100 thoughts on “Conrad Wolfram: Teaching kids real math with computers”

As a real oldie, I love this thesis. It is spot on.

Maths is THE universal language and those who use it best will succeed most. A mental sense of the rough magnitude of things is important to realise when you have done something wrong and got nonsense. Given that proviso, computation should be by calculator or computer – they keep accurate track of the decimal points for one thing. Understanding the concepts and formulating them correctly is what matters.

As a highschooler and rabid Casio Calculator programmer in 1990, I find it sad that what I thought would be the obvious progression of Maths is merely being discussed at TED, 23 years later… I still use that calculator from time to time… Time whip it out and calculate the sheer human lifetimes required to overcome the inertia given the current rate of change.

Yes, I used to write Pascal programs to solve all my physics and maths problems for at at university. By my third year, I had a really nice set of general tools able to rapidly work me through my homework… Understanding how to code a problem almost inevitably requires a deeper understanding of the fundamental concepts than recalling a formula and plugging in the numbers.

That was one of the reasons I preferred Nuffield Physics to London Physics in the late 80s. Nuffield had more qualitative, reasoning type stuff… An indexed book of equations was provided for the exam… Of course, one had to know which equation to use, and how to use it…. Suited my rather holistic, conceptual way of thinking and gave me a very broad knowledge of physical phenomena.

thats true if he is speaking of eliminating calculation altogether, i didn't hear him say that. Also, using computers develops young minds too don't forget.

Computers ARE calculators, more advanced than most, but they still are. I understand the talk just fine very much, I'm quite advanced in CS btw. Calculations give kids incentive to find more efficient ways to do things.

Using calculators in school is realistics. Its very doubtful someone in the real world is going to stop you from using a computer/calculator. I do think learning calculating has its place, but quantifying problems is much more practical.

Its unfortunate that education has not changed much in the last 10 years. The only genuine strides I've seen are competancy based education and gamification.

Couldn't agree with this more. I just got out of Calculus today, and guess what? All I learned how to do is arbitrarily follow step-by-step instructions for something I will NEVER use. The problem is that teachers don't teach TRUE math and the concepts behind it. They teach a mathematician's math, not real-world math. There is no freedom or learning happening.

Today, I wrote a trigonometric function for drawing complex shapes in C++. None of which I learned from an antiquated math teacher.

problem is if somone dioesnt understand the basic principles behind ie, working out the floor space of a room, they may noot knw what they're doing, and wont know how to be dynamic with they're maths skills withou understanding it first.

actualy my point is more so, that you should be able to do very simple math excersises in first place, such as dividing single digit numbers, they'res no real need to be able to divide numbers in their thosands, thats just wasting time, in the real world when faced with a math problem that would take u longer then a few seconds you grab a claculator

To equate math to rote computations would be like typing random letters and calling it literature. I would definitely say it's important to learn logic and symbolic reasoning. However, Mr. Wolfram seems to put too much faith on his algorithms. This is a slippery slope to "black box" computing. You put something in the computer and get an answer. Validity is a much deeper question.

No you know what I am thinking. I think we have already been using calculator to do the chores for years. He is just talking about how we can transform the math taught in school to a visual and realistic simulation. That does not do anything with the math conception and the real math he is trying to refer to. Besides, programming needs strong and rigid logic, and where do we get our logic? From the steps of calculation. Comupter can only do the step, otherwise, it's nothing.

This talk was brilliant and inspirational, and I hope the people that can actually effect change in the way math is taught take notice. If math was taught this way I bet all sorts of students who think they aren't good at math or that the subject is boring would change their minds.

I totally agree with this man.Most math I leARNT IS school i am never gonna use it in the real world.I would have passed out of college if it wasn't for math.

[Esperanto] Ankaŭ mi kredas, ke matematiko estus plej amuza kaj interesa kak utila, se oni povus vivi ĝin per iloj kiel Wolfram Mathematica (kaj aliaj similaj). Mi studis fizikon ĉe la universitato kaj mi faris multajn permanajn kalkulojn. Kaj tamen, mia sperto parolas klare: kiam mi estas fronte al komputilo, mi kapablas vidi kaj ludi kun la funkcioj kaj mi tuj akoras intuician ideon pri ĝi, kiu estas tre utila pri la aplikado.

In other countries cildren are taugt to use a form of a calculator caled an abacus. this has ben the norm for centuries. so my question is why is it that in the " most technologically advanced" counries children are taught to use no technology whatsoever to solve problems that they will never encounter in the real world? my answer is to keep the elites above the common person. The education system is one of the biggest scemes in america and it is purposefully done to kep average people stupid.

In most private schools students are using ipads and laptops to do thier math why? because they are from wealthy families and they are going to grow up into successful educated WEALTHY adults. Knowledge is power but only half of power MONEY is the other half. In order to bridge the gap the elite would have to succumb a portion of thier wealth to the common layman. But they dont want to. I agree with what this man is saying but I doubt any real change in education will take place if the elite

stay in charge. Why would i if i were a fortune 500 ceo want the average person to do my job then there would be no difference and my TITLE would be rather moot. Terefore te class cache system of the middle ages is still the main deciding factor in the decision making of the elite. They have the information and they can bend it all they want.

The problem with math is that no companies is hiring people with degrees in math.
Believing that is too theoretical and not applicable to real life situations which I think is a stereotype what we need to change.
Lots students are afraid that after spending 4 years studying math they find themselves unemployed and their only way out is spending 2 years doing a master and 3 more years doing a PHD.
If only companies take the chance of employing a math student.

