From rockets to stock markets, many of humanity’s most thrilling creations are powered by math. So why do kids lose interest in it? Conrad Wolfram says the part of math we teach — calculation by hand — isn’t just tedious, it’s mostly irrelevant to real mathematics and the real world. He presents his radical idea: teaching kids math through computer programming.
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I could get on board with that. Besides, I think programming should become an essential part of education anyway.
I think it is necessary to use computers in calculate intensive fields. New revolutionary ideas come from interdisciplinary concepts, and using computers for calculations let us spend our time on crucial parts of the different fields in math.
As a math grad student, I have very mixed reactions to this sort of attitude. On the one hand we do turn kids off by doing calculations. On the other hand, if they don’t have a fundamental grasp of numbers and basic arithmetic we’re going to have problems. To use one example, kids aren’t going to be able to do polynomial division (which they need in calculus and other areas) if they don’t have some basic idea how to do long division. And removing amounts of calculation also reduces the amount of internalized experience kids have which helps to recognize when automated or semi-automated computations have given incorrect results. For example, I had a student recently who told me that 625 divided by 8 was a thousand and something. I don’t know what in this particular case he did wrong, but it should have occurred to him that 1) 8 is even so it can’t go into 625 evenly 2) He shouldn’t end up with a number that is larger than what he started with. These are the sorts of little things that people pick up if they have done a lot of arithmetic.
Joshua, you might be surprised how many people don’t pick that up. Estimation is really a separate skill. I do math for a living (mostly as programming, actually). The training here, mostly aimed at math majors, includes teaching strategies for estimation and reasonability checks.
Most important to all of this is developing a math instinct. i completely agree that our time should not be taken up with calculations, but without having actually done some at some point, concepts remain abstract, and often difficult to relate to. I think that doing proofs can be the most boring thing in the world, but to never have done them would be to not fully understand.
Programming is a very good vehicle to teach all sorts of important skills. Logical thinking is a big obvious one. Arithmetic, numerics, and even algebra were a lot easier to learn for me by writing a program to do the calculations.
A few key caveats though.
– Programming to learn basic math should not be “solve it using Mathematica/Maple”. It should be using basic operations (+-*/^…).
– Estimation and verification are important skills to teach. These synergy very well with programming… so that is a plus.
– Higher level languages (say Octave) are perfectly fine when students get to linear algebra, trig, and such. A good practice is to have them implement functions to do various more complex operations before letting them just use the built-in version. (They will learn what the built-in function is actually doing.)
He just verbed synergy.
He should have used “synergize.” At least I can find that “word” in some on-line dictionaries (e.g., http://dictionary.reference.com/browse/synergize), though not in any of the 5 real (= non-virtual) dictionaries I have access to.
Greg, in my on-going flirtation with British poetry I’ve observed something really interesting. The scenario typically goes as follows: A great poet (Shakespeare, Keats, Tennyson, et al.) invents a neologism (’cause it rhymes, or helps the meter, etc.) and gets lambasted by the critics for it. Nevertheless the nasty new word gets used by more and more writers with less and less fuss, until it eventually becomes DICTIONARY-IZED. (How do you like that one?!)
I’m not sure what the moral is here. Maybe this is just punctuated linguistic/memetic evolution in action. Or maybe if you’re already recognized as an important writer you’re granted neologistic dispensation by an Invisible Hand.
Or we could just drop math completely.
Procedural learning is an important part of math. Whether you’re doing calculations by hand or programming a computer to do the calculations for you, you still need to know HOW to do what you’re doing.
Learning procedures involves a set of brain structures called the basal ganglia, which are also implicated in habit formation or the automation of behavior (“stimulus-response learning”). This form of learning is slow. It takes many trials (lots of practice) to properly learn a procedure. Things that initially take a lot of conscious effort (like driving) eventually get taken care of below the level of conscious awareness.
http://www.ncbi.nlm.nih.gov/pubmed/19765552
The requirement for lots of practice is a feature, not a bug, because we don’t want to do things without thinking unless we’re sure that those things make sense and have worked for us most of the time. An unfortunate consequence is that getting really good at anything requires some amount of tedium.
Our culture has an insufficient appreciation for anything that requires hard work and/or sustained attention. Using calculators and computers can save students from boredom in the short run, but they won’t develop an appreciation of what exactly they’re automating and how convenient that automation really is.
Also, it’s disempowering to hide the details of how all our technologies actually work. It’s not good that the technical details of practically everything are left to experts at private corporations that we’re forced to depend on. Even programming in high-level languages doesn’t necessarily teach people how computers really work:
http://www.joelonsoftware.com/articles/ThePerilsofJavaSchools.html
Also, at a time when the public sector is essentially broke, the best use of resources probably isn’t spending large sums of money on gadgets and software to teach the same things that were taught just as effectively (or better) with chalk boards and slide rules for tens or hundreds of years.
Wolfram’s got it wrong too. The “tedious calculations by hand” is only part of the teaching. In addition, once you’re past basic arithmetic and progress to algebra and calculus it is important that you understand how things are derived. The only way you’ll learn is by practicing a lot, not by clicking buttons in his brother’s Mathematica program. In this talk he doesn’t actually state anything of value: *how* are computers meant to teach math and how does it differ from the current methods?
TED is so dull and irrelevant to reality despite the fact that there are many interesting speakers. I can’t believe people actually pay so much money to go to those talks.
