This is so true. I loved all my college mathematics courses, but the one I enjoyed best of all was one called Numerical Analysis. Pretty much the entire course consisted of writing programs in Mathematica to solve various sorts of interpolation and extrapolation problems. I learned SO much in that course.
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.
I completely agree. In the name of Math, we are taught arithmetic mostly. I am a highschool student and I sometimes automate my school lessons such as Eucild division algorithm and Chemical Equation Balancing. While automating these stuffs I also get a good grasp of all the procedures. School should focus more on teaching student to think like a real scientist, mathematician
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.
That statement makes me think of Project Euler (I think it's called that, I can't remember for sure), a site with a bunch of mathematical challenges which you are meant to write computer programs to solve. It's a really neat example of programming used to help you learn mathematics and computer science. I haven't gotten around to doing much of it myself (though it would be good practice for my problem solving) but I know programmers who swear by it.
This agenda doesn't "only" teach practical applications, as you state. Rather, I gathered that practical applications would get more attention. Currently, the vast majority of math instruction focuses on calculating by hand. He is not advocating for the complete elimination of this instruction, but a better balance. Conceptually understanding math by hand was a great benefit to my intellectual development as well.
That's precisely why he talks about practical hand calculations approximating answers, to give you ideas about how the answer should be, and also why he talks about computer program. Try for yourself, download scheme or python and calculate, say some linear graph like y = 4x -2, with increments being 1. And experiment with making it more and more general. This is a basic problem, but getting it right means that you really have to understand how these types of equations work.
Bryon Lape If you purchase of copy of Wolfram Alpha you can prolly type that inquiry into the searchbar and get some pretty interesting algorithms. I'm gonna guess that the trajectory of change for schools will put this solution somewhere in the 35th century. :-/
+Jennifer Grove (Dark Moon) , this is not new in USA, it has been discussed for decades by NCTM, specially their document of 1980 Problem solving: an agenda for action , and the following discussion and additions.
Teaching math through programming is great..we have to do it, but its dumb to say the conventional approaches are irrelevant and dated. Computational approaches can only enrich the analytical methods. not replace them. For example how else can we develop the differential calculus if not by the ab initio methods that involve taking limits of the rate of change as independent variable tends to zero? Without an appreciation of such first principles , its impossible to learn math
Hi, I recognize this is an old response, but he has been working heavily with the government of Estonia (post-Soviet darling of the tech world) to reform their curriculum.
@chessfan6 i dont know about you but when i was taking calc we didnt just sit and cranked out graphs and equations. It was always learn to concept and then practice it by calculating it. the actual calculations are not hard if you know the concept but by doing them by hand you can see where the error was made while with a computer you often cant (depends on program of course)
What he's saying is what I've been saying since I was in junior high. They make math WAY harder than it actually has to be. They use the wrong type of language to describe what's going on, spend too much time on the tedious aspects and not enough time on building a perspective by explaining the symbolism of equations and the context of procedures. At its heart, math is just like doing a puzzle. It takes more logical computations to talk to people than it does to do calculus.
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.
He makes a compelling and well backed argument. The current way math is taught really is like trying to teach driving by showing how an engine works. Computers are now everywhere and can do many tedious tasks that are no longer necessary for humans do to, but the curriculum has not yet changed in response to this. As mathematician Paul Erdos once said, mathematics is not about computation, it's about making connections. Let computers do the number crunching.
@anotherelvis if you teach your students the same problems, but allow them to use the computer instead of/in addition to paper, a lot of them may benefit. If you f.ex. use MS word's integrated formula writer to write formulas and the calculator to do calculations, the students may simply formulate the algorithm (formula) necessary to solve a given problem once, copy it to where they are going to use it, and substitute the variables with their input. The end result and thought process is the same
Since leaving school I've had two attempts (in my own time) at learning math. Both times I've got to differentiation, managed to do it from first principles, and then stalled and got no further. I think it was the sheer effort involved in the working out that made me lose momentum. I think he has a good point. Worth remembring there might be a bias as he's got financial interests in Wolfram alpha and Mathematica.
So true. I remember in my HS calculus class, I literally came up to the front of the class a few times to show the teacher and the class why they were arriving at answers different from the answer key. My calculus teacher didn't even understand calculus.