Could not agree with the message of this video more. to quote a man of highest respects "Education is what remains after one has forgotten everything he learned in school". Emphasis on other aspects of mathematics needs to be of focus when we learn the subject. Leave the routine work to the machines that do routine things.

the math ability that older people have, doing arithmetic in their head, is fantastic and there's no reason why that shouldn't be taught. I doubt it'd take a huge amount of time to teach. One may not have an excel sheet in front of them, and it may be quicker sometimes to do something in your head.

Why is a written javascript exam a bad thing? it can show you really know it. You're not going to have to write how to use 3rd party tools – knowing all their procedures. But the fundamental parts of the javascript language, you should know enough to do them pen on paper. And doing them on pen and paper tests that.

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Brilliant. He's exactly right. Let the computers do the calculating and let's start asking the kids some tough conceptual questions about the material. Have them assemble the pieces of the puzzle we put in front of them. The way we teach math is changing, and we should embrace that change.

I'd like to discover ways to get laid. My buddy has started seeing a stunning young woman mainly because 60 days back he registered to a website called Master Attraction (Google it if you want to know more.) I'm so jealous since I would like to just fall in love too. I'm going to look into this Jake Ayres man's stuff. Surprising thing is, he once had no joy with women. How can you transform that swiftly? His lady's like a model.

I think Wolfram covered this though. Much of the basic math should still be tought in the same way. Learn your addition rules, your times tables, long division, etc by hand. It's when you move into calculus, trigenometry, and all the other maths that are hard to say and harder to do that we need to move away from the traditional model and teach students to see them as logical problems rather than squiggling numbers.

I used to call the alumni for my school. 90% of the math majors I called were employed as programmers – a lot of high level computing is nothing more than converting a huge forumla into machine instructions. The other 10% were PHD's doing research. This is in the US though, it may be different around the globe.

Coding is logic, not memorized libraries. As long as you know the fundamentals – you know that something CAN be done and have an idea about how to do it – does it really matter if you have the documentation up in a separate window to make sure you're passing the right values?

When I said fundamentals, I meant not involving libraries. Just knowing things like iteration, invoking functions, As well as being able to write the algorithms in that language. Though I suppose knowing the libraries to the extent you mention, is fundamental, and indeed, for knowing libraries, using documentation is fine and even normal! I seriously doubt anybody would be given an exam on pen and paper where they had to have memorized libraries.

nobody that learns math and does well in a quality exam, is going to think it's just "squiggling numbers". If somebody managed to learn the process without understanding what they're doing, then maybe the exam should have picked that up.. What are "your addition rules"? I'm talking about doing math in your head. We actually had exams in calculus and trig, so I know them.We didn't have drills or final exams on mental arithmetic, neither would teachers of today have had.

Isn't this unethical? Mr. Wolfram has a huge stake in the computerized algebra systems market. He has 0 experience in teaching at the collegiate level, much less high school or elementary school. I do think that Mathematica can help speed things up, but there is a lot gained and much missed by skipping the hand calculations. I think Mr. Wolfram means well, but that is how the highway to hell gets paved.

I would like to see how a student can prove the rationals are dense in the reals, using Mathematica®. Does mathematica have a theorem prover that could actually be used to teach elementary kids rather than graduate students? When that is done, then there is a hope to teach mathematical reasoning using computers.

You're saying that there's a conflict of interest in the guy encouraging children to learn, design and implement, on their own, the software that he currently sells?

When did the alumni graduate?
They are not employed in math related jobs, they changed careers.
Companies now prefer computer science rather math majors for programming work.
And back in the days there weren't computer science majors they were are math majors, bill gates was in applied math.
Right now there is a distinction between math major and computer science major.

that computer program is a nice toy for children, not suitable for teaching math making the mind rely on computers for every calculation, also what would you do if computer broke down or anything happened to it? We need hand calculations in many situations were computers are not available or it would take time to operate one, also computers are dumb anyway. By learning hand calculations we are learning how to create computers, and then use computers only when they are needed. I disagree with you completely And I believe that computers dumb math down

As a programmer I agree that programming is an excellent tool to really force yourself to learn concepts. The logical thinking skills I have gotten from programming and computer science are simply unmatchable from anything else. If your school offers computer science, I urge you to try it.

I totally agree to this speech and I am a huge fan of Wolfram Research.

I recently signed up for the free pro trial of Wolfram Alpha and tried the Problem Generetor. What I found there were exactly that kind of problems Conrad was pledging against in this speech. Why? I'm kind of disappointed right now.

If I follow his idea to its extreme, why would I learn anything at all ? Why not have a chip with an unlimited access to internet grafted in my brain and just vegetate all day watching cat videos ? I agree on 1 point: it's more important to learn the why than the how of a problem. If I know the laws of physics, I'll know what to do to resolve a problem. If I know economics, I'll know how to calculate investments, depreciation and whatnot. But what he suggests is to become intellectually lazy and dependant on machines.

Does anyone find it strange that we only teach students how to program in Pre-Calculus? In my grade school years math classes had zero programming involved, until my Pre-Calculus course(which was on a graphing calculator).

Math is a beautiful world of numbers. Numbers are the keys of our everyday life. By teaching calculating, we make people think faster and better. we tech 'em to get out of different unexpected situations by finding the better way of solving 'em out. Math makes people better. In fact that in almost every school people are divided in two huge groups: the ones who are better at math and physics, and the others who are better at learning history or literature. I'm not saying that the way they teach us in school is completely good, We surely need to be taught more about why we all need to get all that information. But I hope us to never get rid of basic calculations by hand in order to make all of us to love math. Pardon my english

Wolfram talks a good game, but his talk is vacuous because he doesn't really focus on the formulation and analysis of a mathematical problem before you can use a computer to do the "calculations." Moreover, he make no mention of the fundamental axiom of computing, which I mastered so well when I was interacting with the Operations research and DP Systems (now called IT) Departments of a large corporation: "GARBAGE IN, GARBAGE OUT."

