[kiba]

I think we should incorporate programming into mathematic classes starting with the earliest grade possible.

The way people are taught mathematics is mostly useless. It's a bunch of equation and calculation that people are doing by hand. Nobody is trying to identify problems, break them down, make hypothesis, and so on. With programming, we could take the usefulness of mathematics to a whole new level by breaking the bottleneck of calculation.

In the end, we may be able to produce even more mathematicians, engineers, and scientists at an earlier age, because they learn the skillset needed to be in those profession.

[nhaehnle]

The way people are taught mathematics is mostly useless. It's a bunch of equation and calculation that people are doing by hand. Nobody is trying to identify problems, break them down, make hypothesis, and so on.

I recall some episodes of five minutes wasted by research mathematicians because they were unable to quickly multiply some 2x2 matrices in their heads.

Being able to perform the low-level skills like arithmetic very rapidly in your head helps tremendously when it comes to narrowing down hypotheses. You can often reject a hypothesis quickly if you are fast enough at doing some computations in your head.

So yes, more teaching of how to identify problems and break them down is a good idea. But you also need to be rock-solid in those elementary but fundamental skills, and you don't get there without a lot of practice.

[tsurantino]

I don't think that it should necessarily be the case. Part of the reason why mathematics & sciences are taught by hand is to demonstrate the process and confront the complexity at hand. "Nobody is trying to identify problems, break them down, make hypothesis, and so on." This is not necessarily true. Sure, after you are first shown the problem you then trudge through multiple calculations and variations of the problem, but the purpose of this isn't to grind it out and memorize it, but to reinforce the process and underlying parts to solving the problem.

There's kind of a reason why at some point we teach certain elements of programming by hand too.

Maybe I'm reducing your question but I think it's important to note the intrinsic value of teaching by hand vs. always incorporating automation by programming.

[kiba]

Part of the reason why mathematics & sciences are taught by hand is to demonstrate the process and confront the complexity at hand.

So what? Programmers deal with lot of complexity all the time.

This is not necessarily true. Sure, after you are first shown the problem you then trudge through multiple calculations and variations of the problem, but the purpose of this isn't to grind it out and memorize it, but to reinforce the process and underlying parts to solving the problem.

All you have to do is recognize the problem and apply the calculation to derive an answer. The calculation will also be particularly tedious. Does that sounds like "reinforcing the process" to you? It's all busywork that can be done by machines.

There's kind of a reason why at some point we teach certain elements of programming by hand too.

I was never taught that way, or rather, I taught myself. I learn a few basic concepts and apply it to projects. I also learn how to use tools like debuggers that help make me figure out things a lot easier.

Maybe I'm reducing your question but I think it's important to note the intrinsic value of teaching by hand vs. always incorporating automation by programming.

There's a big difference between teaching some mathematical concept by hand and forcing students to calculate by hand everytime they confront a problem. They should be able to program a solution to the problem and then move on to the next problem.

[celer]

Important point here: You are not representative. If you are on Hacker News, you have probably been called brilliant at least once. You are almost certainly, given that you don't seem to be a non technical co-founder in a startup, in the top 5% of the population for mathematical/logical(not necessarily arithmetic) abilities. Just because you find the calculations tedious does not mean that most people don't benefit from them. From what I recall, most people forget a concept that they are exposed to once and only once.

[kiba]

Important point here: You are not representative. If you are on Hacker News, you have probably been called brilliant at least once. You are almost certainly, given that you don't seem to be a non technical co-founder in a startup, in the top 5% of the population for mathematical/logical(not necessarily arithmetic) abilities.

That's because I learn to program. If people learn to program, they'll be more "mathematical/logical" too. I am "brilliant" through hard work and curiosity, not because I have high IQ.

Just because you find the calculations tedious does not mean that most people don't benefit from them.

I meant we humans suck at calculation. We are not like computers that can follow steps perfectly. Even when we know the steps, we often get the answer wrong due to our mistakes in following the steps.

From what I recall, most people forget a concept that they are exposed to once and only once.

What make you think it doesn't apply to me or to the rest of people on hacker news?

[jisaacstone]

I also think math classes could be better if they were built around an interactive interpreter.

perhaps all sciences?