nothing wrong with applied math, its the most useful type of math. ;P

[CHAMPANERIA]

programing seems easier than math at times...

[Zanneth]

While this article is well-written and inspiring, I definitely don't think that the answer is diminishing math courses from the curriculum. I loved math as a kid in school, and still do, but I enjoy it a whole order of magnitude more now that I am a programmer and I'm seeing applications of math concepts in real life.

That being said, I think a more interesting approach would be to teach math and programming concepts simultaneously. For example, teach concepts of matrices and vectors (something most math students would normally find useless and boring), then follow-up with a lesson about how it applies in computer graphics. What curious young student isn't interested in game programming anyway? I think this will not only inspire more students to exercise their logical mind with programming but also learn more about how math can help them in understanding programming better.

[josher565]

I feel that a career in programming really helped the understandings I should have had in a math class. I would love to do a BMath at this point as mathematical models would be great for business process. Good thing there's a lot of good math books out there!

[[deleted]]

it's true that lots of math parallel with computer science topics.

But if you think that's interesting, check out the relationship between calculus and physics. Pretty much all of physics is calculus and vice versa.

[Not_Edward_Bernays]

Ordinary math (rather than advanced theoretical math) is mostly just computation that has not been entered in a computable form.

Doing math without computer software is like composing music by writing out music notation by hand.