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Conrad Wolfram’s TED Talk: “Stop Teaching Calculating, Start Teaching Math”

November 23, 2010 — Wolfram Blog Team

“We have a real problem with math education right now,” is how Conrad Wolfram starts his TEDGlobal 2010 talk in Oxford, in which he reasons through what’s wrong, why, and how we can fix it.

Central to Conrad’s argument is the role of calculating—that for the mainstream subject it’s not an end in itself, but a means to an end, and therefore should be wholeheartedly computer based. As he puts it, “Math ≠ Calculating, Math >> Calculating”.

He’s optimistic about what’s possible. “We have a unique opportunity to make math both more practical and more conceptual simultaneously,” and to get people to “really feel math”.

Couldn’t agree more? Dramatically disagree? Let us know.

PS: If you would like to get involved, check out and join computerbasedmath.org.

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27 Comments


Luboš Motl

After some back-and-forth reasoning, I think that I still completely agree with his message.

Most ordinary people – like my parents – can’t imagine anything beyond “merchant’s arithmetic” (sorry, I am literally translating the familiar Czech term) under the word “mathematics”.

But mathematics is so much more. And if something is easily done automatically, it can no longer be a part of “professional mathematics” in any sense.

So when we were schoolkids, technology’s ability to do maths that was available to everyone was just about calculators – say in 1980. However, since that time, computers can do many things. And people – and schoolkids – have to understand the hard work that the computers can make, but they shouldn’t necessarily be forced to do it themselves, all the time.

Mathematics is much more conceptual than merchant’s arithmetics; it is also much more useful and much more fun. I think that the first step is to use appropriate names for various courses. Merchant’s arithmetics should be called in this way and people – as well as teachers and kids – should be made sure that there’s much more about maths.

Posted by Luboš Motl    November 23, 2010 at 11:15 am
Mark

Trigonometry and geometry always seemed very distant to me until I started playing and working with the programming language Logo. Mathematica, of course, is vastly more powerful than any Logo implementation, but the “low threshold high ceiling” simplicity and focused design of Logo and turtle graphics isn’t immediately visible in Mathematica. But I agree with your principle — math is the thinking part not the calculating part and resources like Mathematica and others help make it fun to _start_ thinking in a math way rather than just doing grunt work with numbers.

Posted by Mark    November 23, 2010 at 2:45 pm
roby

Just watched.
Very very good.

Posted by roby    November 23, 2010 at 4:32 pm
Irvine Homes for Sale

I just heard something in the news again about how bad America ranks compared to other countries and their math skills. Math is a very important and fun skill, we should focus more on it.

Posted by Irvine Homes for Sale    November 23, 2010 at 8:41 pm
Allan

Spot on!

There is a need for a revolution. Spend more time on teaching modeling and programming and let the computers do the “hard work”.

Posted by Allan    November 24, 2010 at 5:40 am
Birgit

Wow, what a revolutionary yet realistic idea. As a maths teacher I struggle daily to inspire and encourage logical thought amongst my learners. As great as the idea sounds I do however have some very real concerns in terms of financing this whole project. I teach at a fairly well off school in South Africa yet even at our school not every learner has access to a computer in a Maths lesson. Furthermore has any thought been put into what training will have to be done amongst educators? I am sad to see that this type of development will again benefit those that have and neglect those that don’t.

Posted by Birgit    November 24, 2010 at 1:38 pm
Bernard Gress

First teach American college students to do gradeskool arithmetic, then teach them Math.

Posted by Bernard Gress    November 24, 2010 at 2:50 pm
SpCV

In china,among high school the “calculate everything with your head and hand exclusively” stupid method is taught everywhere.

Posted by SpCV    November 25, 2010 at 1:15 am
Missmath

This présentation is a must. Very inspiring. Thank you.

Posted by Missmath    November 26, 2010 at 8:54 pm
hoppah

“Math” never became meaningful to me as an art or science until I learned the calculus. Calculus is the font from which all the basic math flows, intuitively and beautifully. Teach it first, and capture the mind of the student with its beauty and versatility, and they will respond with calculation – among other things.

I’ve used this method tutoring friends and family’s children and rekindled their interest in math (and calculating) as well as increased their proficiency.

Posted by hoppah    November 27, 2010 at 2:59 pm
Dudley Burns

Conrad Wolfram is a visionary. Once you get past the Marx brothers type appearance his message resonates.

Posted by Dudley Burns    November 27, 2010 at 4:43 pm
rees evsns

Amen!

Posted by rees evsns    November 29, 2010 at 4:55 pm
Dudley Burns

@ress evsns

Amen! to visionary or amen! to looking like Harpo Marx?