A very good video indeed, and I agree, this is the way math should be taught. But I don't agree we should discard teaching the calculation process. We'll never understand how the computers are doing it if we do so. We'll never doubt what the computers tell us is the answer. Computers can make mistakes, because humans can make mistakes, and computers were built by humans.

I do however think that calculating by hand is an absurd way to do math, we should be teaching kids to do it mentally. And there are two ways I know we could approach this, one is doing what some schools in Japan, China and Korea among others are doing, teach them to use an abacus (and by abacus I mean chinese or japanese abacus; not the western crap), when you're good with an abacus I hear it is very easy to do math with an imaginary abacus instead of a real one, and that it can be done on average in about 1/10 of the time it would take on a real abacus. Meaning not just mental math, lightning fast mental math. For everyone. The calculating process is important because it is literally teaching kids how to solve problems or puzzles on their own. They need to understand the process if they're ever caught in a situation where they do not have access to a computer, or if they are trying to solve a problem they can't properly express to a computer.

The second approach I can imagine for tackling mental math is looking to mental math geniuses like Scott Flansburg for ideas on how to properly teach mental calculation. Our brains are more powerful than computers, and we have a good chunky part of our brain dedicated to calculation only, it would be an absolute waste of resources not to use it.

As for bringing computers to exams, this is not a problem when we have things like the raspberry pi (easily affordable to schools) and linux (highly customizable), it wouldn't be hard to set things up, computers wouldn't be hooked to the internet, no USB ports to thwart cheating, just offline computers with all the applications the students have learned to rely on (like a set of programming languages, and perhaps libreoffice or something to write answers to the questions on the exams)

Don't agree much. There's oddly an acquired satisfaction from the gained ability to successfully perform tortuous computation. This developed satisfaction is extends then to making useful things. It's actually more than hand calculating, it's an exercise in ability to concentrate, to keep a line of though, to pay extreme attention to detail, to apply and employ creatively a handy set of tools. This whole process then leads to people that can make computers, program and come up with new technologies.

Sorry but teaching math fundamentals / basics by practicing programming is pointless. Why? For programming in a high computer language you don't need math at all. What you need is logical thinking, systematical thinking. But even after 20 years of practicing programming — even "professional" — you won't understand any equation better than before, given you never solved one before. I started programming when I was 11 years old. My brother was teaching me Turbo Pascal and Basic programming in 1996. First on a very old C64. Later on the first Pentium machines, 90MHZ, 4 MB RAM if you know what I mean. I started "real" programming in C by 1999 when I was 14 years old. Beyond my logical thinking and the most basic math skills (add, sub, mul, div, etc.), I never ever needed any further math. And it would have been a blocker for me, if it would be like that. The schools I visited were terribly low-level. I learned only the very basics in school. And even after 18 years of programming, I never needed to solve an equation. Why? Because all mathematical problems are already solved in high level programming languages. What you need is logical thinking. And yes, for training logical thinking, practicing programming helps. But NOT for understanding math. Im 29 years old now. I'm programming since 18 years. And I can't solve any equation because I never learned the basics. Now I want to study psychology and for this I need decent skills in statistics. That's why I'm motivated to learn math now. And it's not as easy as described in the video. A lot of things are even more irritating to me. A function is programming has a different concept than a function in math. When you do programming, you can write down the logic in a specific, well-defined and formalized way. In math, you have a formula composed out of "elegant" math terms. Math formulas are like a recursive summary of summaries compared to computer programs. If you come from programming this looks like a limitation or like totally abstract logic and you don't know how to apply that for a specific problem. You can't learn such things using a computer. After a lot of years I'm using paper again: To practice writing down those equations. Solve them. MANUALLY. To understand the basic concepts. BUT AFTER I've understood the basics of a specific math problem, I use Wolfram Alpha to proof my calculation results. So yes: Computers are GOOD for COMPUTING 😉 For proving my results while I'm learning math on paper. But they are worthless for learning the fundamental concepts of math. Today, as a professional programmer with lots of years of experience, I wish I would have had a good math teacher and the motivation to learn it back when I was a kid in school. With the lack of basic understanding I'm using my computer to consume A LOT of YouTube videos, teaching me how to solve equations by hand — like a teacher would do in school. This is what helps me to understanding math. For my understanding, most of the difficulty in learning something new relies on MOTIVATION. I mean, I want to study psychology — I have specific questions in my mind. Questions, I can answer by using math only. So I have the motivation to learn it. I don't need a computer to have fun learning math. I have fun while understanding more and more because it makes sense to me and I'm seeing a progress in my self-development.

I know what modern High school math classes look like. I see them several times a week. They use computers to look at what is effectively YouTube videos, though they are forbidden to go to actual YouTube. To copy the notes that the teacher and the books should have given them. They assume everyone has internet, and the teacher explains how to do the simple things that they already know, and the things they do not understand despite reading the book, the teacher reads the book word for word. Don't you think they already tried that. Only those in engineering and or programming clubs begin to understand the processes. They learn it from each other and their couches not their math teachers. I know states think just because it is on a computer it is automatically easier, it is not. Math on computers is easier if put in the right contexts, like building a program to solve an equation or a calculator. It is far more complex when solving problems in a way that is meant to be done by hand.