OK, after actually watching (rather than just listening) I’ll have to say that Conrad Wolfram is an idiot. He’s a wealthy idiot, but an idiot nonetheless.
What he seems to be advocating here is doing bogus math by clicking and dragging sliders in a GUI. Someone would have had to program that, and he seems to imply that the programmers will be the ones “learning math” somehow. Let’s see – they’ll magically know math by doing some programming. Suuuure. Well, the click n’ drag group can design the bridges in Wolfram’s neighborhood. He completely avoids any mention of *how* humans are meant to learn math with computers. Personally I think they’re great for learning arithmetic – in the 1970s there were things like the “Speak and Math” and later some kid’s games like “Monkey Math” and I think those tools were very good for practicing arithmetic.
Wolfram seems to be advocating that people mindlessly use software like his brother’s Mathematica and so on. Personally I encounter too many people like that. Mathematica’s a good tool, but you need to understand math *before* you use it if you wish to use it effectively. Then there are other tools like Statistica which are more prone to abuse than Mathematica. People click buttons without understanding what they’re doing and they come up with 100% bullshit – worse still there are obviously so many innumerate people out there that the bullshit gets published! That is not mathematics, that is pseudo-mathematics. It’s every bit as bad as the “Bayesian Mania”. Bayes’ work was great stuff and I make use of it every few years, but there are tools out there being used by clueless people who make ridiculous claims in the mistaken belief that the claims must be true because they used a tool which mentioned Bayes.
Doesn’t this all depend on the final most likely outcome? Should any of fields i K-12 (or equivalent) be designed to move students towards mastery, employment, expertise in the field? That is how it is done. I’m not sure it is or isn’t, but if it isn’t, let the computers do the hand calculating. Maybe. Students who show extra ability and interest can be branched off into learning how to make the sliders.
Re: synergy vs synergize…
Yeah, I suck at natural languages. But I claim spell-checker malfeasance on this one :p
PS: I’m actually a lesser author on several papers about language evolution form a theoretical standpoint. So maybe I should have said “I meant to do that” 🙂
I think a lot of people, including C Wolfram, don’t really get how using computers to teach math is really useful. It isn’t about avoiding boring repetition (well, not primarily).
IMO, the real teaching power comes from the students *teaching* the computer. Instead of teaching kids to use the ‘stdev’ function… you teach them what a standard deviation is, how it is useful, how to compute it, and then have them write their own function to compute it.
From that point they can just use the function and further explore / illuminate the properties.
The idea of just using Mathematica to solve algebra or calculus problems for you is not very useful for teaching. At least until after the students already understand what the program is actually doing at a conceptual level.
Greg,
When posting video, especially when it’s Flash video, please post a link to the original video. I among a growing number of people who just deleted their Flash plugin. In most cases, this has no impact, as most sites now provide HTML5 content anyway.
Of course, using HTML5-friendly code in your post would be the best option, but at least give an outside link.
In this case I had to dig out your page HTML source code to find that the video comes from TED, then dig out the web page where I can play it from without Flash:
http://www.ted.com/talks/lang/eng/conrad_wolfram_teaching_kids_real_math_with_computers.html
BTW, getting rid of the Flash plugin let to a very significant battery-life increase in my laptop. I can now use it for a full work day without recharging (as it happened this week when I forgot my AC charger at home when leaving for a client’s facility for a full day work).
@Greg #13: The problem there is that even the potentially good kids will all have addled minds by the time they get to the stage to learn something more than basic arithmetic. So do we start teaching arithmetic in college or something? Let the kids use calculators when they’re out working in the real world; don’t cripple their minds by telling them they don’t have to understand stuff, just punch buttons. Try to devise the classes so that children understand math – computers are also great tools for helping them practice arithmetic (or even algebra, but they probably still need a pencil and paper). Otherwise we might turn out kids who resemble that Japanese guy from one of Richard Feynman’s stories. The guy had an abacus and was adept at rote calculation. Feynman eventually figured out that the guy didn’t actually understand mathematics though, so he managed to challenge the guy and win.
Also keep in mind that the pencil and paper are merely tools to help students keep track while performing more complicated series of operations. The writing is not meant to teach at all as Wolfram suggests – it is merely a convenient set of tools. If you can come up with a computer program that allows students to express these intermediate steps and students can operate the computer much quicker than a pencil then that would be fantastic – it would be genuinely useful. Think about command line vs. GUI. For me the good thing about computer arithmetic games is that they exercise your memory as well as your arithmetic, but I would not expect many people to be able to do things like long division in their heads – for that they’d still need to express the intermediate results.
I don’t think were are talking about not teaching arithmetic. You need and use arithmetic and to be able to do it.
I’m not sure I’m the one to fix the flash problem. Frankly, I post the TED videos because they are very easy to post and one if five creates an interesting conversation like this one. If it became one step harder I’d not do it.
But I do fully support the elimination of flash. I will take this up with TED and we will try to make this happen at a higher level.
But first tell me what the alternative would be: What type of embed code or plug in is better. It has to be simple, so a blogger can cut and paste it just like one does youtube videos and then it basically works in everybody’s computer.
Yes, I don’t think you can fix the Flash problem either. That’s why I suggested that you also provide a link to the original content provider when your video is Flash.
Of course, I also emailed TED to suggest they improve their embedded player: their content *is* available as plain mp4 video after all.
You know what the linguists say: It’s not the verbing of nouns that weirds language, but their renounification.