Posted by Dudley Burns    December 3, 2010 at 11:22 pm
Kim Bauer

Hi Conrad,

I am a homeschooling mom with two gifted children. I was blessed to find your TED talk at the right time. I have been intuitively feeling many of the things you mention in your speech. Our math education is disjointed and irrelevant and when I showed my son your models, his eyes lit up. He was on your site for a solid hour before I had to pull him away for something else. I am very interested in any pilot programs you are putting together and would love my children to participate. Please let me know if this is a possibility and how we can become involved.

So far, I have been integrating your models with my traditional math. For example, we are currently calculating the area of rectangles, prisms, etc… So I go on your site and try to find a model that looks applicable and we study it to the best of our ability. I am not exactly what you would call a math whiz, so I don’t think I am adding much to the learning experience, although I can totally see the potential of your models to exponentially increase kids understanding of the topics.

Please let me know if there is a way to get involved.

Kindest regards,

Kim Bauer

Posted by Kim Bauer    December 9, 2010 at 4:30 pm
Boston S.

I’m 33 and after 15 years without anything more than a business math course, and a pre-calc course I failed miserably, I just completed a combined Elem. and Intermediate algebra course.

I was terrified of the course thanks to what was a deep seated fear of math, but thanks in part to the structure of the curriculum and in large part the instructor, I aced both courses with the highest score in the class.

I’ve long struggled with the “why” of things – I need to understand the mechanics to fully realize the big picture, which is a blessing and a curse. The difference this time was the instructor – an instructor from Thailand who believes first and foremost in the fundamentals – the mechanics. And that once you have that down, the rest is cake, and only then can should you begin to use a calculator.

She was able to show the class what Algebra meant within mathematics in a way I’ve never seen, and a way that immediately clicked. Once I had the basics down I found myself looking for math challenges everywhere – even those well beyond my level. I fell in love with it.

For whatever reason I can now look at numbers and situations that relate to or can become numbers, and I begin to see patterns and relationships I never considered.

It is my belief that everyone should learn to use their head and their hands first to understand the basics – to see how things work, before ever moving on to the computer. I would like to add that having a background in programming also helped me understand certain kinds of relationships that I struggled with before.

Posted by Boston S.    December 17, 2010 at 9:55 pm
Ann

I completely agree. I have a B.S. in Math and Computer Science and am M.S. degree in Electrical and Computer Engineering. I was a fair math student until I started programming computers. Once I started writing C/C++ programs to do computational math, the math became so much clearer to me. I am now a high school math teacher and am trying to think of how to do this with my students. It isn’t easy to find the time to teaching programming in a math class — especially with looming state tests.

Great talk.

Posted by Ann    January 2, 2011 at 10:46 pm
John

Unfortunately, the attitude that calculating should be left to machines IS one of the main reasons America is dead last in everything mathematical. NOWHERE is this attitude more prevalent than in the US, especially among our poorly educated and arithmetic-challenged ‘teachers’. It is not surprising to find a salesman for computing pushing that enterprise for his own financial gain; what IS surprising is that he finds it so very easy to dupe so MANY supposedly thinking people.
Wake up folks. Without maximal ability to hand-calculate, one cannot begin to appreciate – or even effectively use – computers. This includes most of YOU.

Posted by John    January 10, 2011 at 8:19 pm
John

Perhaps one reason so many here find it hard to resist Conrad’s appeal is that all of us – myself included – are simply in love with Mathematica.

John

Posted by John    January 10, 2011 at 8:28 pm
Bob

Well, I just finished watching the TED presentation. I have taught 5th grade math for 15 years, algebra and algebra II for about 22 years. I incorporate the graphing calculator in my teaching when I can. I am not an old teacher that can’t learn new tricks. I teach computer technology to grades 4-8 and keep pushing my curriculum down each year. I have 4th graders now doing powerpoints and 6th graders using Word publishing. However, I really have mixed feelings about a few of his ideas. I agree that we should use computers where necessary since this is what really runs the real world. In his analogy in driving a car – do you need to know how the car is put together to drive it? Do you need to know how the engine works? Probably not, but do you need to know how to read numbers and signs; know left from right; and how to mentally calculate if you have enough money to put 10 gallons of gas in your car at $2.98 per gallon? I would think these are the basics needed. I love it when someone says “I think estimation is important”; Question is how do you estimate if you don’t know the basic number facts? How do you estimate a percent of 4/5 if you can’t multiply by 20? Obviously, he is a very intelligent person whose math skills probably came very easy. He has the basic skills under his belt. He can relate all of the computer mechanics that he proposes to hand written problem because he KNOWS how to do the hand written problems. I have kids coming to me not knowing area, perimeter and volume as 8th graders. Is it necessary to know these formulas and/or concepts? Are these basic skills? Or do you just have a computer program that asks “What area do you need?” and you type rectangle? Oh, I don’t know what a rectangle is you need to show me a picture…. What is the length of your rectangle? Type the number here. What is the width… type the number here. Your answer is 3,000 square feet for a rectangle this is 30 by 10 feet. Sounds good to me. Oh maybe I should estimate… How do I estimate the area of a rectangle???? Even if I knew the formula, what is 30 times 10? See where I am going with this? There are certain basic skills that we all need to be successful in mathematics. Those are the important issues as I see it. Sure you can incorporate computers for real life problems, but let’s not let them do the thinking for us. How do you determine reasonableness of answers?