While I do believe in the immeasurable value of using computers in math education, I do think there is the danger of its over-dependence. For instance, just because a computer can calculate faster than a human, that does not mean it is necessarily correct. Someone had to know the math and the most efficient algorithm to program the solution into the computer. The problem is how do you know that programmer did their own math correctly or chose the correct algorithm? You don't unless someone else has verified it.

I also disagree with Wolfram's statement that calculations are more suited to computers than humans.

The purpose in learning math and calculations is not just to get an answer.

Learning to do calculations as much in your head as possible develops the cognitive skills that you would not get in just relying on a computer.

Part of the reason we learn math is NOT just to get the right answer, but it is to develop the mental muscle.

Body builders do not get their physical muscles developed by getting a machine to lift their weights for them.

The analogy of developing a mental brain builder can only be accomplished by doing as much as possible in your head.

Machines can help build bridges and buildings, but someone has to have the knowledge and skill to design those machines.

Computers are just toolsto help you do calculations, but they can not do the thinking for you.

Wolfram is an misguided idealist that believes that he can build a thinking machine that can completely replace a human.

Can he provide us some sort of guidelines or a "syllabus" kind of thing? I think the idea is great! Not only for math, but programming as well. I am a programmer and I still struggle with some math concepts, anyone up for designing such a syllabus?

This lecture in beginning confuses math with analytics and statistics. The 4 steps are fundamental to how to solve a problem analytically. Makes some good points about teaching math early. I am not a great mathematician like wolfram however as much I know about math, I respectfully disagree that we teach computer based math. This would not allow individuals to understand mechanics of math conceptually. By reading once we shall retain less and lose math specialists. If we have not done matrices by hand can not explain what is going on or how to feed computer with right form of vectors. It will weaken foundation….

I pay for YouTube red. This video, by embedding a blackberry ad towards the end, violates the contract I have between YouTube and myself to not play ads in YouTube videos. Despite this video being a high quality ted talk, I have reported the video to customer support for spam.

this is amazing, ive been thinking about this since I was in high school, I always hated not knowing the formules and the use for them, hence why no one ever remember them or cares for them

I use Mathematica myself, as a degree holder and math hobbyist, and a lot of the time I just use it to help me clarify and visualise things. I actually ENJOY figuring out real word problems WITHOUT using a computer, then use the technology to verify the answer, as it's so much more satisfying to do it yourself.

I'm using Mathematica to study Calc 2 and Multivariable Calc, and ODEs…I now resent all my teachers that insisted doing computations by hand. I am learning more concepts per day than I learned in an entire week in High School math. Any curriculum that focuses on computation rather than emphasizes concepts is a weeder class and against your interests as a student.

At 10:35 his quick substitution of x^2 with x^4 had me ROTFL. It's even funnier because he stopped at 4 for the deepest and most abstract reason, completely at cross purposes with his own narrative, and yet his original point stands.

really compelling. I think it is great future in the math educational domain that math teaching would be divided into two sides. first it is the compulsory course which teach students about step 12and 4 and the elective course to teach students step 3

i went to the wolframalpha and it said become a pro member to see the equation's solution. This fuckin why people learn to calculate, to not to be the slaves of the likes you!!

The man speaking is a great mathematician. So many people in this comment section are misunderstanding what he is saying, his core arguments. Math is something beautiful, but most students in schools today, will never see that beauty. Their curiosity will get bogged down in repetetive, time-consuming calculations, that they do not understand the ultimate purpose for. Teach the children firstly creative maths, how to use it like an artist uses language, make it fun, interesting, challenging. Then learn them how to use the maths for solving different problems, that has a real-world potential. Teach them how to ask mathematical questions first, how to play with the math, how to visualise it, how to sense it.

To be honest i think it's time to stop saying what's better for other people. It's impossible to predict that, so i think the only solution for education is the free market.

I decided I was going to re-teach myself integral calculus; that my "A" grade in the 3d tier university I attended wasn't deserved. I got good at doing really difficult integrals. But I found that for any integral I could solve (evaluate), some truly obsessed math geek could solve an even more difficult one that I had no clue how to approach. So feeling "adequate" was always moved one more step away. It finally hit me that not only wasn't this making me any better at math, but I was forgetting the basic structure of what integration does. I was forgetting the art of "setting up problems." I was solving puzzles, like a retired man in a coffee shop solving a crossword puzzle. Ultimately it had no value besides self-satisfaction.

As a real oldie, I love this thesis. It is spot on.

Maths is THE universal language and those who use it best will succeed most. A mental sense of the rough magnitude of things is important to realise when you have done something wrong and got nonsense. Given that proviso, computation should be by calculator or computer – they keep accurate track of the decimal points for one thing. Understanding the concepts and formulating them correctly is what matters.

Thank you Wolfram!

As a highschooler and rabid Casio Calculator programmer in 1990, I find it sad that what I thought would be the obvious progression of Maths is merely being discussed at TED, 23 years later… I still use that calculator from time to time… Time whip it out and calculate the sheer human lifetimes required to overcome the inertia given the current rate of change.

Yes, I used to write Pascal programs to solve all my physics and maths problems for at at university. By my third year, I had a really nice set of general tools able to rapidly work me through my homework… Understanding how to code a problem almost inevitably requires a deeper understanding of the fundamental concepts than recalling a formula and plugging in the numbers.