I had a similar experience. I was failing calculus bad at first. I worked so hard. Class working on a big problem. I pointed out they were doing chain rule wrong. So many texts and professors have errors. It's sad we have to verify answers with the answer key. Maybe should have one real world problems that are verified by reality idk I'm not that smart lol
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.
Also, when he suggests writing computer programs, he means writing algorithms that would solve arithmetical problems. Surely, anyone who could write a function from scratch that correctly and efficiently factors any positive integer must have a clear understanding of factorization. I get your point, but writing completely unrelated code that just happens to use a mathematical equation is NOT what he is suggesting.
Continuing the below post....Exeter seems to encourage the use of technology in solving the nightly problem sets. Any and all resource usage is fully encouraged. Many of the problems don't have a "correct answer". HOW students present their solutions (in writing and orally) is just as important as whether their answer is correct (if there even IS a "corrrect answer"). The approach they take is called the Harkness Table method, and they certainly produce some extremely talented students.
I find the approach interesting, as it somewhat forces a rethinking on how we teach math. Especially in a country where math is often regarded skeptically in the first place. I have had so many teachers and instructors that never truly understood the material, which ended up losing the other students. They wanted to learn, but didn't have the proper avenue to follow. Nice presentation, thanks
@Crazylalalalala Highschool went into memorization of formulas with no explanation. Being curious I figured out the reasons behind things on my own which is part of why I managed to get through the terrible system. Our teachers did not understand or have any curiosity beyond what formulas they needed to teach. Formulas with such simple explanations, such as the area of a triangle, were presented as one of a million things to memorize and not to understand the meaning of.
Not necessarily. In my high school calculus class, I was one of the only people who understood related rates. Turns out, it was because, since I had to draw derivative graphs BY HAND, I had a better intuitive understanding of what maximums and minimums meant, and therefore understood how to get the information I needed. (admittedly, this example does not a trend make, and is a correlation-causation case: it may be that because I'm good at math, I never got a calculator, rather than vice-versa)
@Nigrescence I have to agree with you. Using computers can become a crutch for many people; just plugging a problem and hitting 'solve'. But I think it is possible to have a curriculum which combines learning things by hand and programming what you learn to solve more difficult and complex problems. I think it builds character to learn math by hand, but we can also use computers to take shortcuts so we can examine the meat of a problem rather than spending hours getting to that point by hand.
@HarveyMushman85 Programming is the same thing as writing it on paper, but with programming you also learn how to program. Given a word problem, you write down the variables and constants in the order and arrangement that will allow you to come to an answer. You do the same when programming. You must figure out how to arrange the information and determine what operations you do on that information and then you tell the computer how to do it. The student becomes the teacher.
I think what he's saying is valid to a point. If no one knows how to solve d[(x^2)/3x] then we cant create the program to solve it. It is essential to learn the fundamentals of each subset of mathematics (algebra calculus) so that people do know how to do it. Once the student has those fundamentals, they shouldn't be forced into "grinding them out" them for every subject though. Learn algebra the hard way and when you get into calculus don't worry about the algebraic details as much.
@LeMegasandwich You missed the entire point of the presentation - we're not going to lose those people that go on to a deeper understanding of these concepts, just like not forcing everyone to be a mechanic before they drive a car hasn't limited the progress in developing new means of transportation. The mechanics are still learning to be mechanics while the rest of us proceed with our lives using transportation in the way it's intended to serve us.
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.
Teaching calcculation is importat too. Calculating by hand helps us understand how it works, and if we understand how it works we can create new proofs->new rules->new, better methods
I think he has some really valid points here and I think that he's right in not calling this education math, but how to use math. I would have loved to learn math this way, applied concepts would have kept me more interested and focused I'm sure there will be those that would still want to learn how to solve formulas by hand and that's great. We can driver cars, use computers, travel in planes, and talk on our cell phones without knowing how all the items inside work. They are means to the end
I wish this was the way of teaching maths when I was at school. Last year of school I got a D, retook maths at college, 1st year got an E, retook it again, got an F, took it again, finally pulled of a C. That is 4 years of maths education, the most challenging part of my education so far. Learning maths needs to be done when you are young, and done correctly, and excitingly. Its inspiring to see that those with a passion for teaching maths KNOW how it should be taught.