Posted by Bob    February 15, 2011 at 6:42 pm
    AnnMaria

    I teach graduate-level statistics and I also run a company that makes math games. Our games DO teach computation – what is 7 x5, what is 56 divided by 8 – but most of this is done within the dreaded “word problems”. Where I completely agree with Wolfram is the idea that we overemphasize computation and underemphasize everything else. What I need my employees to do is not tell me the answer to 25 times 5 but “If we have five employees working at $25 per hour, what is the total hourly cost to staff the support desk? What is the difference in cost for 24-7 coverage versus a 40-hour week?”

    Posted by AnnMaria    June 22, 2013 at 1:41 pm
silver

Bob, you are missing the fine point. He never says don’t teach people how to calculate. He says, quite equating calculation with math. You need to figure out when can we move beyond over doing it on computation. Plus, you characterize entering computer values into a program as a thoughtless exercise That’s a strawman argument. Any teacher with skills can encourage computational and mathematical reasoning with a computer that goes beyond ‘ enter number here.’ No one would do what you are describing, and if they did, they’ve be worthy of critique.

Posted by silver    March 31, 2011 at 4:09 pm
    counsel dew

    Actually, he does say to let computets do step 3. To “we should be assuming computers to do the calculating. “only doing hand calculations when it really makes sense to teach people that.” Sorry, but driving a car != engineering a car. I am, however, bothered… Those who don’t know would be more dependent on those who do… Who would program the computers to compute? Right, only those who learned how to calculate…

    Again, teach logic to get #1 first. Then, use reason to move through the steps until you get to #4. Have computers made English use better or worse? Easy != better. Just my 2 cents. Computers might work for you better than calculating. The same is not true for everyone. Perhaps only the few geniuses will ever “feel mathematics.”

    Posted by counsel dew    June 22, 2012 at 5:10 pm
Hosenfepper

Loved this video presentation. Why? It simply makes sense. As someone who learned Auto-Mechanics back in the late 70′s in high school, very little of what I learned then is practical now with all of the computer based equipment & engines under the hood. Times change so does technology, thus WHY continue to teach rote calculations when a machine can do the hard work for you? I can use a Sun computer to diagnose what’s wrong with a car FASTER than I can the trial & error method taught in auto-mechanics. And at $75/hr for service, would you want me doing a trial & error method to find out why your car’s idiot light is on OR should I use the Sun Diagnostics computer?

Calculations can be done by computers & hand calculators so let them. Society is changing. Cursive writing is being phased out just like Latin was in public schools. If America does not keep up with the times, the times will pass America by.

Posted by Hosenfepper    August 10, 2011 at 11:53 am
    Tom

    Your comments about computer diagnostics reminded me of something I read a few years ago, regarding the observation by many college physics professors that the problem solving abilities of their incoming students had declined from what they used to be. One thing that many of them felt contributed to this situation was that they now had a generation of students who had not worked on their own cars when they were in high school. I would not suggest that we reject the modern technology of automobiles, but I do think that the need to get your hands dirty (literally or figuratively) is often part of gaining a deep and creative understanding of a subject.

    Posted by Tom    December 3, 2014 at 2:18 am
Terry V

I agree with integrating math and technology. If 21st century skills include compute technology, then computers should become part of the math teaching arena. As instructors begin to incorporate technology and experiment with new strategies and activities in the delivery the course, such as using technology to make calculation, the dynamics in the classroom will change as students becoming more involved in the learning environment. Math instructors should move this agenda forward.

Posted by Terry V    December 6, 2011 at 4:56 pm
counsel dew

In a disaster, where we may have little computer-power, what then? Did Einstein have trouble doing 1, 2, or 4? No. What we need is to figure a better method to teach everyone how to think-how to use logic to define 1 and then to go from 1 to 2, from 2 to 3, and from 3 to 4. Unless you can send computers to all that need them, I can calculate. If kids don’t learn #3 and can’t calculate without a computer, the next question we will have a TED presentation asking will be, “Who can?”

Posted by counsel dew    June 22, 2012 at 4:47 pm
counsel dew

Ok…I’ll say it… Not teaching step 3 and letting computers do step 3 really benefits … oh… a company that makes a program that … calculates. Making more people capable isn’t easy, but I think we aren’t asking the right question (#1) to solve the problem. YMMV.

Posted by counsel dew    June 22, 2012 at 5:27 pm


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