That was one of the reasons I preferred Nuffield Physics to London Physics in the late 80s. Nuffield had more qualitative, reasoning type stuff… An indexed book of equations was provided for the exam… Of course, one had to know which equation to use, and how to use it…. Suited my rather holistic, conceptual way of thinking and gave me a very broad knowledge of physical phenomena.

i don't recall him saying anything about eliminating

natural pure mathematicians are going to coast through where others struggle, he's worrying about the other 99% of students.

he is talking about computers not calculators. Listen again and try to understand instead of reacting

thats true if he is speaking of eliminating calculation altogether, i didn't hear him say that. Also, using computers develops young minds too don't forget.

he's not talking about elimination.

he said we need to address 1, 2, and 4, he doesn't recommend eliminating 3!

Computers ARE calculators, more advanced than most, but they still are. I understand the talk just fine very much, I'm quite advanced in CS btw. Calculations give kids incentive to find more efficient ways to do things.

Using calculators in school is realistics. Its very doubtful someone in the real world is going to stop you from using a computer/calculator. I do think learning calculating has its place, but quantifying problems is much more practical.

Its unfortunate that education has not changed much in the last 10 years. The only genuine strides I've seen are competancy based education and gamification.

Boop

Anyone interested in this should read Mindstorms by Seymour Papert

It seems like he's suggesting that schools should teach students math in a practical manner?

Couldn't agree with this more. I just got out of Calculus today, and guess what? All I learned how to do is arbitrarily follow step-by-step instructions for something I will NEVER use. The problem is that teachers don't teach TRUE math and the concepts behind it. They teach a mathematician's math, not real-world math. There is no freedom or learning happening.

Today, I wrote a trigonometric function for drawing complex shapes in C++. None of which I learned from an antiquated math teacher.

problem is if somone dioesnt understand the basic principles behind ie, working out the floor space of a room, they may noot knw what they're doing, and wont know how to be dynamic with they're maths skills withou understanding it first.

actualy my point is more so, that you should be able to do very simple math excersises in first place, such as dividing single digit numbers, they'res no real need to be able to divide numbers in their thosands, thats just wasting time, in the real world when faced with a math problem that would take u longer then a few seconds you grab a claculator

To equate math to rote computations would be like typing random letters and calling it literature. I would definitely say it's important to learn logic and symbolic reasoning. However, Mr. Wolfram seems to put too much faith on his algorithms. This is a slippery slope to "black box" computing. You put something in the computer and get an answer. Validity is a much deeper question.

No you know what I am thinking. I think we have already been using calculator to do the chores for years. He is just talking about how we can transform the math taught in school to a visual and realistic simulation. That does not do anything with the math conception and the real math he is trying to refer to. Besides, programming needs strong and rigid logic, and where do we get our logic? From the steps of calculation. Comupter can only do the step, otherwise, it's nothing.

This talk was brilliant and inspirational, and I hope the people that can actually effect change in the way math is taught take notice. If math was taught this way I bet all sorts of students who think they aren't good at math or that the subject is boring would change their minds.

I don't think math is just real world application, whatsoever. It's surprising to hear someone say that, who loves math so much.

They need to teach math reasoning and logic more than computation.

@ayoama Yeah, my comment wasn't meant as a disagreement, I was just making a statement about my general opinion.

@ayoama Although my first comment was in reply to the video.

fuckin a, why do u have to calulate when a little machine will do it fast & correctly

I just noticed he's running OSX on a thinkpad.

but what about proofs?

I don`t mean to burst your bubble,but is spelled 'parabola' not 'pararbulas'.

I totally agree with this man.Most math I leARNT IS school i am never gonna use it in the real world.I would have passed out of college if it wasn't for math.

I think computation is a vital part of education, but I do agree that math reasoning should be taught more than it is.

[Esperanto] Ankaŭ mi kredas, ke matematiko estus plej amuza kaj interesa kak utila, se oni povus vivi ĝin per iloj kiel Wolfram Mathematica (kaj aliaj similaj). Mi studis fizikon ĉe la universitato kaj mi faris multajn permanajn kalkulojn. Kaj tamen, mia sperto parolas klare: kiam mi estas fronte al komputilo, mi kapablas vidi kaj ludi kun la funkcioj kaj mi tuj akoras intuician ideon pri ĝi, kiu estas tre utila pri la aplikado.

In other countries cildren are taugt to use a form of a calculator caled an abacus. this has ben the norm for centuries. so my question is why is it that in the " most technologically advanced" counries children are taught to use no technology whatsoever to solve problems that they will never encounter in the real world? my answer is to keep the elites above the common person. The education system is one of the biggest scemes in america and it is purposefully done to kep average people stupid.

In most private schools students are using ipads and laptops to do thier math why? because they are from wealthy families and they are going to grow up into successful educated WEALTHY adults. Knowledge is power but only half of power MONEY is the other half. In order to bridge the gap the elite would have to succumb a portion of thier wealth to the common layman. But they dont want to. I agree with what this man is saying but I doubt any real change in education will take place if the elite

stay in charge. Why would i if i were a fortune 500 ceo want the average person to do my job then there would be no difference and my TITLE would be rather moot. Terefore te class cache system of the middle ages is still the main deciding factor in the decision making of the elite. They have the information and they can bend it all they want.

Awesome Talk! So funny the camera man in the back! Go camera man!! (Y) (Y)

Asking kids to select life insurance would be pretty funny. 14:30

The problem with math is that no companies is hiring people with degrees in math.

Believing that is too theoretical and not applicable to real life situations which I think is a stereotype what we need to change.

Lots students are afraid that after spending 4 years studying math they find themselves unemployed and their only way out is spending 2 years doing a master and 3 more years doing a PHD.