@digitalcrypt well as i dont know what your education was like 20-30 years ago i can tell you that mine was not just about calculations. In fact students these days already use fairly advanced programmable calculators that allow you to do all of the time consuming calculations (deferential, integration, matrix, graphs) quickly. And most of the questions are not just Solve this, the questions usually test your understanding of the math not just how to do it but what does it mean.
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!
An Indian script writer named Ravi Naik, told once that "there's a link between heart and books" when we were talking about the failure of eBook readers in India. We definitely are going to need some paperwork before we jump to the next level. Computer is about making things faster, and paperwork is about trying to inject the knowledge into ourselves. Paperwork first, and then programming (same applies for learning basic programming, too). So I believe it would work after sufficient paperwork.
Ten years ago, university teachers were experimenting about how to do this using Wolfram's Mathematica. This stopped when their competitor Maple basically gave their software to bona fide students for their own use, probably reasoning that they would hack it anyway. It would be great to implement what Conrad is suggesting, but Wolfram has got to come up with a better licensing model to recapture this market.
It is important to know how solve mathematical problems without computers. This doesn't mean that the best way to teach people to do this is by teaching hand calculation particularly to the determent of other important aspects of math education. I think Wolfram is at correct in suggesting that the best way to do this is to increase our use of computers in teaching math. While any problem can be solved by hand given enough time we should be teaching efficiently.
I remember doing Calculus 1+2 via Woflram Mathematica and I really didn't gain much out of it, but that's simply because I didn't really find it interesting. When I got to Differential Equations and we did it by hand I learned the material very well and aced it... But that had more to do with the material being useful. The biggest issue was that the problems they had us do in Calc 1+2 were all basically physics problems we could solve without doing any calculus :/.
@Phyrexious I completely agree with you. I am pretty good at "math", in the "school" sense. I can crunch my way through complex equations, differential equations and stuff, yet I couldn't "use" that skill. As far as 20 minutes ago, I had the concept that "math" was simply a series of calculations, at the end which we get a number or an exact answer. However, as this video explains, math is so much more than just that. Let's stop teaching "math" as we knew it, and focus on the "real" math!
Thesis, although thought-provoking, has at least one problem: there is a difference between analytics and numerical simulation, i.e., going logically through all the steps and just computing. And you need both.
@jamma246, there's no one "correct version" of the abbreviation, only what your ears are used to hearing. The UK says "maths" and the US says "math". They're simply two different abbreviations for the same word, mathematics. I'm guessing that Wolfram probably says "maths" by convention, but since he was doing this presentation in (I think) California, he said "math".
I wish i had learned math this way. The old academic way of math teaching bored me in school since i got the concepts the first lecture, and then spent a lot of time doing mindless repetition. I actually made programs on my calculator in basic to solve the equations because i was so bored with calculating on paper. If i had learned programming + conceptual computational math instead, i'd be a lot better at math. I've been using math in hobby projects since, and learned a lot there.
@zipporapper Me being an engineer and very often requiering some computational muscle, I can't just put the numbers in and expect result, the computer doesn't even know what the hell do you want to do with them. What I allways invariably endout doing is to "teach" the computer how to do what it is that I want to do and then let it crunch the numbers (and sometimes it is faster to just do it by hand).
Source? As a veteran AP Calculus teacher, I'm pretty confident that my colleagues know quite a bit more about math that you do. Most math teachers are required to take several classes of advanced mathematics beyond calculus for their endorsement. And the statement "apply calculus to real life" is about as inane as expecting organic chemistry be taught to "apply to real life". Both are far more useful in a specialized career setting than a mundane one.
Agreed. I tutor students in algebra at my university and they have a computer program that they use. They all start off hating me because I won't let them use a calculator until they've shown they can do the work by hand, but the first time that they catch a mistake (from punching the wrong button on a calculator) before they put it into the program, they feel so powerful. Then they realize they can actually do the stuff and really take the reins because they aren't using computers as crutches.
about time... used LOGO in my classes to encourage programming because the IT subject didn't teach it... BUT the shift that is required, imho, is not technological but social: schools are still factories rather than nexi for genuine enriching engagement whether maths or any other subject...
1 That 17 min talk felt like 5 mins. Really interesting to listen to. 2 From UK, shame we haven't had this new approach to teaching maths trialled in schools.
@Demagogue88, personally I wish I learned calculus before I took physics, because I thought calculus simplified a lot of it. Sure, you can memorize 20 different already-derived formulas and doing a "plug 'n chug" on the right one, but with calculus you can usually just do integrations on ONE formula (e.g., v = ds/dt) to derive what you have to use. Likewise, Diff Eq'ns saved me from having to memorize a lot in thermodynamics classes.