If only companies take the chance of employing a math student.

2+2= Chair.

Could not agree with the message of this video more. to quote a man of highest respects "Education is what remains after one has forgotten everything he learned in school". Emphasis on other aspects of mathematics needs to be of focus when we learn the subject. Leave the routine work to the machines that do routine things.

the math ability that older people have, doing arithmetic in their head, is fantastic and there's no reason why that shouldn't be taught. I doubt it'd take a huge amount of time to teach. One may not have an excel sheet in front of them, and it may be quicker sometimes to do something in your head.

Why is a written javascript exam a bad thing? it can show you really know it. You're not going to have to write how to use 3rd party tools – knowing all their procedures. But the fundamental parts of the javascript language, you should know enough to do them pen on paper. And doing them on pen and paper tests that.

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Brilliant. He's exactly right. Let the computers do the calculating and let's start asking the kids some tough conceptual questions about the material. Have them assemble the pieces of the puzzle we put in front of them. The way we teach math is changing, and we should embrace that change.

Let's make math into a humanity? That sounds great!

//play.google.com/store/apps/details?id=sum.math.game&hl=en

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math'S

I think Wolfram covered this though. Much of the basic math should still be tought in the same way. Learn your addition rules, your times tables, long division, etc by hand. It's when you move into calculus, trigenometry, and all the other maths that are hard to say and harder to do that we need to move away from the traditional model and teach students to see them as logical problems rather than squiggling numbers.

I used to call the alumni for my school. 90% of the math majors I called were employed as programmers – a lot of high level computing is nothing more than converting a huge forumla into machine instructions. The other 10% were PHD's doing research. This is in the US though, it may be different around the globe.

Coding is logic, not memorized libraries. As long as you know the fundamentals – you know that something CAN be done and have an idea about how to do it – does it really matter if you have the documentation up in a separate window to make sure you're passing the right values?

When I said fundamentals, I meant not involving libraries. Just knowing things like iteration, invoking functions, As well as being able to write the algorithms in that language. Though I suppose knowing the libraries to the extent you mention, is fundamental, and indeed, for knowing libraries, using documentation is fine and even normal! I seriously doubt anybody would be given an exam on pen and paper where they had to have memorized libraries.

nobody that learns math and does well in a quality exam, is going to think it's just "squiggling numbers". If somebody managed to learn the process without understanding what they're doing, then maybe the exam should have picked that up.. What are "your addition rules"? I'm talking about doing math in your head. We actually had exams in calculus and trig, so I know them.We didn't have drills or final exams on mental arithmetic, neither would teachers of today have had.

For some reason, this guys face appearance looks like Mark Zuckerburgs

Isn't this unethical? Mr. Wolfram has a huge stake in the computerized algebra systems market. He has 0 experience in teaching at the collegiate level, much less high school or elementary school. I do think that Mathematica can help speed things up, but there is a lot gained and much missed by skipping the hand calculations. I think Mr. Wolfram means well, but that is how the highway to hell gets paved.

I would like to see how a student can prove the rationals are dense in the reals, using Mathematica®. Does mathematica have a theorem prover that could actually be used to teach elementary kids rather than graduate students? When that is done, then there is a hope to teach mathematical reasoning using computers.

You're saying that there's a conflict of interest in the guy encouraging children to learn, design and implement, on their own, the software that he currently sells?

When did the alumni graduate?

They are not employed in math related jobs, they changed careers.

Companies now prefer computer science rather math majors for programming work.

And back in the days there weren't computer science majors they were are math majors, bill gates was in applied math.

Right now there is a distinction between math major and computer science major.

that computer program is a nice toy for children, not suitable for teaching math

making the mind rely on computers for every calculation, also what would you do if computer broke down or anything happened to it?

We need hand calculations in many situations were computers are not available or it would take time to operate one, also computers are dumb anyway. By learning hand calculations we are learning how to create computers, and then use computers only when they are needed.

I disagree with you completely

And I believe that computers dumb math down

As a programmer I agree that programming is an excellent tool to really force yourself to learn concepts. The logical thinking skills I have gotten from programming and computer science are simply unmatchable from anything else. If your school offers computer science, I urge you to try it.

I totally agree to this speech and I am a huge fan of Wolfram Research.

I recently signed up for the free pro trial of Wolfram Alpha and tried the Problem Generetor. What I found there were exactly that kind of problems Conrad was pledging against in this speech. Why? I'm kind of disappointed right now.

If I follow his idea to its extreme, why would I learn anything at all ? Why not have a chip with an unlimited access to internet grafted in my brain and just vegetate all day watching cat videos ?

I agree on 1 point: it's more important to learn the why than the how of a problem. If I know the laws of physics, I'll know what to do to resolve a problem. If I know economics, I'll know how to calculate investments, depreciation and whatnot.

But what he suggests is to become intellectually lazy and dependant on machines.

Does anyone find it strange that we only teach students how to program in Pre-Calculus? In my grade school years math classes had zero programming involved, until my Pre-Calculus course(which was on a graphing calculator).

If Stephen Wolfram listened to his brother Conrad, he would not be able to create Mathematica

Teachers really can't say much. It's the higher up's decision.

Math is a beautiful world of numbers. Numbers are the keys of our everyday life. By teaching calculating, we make people think faster and better. we tech 'em to get out of different unexpected situations by finding the better way of solving 'em out. Math makes people better. In fact that in almost every school people are divided in two huge groups: the ones who are better at math and physics, and the others who are better at learning history or literature. I'm not saying that the way they teach us in school is completely good, We surely need to be taught more about why we all need to get all that information. But I hope us to never get rid of basic calculations by hand in order to make all of us to love math. Pardon my english

Wolfram talks a good game, but his talk is vacuous because he doesn't really focus on the formulation and analysis of a mathematical problem before you can use a computer to do the "calculations." Moreover, he make no mention of the fundamental axiom of computing, which I mastered so well when I was interacting with the Operations research and DP Systems (now called IT) Departments of a large corporation: "GARBAGE IN, GARBAGE OUT."

A very good video indeed, and I agree, this is the way math should be taught. But I don't agree we should discard teaching the calculation process. We'll never understand how the computers are doing it if we do so. We'll never doubt what the computers tell us is the answer. Computers can make mistakes, because humans can make mistakes, and computers were built by humans.

I do however think that calculating by hand is an absurd way to do math, we should be teaching kids to do it mentally. And there are two ways I know we could approach this, one is doing what some schools in Japan, China and Korea among others are doing, teach them to use an abacus (and by abacus I mean chinese or japanese abacus; not the western crap), when you're good with an abacus I hear it is very easy to do math with an imaginary abacus instead of a real one, and that it can be done on average in about 1/10 of the time it would take on a real abacus. Meaning not just mental math, lightning fast mental math. For everyone. The calculating process is important because it is literally teaching kids how to solve problems or puzzles on their own. They need to understand the process if they're ever caught in a situation where they do not have access to a computer, or if they are trying to solve a problem they can't properly express to a computer.

The second approach I can imagine for tackling mental math is looking to mental math geniuses like Scott Flansburg for ideas on how to properly teach mental calculation. Our brains are more powerful than computers, and we have a good chunky part of our brain dedicated to calculation only, it would be an absolute waste of resources not to use it.

As for bringing computers to exams, this is not a problem when we have things like the raspberry pi (easily affordable to schools) and linux (highly customizable), it wouldn't be hard to set things up, computers wouldn't be hooked to the internet, no USB ports to thwart cheating, just offline computers with all the applications the students have learned to rely on (like a set of programming languages, and perhaps libreoffice or something to write answers to the questions on the exams)

Don't agree much. There's oddly an acquired satisfaction from the gained ability to successfully perform tortuous computation. This developed satisfaction is extends then to making useful things.

It's actually more than hand calculating, it's an exercise in ability to concentrate, to keep a line of though, to pay extreme attention to detail, to apply and employ creatively a handy set of tools. This whole process then leads to people that can make computers, program and come up with new technologies.

OMG… its not "math" its mathematics and maths at the very least. Maths is not singular its plural.

Very informative video 100% correct

Is that Mark Zuckerberg's father?

Conrad, are you training teachers already?

Meanwhile in the US, the math curriculum is written without a Math teacher and simple arithmetic now takes 133 steps instead of 6.

I guess there is a part 2 somewhere in which he actually describes how to change school math.

Sorry but teaching math fundamentals / basics by practicing programming is pointless. Why? For programming in a high computer language you don't need math at all. What you need is logical thinking, systematical thinking. But even after 20 years of practicing programming — even "professional" — you won't understand any equation better than before, given you never solved one before. I started programming when I was 11 years old. My brother was teaching me Turbo Pascal and Basic programming in 1996. First on a very old C64. Later on the first Pentium machines, 90MHZ, 4 MB RAM if you know what I mean. I started "real" programming in C by 1999 when I was 14 years old. Beyond my logical thinking and the most basic math skills (add, sub, mul, div, etc.), I never ever needed any further math. And it would have been a blocker for me, if it would be like that. The schools I visited were terribly low-level. I learned only the very basics in school. And even after 18 years of programming, I never needed to solve an equation. Why? Because all mathematical problems are already solved in high level programming languages. What you need is logical thinking. And yes, for training logical thinking, practicing programming helps. But NOT for understanding math. Im 29 years old now. I'm programming since 18 years. And I can't solve any equation because I never learned the basics. Now I want to study psychology and for this I need decent skills in statistics. That's why I'm motivated to learn math now. And it's not as easy as described in the video. A lot of things are even more irritating to me. A function is programming has a different concept than a function in math. When you do programming, you can write down the logic in a specific, well-defined and formalized way. In math, you have a formula composed out of "elegant" math terms. Math formulas are like a recursive summary of summaries compared to computer programs. If you come from programming this looks like a limitation or like totally abstract logic and you don't know how to apply that for a specific problem. You can't learn such things using a computer. After a lot of years I'm using paper again: To practice writing down those equations. Solve them. MANUALLY. To understand the basic concepts. BUT AFTER I've understood the basics of a specific math problem, I use Wolfram Alpha to proof my calculation results. So yes: Computers are GOOD for COMPUTING 😉 For proving my results while I'm learning math on paper. But they are worthless for learning the fundamental concepts of math. Today, as a professional programmer with lots of years of experience, I wish I would have had a good math teacher and the motivation to learn it back when I was a kid in school. With the lack of basic understanding I'm using my computer to consume A LOT of YouTube videos, teaching me how to solve equations by hand — like a teacher would do in school. This is what helps me to understanding math. For my understanding, most of the difficulty in learning something new relies on MOTIVATION. I mean, I want to study psychology — I have specific questions in my mind. Questions, I can answer by using math only. So I have the motivation to learn it. I don't need a computer to have fun learning math. I have fun while understanding more and more because it makes sense to me and I'm seeing a progress in my self-development.