@KawallaBair I implore you to not make assumptions about my abilities or my personal biases against programs for calculations. I suggest a happy medium because not everyone gets true understanding without the calculations behind a concept. It's 2 fold. The calculations help us check ourselves and avoid automatic assumptions that something is always true. Dynamics are not linear and there is no such thing as "always"
Hand computation is an end in itself since, by virtue of being rational beings, we may derive intrinsic value for computation. Also, even if a majority may believe computation is unpleasant and thus simply a means to an end does not justify that mastering hand computation is unnecessary to the art of problem-solving. Although posing proper questions is essential to problem-solving, working directly with numbers is too. Think of a builder who builds using a computer but never picks up a hammer.
@FmMan33 Solar flares don't affect textbooks nor would it destroy all our electronics. At worst, it would blow out any electronics running at the time in one region of the world. The other side of the world would be just fine. In any case, any extremely unlikely and limited occurance such as a solar flare is nothing to base a policy around.
Completely agree. Calculating is a right brain activity that develops more than mere methods that will never be applied in the real world. Incoorporating programming and mathematics is a great idea, however, it would limit the accessibility of mathematics education.
as long as the people knows how to do it manually, they can be taught to program it. so this has a point and the only problem to get through is making the children learn the process itself.
You need to do some computation. If you've ever done regression analysis in Stata, Sas, etc, you know what it's like to have no idea why standard errors are changing based on what dependent variables you use, what it means when your computer is complaining about multicolinearity, etc. In higher math, I never fully got the concept of a vector space, topological space, metric space, etc until I went through the routine calculation once or twice of checking the axioms. Point valid but 2 strong.
@Crazylalalalala College improved upon this hugely, because suddenly our instructors were (mostly) people who had the curiosity to be able to explore questions they were asked, they had put a lot of thought into the material, they hadn't just memorized all of the formulas in the world - that kind of lack of understanding we are taught with would never get someone past maybe a bachelors degree in math at best.
he told everything as i really thought of education i am an engineering student(computer science). im messed up with computer programming. i have back in my c,c++,java subjects. but ive interest in Nature of nature and now i am gonna make them true using real math(PROGRAMMING) jsk
You don't need programming to know that. n^2 = (n+a)(n-a) +a^2 = n^2-a^2+a^2. I know a few other ways squaring numbers. n^2 = (n-a)^2+a(n+a) is another way. Another way is to treat it as a quadratic. For example (10 2)^2 = 100 +40 +4 (put an extra 0 for 10s place and two 0 for 100s place) so it becomes 10000+400+4 = 10404. No programming is necessary.
Using a calculator is exactly like programming, except that usually with the calculator you're still doing part of the algorithm in your head or on paper. Either way you are using an algorithm, if you're solving it correctly. In fact, it's pretty common for us to solve problems on paper before write programs.
@Crazylalalalala I know that is a simple example but in the real world, nobody ever sits down and does calculus. They have computers. The thing calculus gives us is accuracy, but our job (the job of the humans) in the real world is to understand what to calculate, ask the questions. That takes an understanding of the concepts, not the inner workings of equations.
@hypermath Wolfram Research has, for many years now, provided site licenses to universities and schools that cover all students for their personal computers. If your students don't have access, then talk to your site administrator. It is certainly our aim that schools that want to use Mathematica for teaching face no practical licensing or deployment barriers.
TO use calculators or not to use is not important. Important is to teach kids to think. Which can be done by : * asking children questions instead of providing them with the answers * guiding children to the right solution instead of telling them what to do * involving children in non-standard and inquiry-based problem solving * showing children different methods and approaches to solving a problem * simply asking children “Why do you think this way?” Yasmina, math4u.ca
@digitalcrypt sure if you ignore the part that i said that our schools are already focusing on the understanding the meaning and purpose of math and how it applies to eveyone's lives and less on doing by-hand calculations. our schools are already doing this. It is not a new idea that he presents.
@SuperiorApostate : Except for the fact that it's "Maths". The word is a shortened version of "Mathematics"... not "Mathematic". It's a shortened version of a plural, and hence should also be plural. Ergo : "Maths".