I know what modern High school math classes look like. I see them several times a week. They use computers to look at what is effectively YouTube videos, though they are forbidden to go to actual YouTube. To copy the notes that the teacher and the books should have given them. They assume everyone has internet, and the teacher explains how to do the simple things that they already know, and the things they do not understand despite reading the book, the teacher reads the book word for word. Don't you think they already tried that. Only those in engineering and or programming clubs begin to understand the processes. They learn it from each other and their couches not their math teachers. I know states think just because it is on a computer it is automatically easier, it is not. Math on computers is easier if put in the right contexts, like building a program to solve an equation or a calculator. It is far more complex when solving problems in a way that is meant to be done by hand.

I also learned a lot of mathematics by programming. However, as soon as you make something a compulsory subject it will be dead.

All very interesting until you consider it's an ad for his computer based math curriculum.

While I do believe in the immeasurable value of using computers in math education, I do think there is the danger of its over-dependence.

For instance, just because a computer can calculate faster than a human, that does not mean it is necessarily correct.

Someone had to know the math and the most efficient algorithm to program the solution into the computer.

The problem is how do you know that programmer did their own math correctly or chose the correct algorithm?

You don't unless someone else has verified it.

I also disagree with Wolfram's statement that calculations are more suited to computers than humans.

The purpose in learning math and calculations is not just to get an answer.

Learning to do calculations as much in your head as possible develops the cognitive skills that you would not get in just relying on a computer.

Part of the reason we learn math is NOT just to get the right answer, but it is to develop the mental muscle.

Body builders do not get their physical muscles developed by getting a machine to lift their weights for them.

The analogy of developing a mental brain builder can only be accomplished by doing as much as possible in your head.

Machines can help build bridges and buildings, but someone has to have the knowledge and skill to design those machines.

Computers are just toolsto help you do calculations,

but they can not do the thinking for you.

Wolfram is an misguided idealist that believes that he can build a thinking machine that can completely replace a human.

brilliant

Can he provide us some sort of guidelines or a "syllabus" kind of thing? I think the idea is great! Not only for math, but programming as well. I am a programmer and I still struggle with some math concepts, anyone up for designing such a syllabus?

*maths

This lecture in beginning confuses math with analytics and statistics. The 4 steps are fundamental to how to solve a problem analytically. Makes some good points about teaching math early. I am not a great mathematician like wolfram however as much I know about math, I respectfully disagree that we teach computer based math. This would not allow individuals to understand mechanics of math conceptually. By reading once we shall retain less and lose math specialists. If we have not done matrices by hand can not explain what is going on or how to feed computer with right form of vectors. It will weaken foundation….

I pay for YouTube red. This video, by embedding a blackberry ad towards the end, violates the contract I have between YouTube and myself to not play ads in YouTube videos. Despite this video being a high quality ted talk, I have reported the video to customer support for spam.

this is amazing, ive been thinking about this since I was in high school, I always hated not knowing the formules and the use for them, hence why no one ever remember them or cares for them

I use Mathematica myself, as a degree holder and math hobbyist, and a lot of the time I just use it to help me clarify and visualise things. I actually ENJOY figuring out real word problems WITHOUT using a computer, then use the technology to verify the answer, as it's so much more satisfying to do it yourself.

Dr Feelgood, people who suck at math suck at programming all the same.

I'm using Mathematica to study Calc 2 and Multivariable Calc, and ODEs…I now resent all my teachers that insisted doing computations by hand. I am learning more concepts per day than I learned in an entire week in High School math. Any curriculum that focuses on computation rather than emphasizes concepts is a weeder class and against your interests as a student.

At 10:35 his quick substitution of x^2 with x^4 had me ROTFL. It's even funnier because he stopped at 4 for the deepest and most abstract reason, completely at cross purposes with his own narrative, and yet his original point stands.

será mesmo? não sei não hein. desconfio.

really compelling. I think it is great future in the math educational domain that math teaching would be divided into two sides. first it is the compulsory course which teach students about step 12and 4 and the elective course to teach students step 3

i went to the wolframalpha and it said become a pro member to see the equation's solution. This fuckin why people learn to calculate, to not to be the slaves of the likes you!!

quem gostou curti

He is not saying to do away with the calculating step completely, but rather to give more emphasis to other steps.

The man speaking is a great mathematician. So many people in this comment section are misunderstanding what he is saying, his core arguments. Math is something beautiful, but most students in schools today, will never see that beauty. Their curiosity will get bogged down in repetetive, time-consuming calculations, that they do not understand the ultimate purpose for. Teach the children firstly creative maths, how to use it like an artist uses language, make it fun, interesting, challenging. Then learn them how to use the maths for solving different problems, that has a real-world potential. Teach them how to ask mathematical questions first, how to play with the math, how to visualise it, how to sense it.

To be honest i think it's time to stop saying what's better for other people. It's impossible to predict that, so i think the only solution for education is the free market.

I decided I was going to re-teach myself integral calculus; that my "A" grade in the 3d tier university I attended wasn't deserved. I got good at doing really difficult integrals. But I found that for any integral I could solve (evaluate), some truly obsessed math geek could solve an even more difficult one that I had no clue how to approach. So feeling "adequate" was always moved one more step away. It finally hit me that not only wasn't this making me any better at math, but I was forgetting the basic structure of what integration does. I was forgetting the art of "setting up problems." I was solving puzzles, like a retired man in a coffee shop solving a crossword puzzle. Ultimately it had no value besides self-satisfaction.

Very correct!Agreed in every possible way

A great counterargument to potential dissents starts around at 6:06.

Oh and… rest in peace, BlackBerry.