@LilSnyperX to be honest i did not pay much attention at middle school. mostly because i moved to the USA at that time and didnt know English too well and in general i was not very enthusiastic about leaving Israel. So i cant tell you much about that. in elementy school in Israel the only thing i do remember specifically is that we work with blocks and other visual tools to learn what the math represents and i do believe that was useful for me. We also competed back then just to show off.
I love wolframalpha, it is a brilliant, brilliant website and one of the most powerfull free tools on the internet! But i have to disagree with the idea of teaching programming rather than learning how to solve maths by hand. You need to know what the machine does, so you can trust the outcome. We have enough blinkered specialists already!
@TheBoneLESS Well, as he points out, part of the problem is that real world problems are often vastly more complex. Of course, if you mean by concrete, a well constructed, highly interactive computer demo of how the integral or derivative of a function relate to the graphs various functions, then we're on the same page. I think you might enjoy a BBC series called "The History of Maths", and if you're really curious, google "MIT ocw" and look at all the stuff they have for math.
I loved this. I'm in graduate school, and at the point where the math is so complex no one does it by hand because it would take an extremely long time to do a basic task. So...we don't learn anything by hand. No basics. It works, we may trust it, it has been proven. Instead, we learn what the professor calls "math appreciation". We understand what the computer is doing, and we learn how to do everything but the tedious week-long paper calculation...steps 1, 2, and 4.
Thats so true! School makes you pretty good at calculating stuff absolutely irrelevant to the reality, instead of actually making you understand the processes.
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
As much as I hate calculating things manually, and as much as I love to use wolfram alpha to quickly solve improper integrals, check series convergence or find limits, I don't think that this is the solution to the problem. I don't even think boring computation is the problem with math education. I think he's right that we should focus on the real-world to math (and back) conversion of problems, but I don't think that means we need to eliminate manual computation.
I understood his point to be exactly as you have explained it. I think it will work for the kids who would get the math anyway. I'm skeptical how well it would work with kids who are not already mathematically gifted.
Dumbing down problems so that they can be reasonably solved by hand always bothered me in school. We weren't learning skills we would need in the real world. Real world problems have messy calculations. This guy is right on.
@Scottium True that.. However, there is a limit to which computers can be trusted, I am an engineer, and yup, I trust computers almost completely, but a computer does not give the full picture ever. For example, if we want roots to a polynomial, using newton's method, we can never converge at the right answers but we can get close.. Close is not good enough to mathematicians.
You may not use calculus in the grocery store but an intuitive understanding of it shows a person that it is present in all of reality, and can be used to solve an incredible range of problems if applied correctly. Mathematicians are biased in their view of this because mathematics is a subject so pure in its objectives that it is not concerned with reality, only with which realities are conceptually possible. If we're to teach math to the general public, "reality" is far more relevant.
As a 10 year old, and currently learning calculus & linear algebra for my Cambridge International Math Exam at the end of this year (2011), I do use Maple math software in my learning. Its important to understand how to solve problems by hand first, b4 using computer. Check out my channel web-page, which I have 4 short videos for solving polynomial identities (algebra), differentiation & indefinite integration (calculus) & also 1 for solving 2-variable linear simultaneous equations (algebra).
This is what i've been thinking like for ever!!!! I want kids learning game programing real early ot go hand in hand with physics and math... also kids have way more creativity and energy.. give them the tools and help they need and they can soar... all i had as a kid was delphi and my own bloody minder persistance... sadly i coud only do so much without a good graphical library... but today i have XNA and C# imagine if i had started out with that! and help!
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.
Some kind of balance gotta be struck. I started learning programming when I was 13. I am now 17 and in my first year for Diploma in Electrical and Electronic Engineering. I must say that it was my exposure to computer mathematics that ignited the passion for math in me and it has really helped me a lot more than just doing dumbed down math at the middle/high school level. In fact, I find my math classes right now boring still and make it fun with code. :P
@TheBoneLESS He's not talking about abolishing calculation, just not cramming it down every throat. Even people who are in math heavy industries and have degrees that required years of courses in calculation don't use it the way it was taught, and have forgotten the rest. Think of it this way. Before writing was widespread, bards and troubadours were trained to memorize hundreds of lines of song at a single hearing, because it was needed. Do you really think we ALL still need that skill?
@Martyj2009 The programmers definitely need to learn all the calculating. But not everyone needs to know, just like the car engineering example given in the video.
@Powervids123 There are some things it's valuable to learn by hand, but take a classic example: Long division. Should we be good at long division? I think not. We have calculators that can do it far better than any human. And being good at long division doesn't increase our capacity to form mathematical models of reality. It's all of the things like that that need to be computerized.
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.
So if this idea is applied, then it's learning how to use the "calculating" device that needs to be taught. Try learning to use a scientific calculator, or a complex computer program. In my opinion, it may not be any easier than learning to do math by hand. But I do agree that being able to articulate complex problems and figure out the answers would push us faster in an advantageous direction. I'm just not sure that eliminating the "calculation" stage is how to do it.
@g0m99 But I think he's right in that how we're framing Math is incorrect, and it's conducive to kids not enjoying Math & Sciences. But I think this has a lot to do with Parenting as well.
My key takeaways: Mathematics involves four steps: 1. Posing the right question 2. Translating the real world problem into a mathematical formulation 3. Performing the computation 4. Interpreting the mathematical result in the real world context and verifying its validity Schools focus too much on step 3, which computers can do better than humans, and neglect the other steps, which computers cannot do well and require human creativity and intuition.
Finally! I've always believed the brain should be used for higher order thinking & computers for computation. If we could implant or integrate (including instant connection between the web and the brain), we can get to the next level. But.. i realise my reference is from the other side of really understanding math and application. Given the shortcut, i might only have developed to learn "moving the slider does x" and nothing more. And program procedures can ALSO be learnt without understanding.
@LilSnyperX the grading curve is one of the real problem i think. i understand what you are saying but even in school i did not do RREF or almost any complex calculations after they were first introduced because we already were using TI-83 as well as software like MatchCAD and MATlab which all do that on their own and the instructors encouraged that.
this is obviously still a very new and imature idea, but it shows great potential. the key point is to understand that we have to be more practical in education yet stimulating and make education the reflection of what actually happens in the world. its silly really to cram our brains with so much unecessary information
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.
as a 4th year student for mechanical engineer and math minor i can not even begin to explain my complete agreement with wolfram. I am going to graduate soon and at this moment i feel like i have very little knowledge on anything outside of writing math formulas down and solving them, but dont ask me how any of it relates to the real world. outside of arithmatic, algebra and geometry everything else to do by hand is a frivalous waste of time.
I don't see how what he's saying is different than how math is taught now in HS and College. I used calculators to calculate. I only did things by hand the 1st time we learned them. Math and Computers are how we are being educated today. I used a TI-93 in AP Calculus, on the AP exam there is a section with a calculator and a section without. The section without asks you to solve real word problems. In college we used the Calculator, Maple & Matlab.
@iamwhoiamnow42 I'd actually go a step further, as the speaker does. Basic concepts that are vital to higher math are not all that hard to understand, and some of them can be easily integrated into either math or science classes at a very early level. You could easily integrate basic set theory and propositional logic into existing curriculum wholesale, and there are dozens of easy to understand ideas used in subjects as advanced as vector geometry that don't even require algebra to explain.
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.
This is so true. I loved all my college mathematics courses, but the one I enjoyed best of all was one called Numerical Analysis. Pretty much the entire course consisted of writing programs in Mathematica to solve various sorts of interpolation and extrapolation problems. I learned SO much in that course.
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.
I completely agree. In the name of Math, we are taught arithmetic mostly. I am a highschool student and I sometimes automate my school lessons such as Eucild division algorithm and Chemical Equation Balancing. While automating these stuffs I also get a good grasp of all the procedures. School should focus more on teaching student to think like a real scientist, mathematician
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.
That statement makes me think of Project Euler (I think it's called that, I can't remember for sure), a site with a bunch of mathematical challenges which you are meant to write computer programs to solve.
It's a really neat example of programming used to help you learn mathematics and computer science.
I haven't gotten around to doing much of it myself (though it would be good practice for my problem solving) but I know programmers who swear by it.
I tried, I'm still doing it and loving it.
This agenda doesn't "only" teach practical applications, as you state. Rather, I gathered that practical applications would get more attention. Currently, the vast majority of math instruction focuses on calculating by hand. He is not advocating for the complete elimination of this instruction, but a better balance. Conceptually understanding math by hand was a great benefit to my intellectual development as well.
That's precisely why he talks about practical hand calculations approximating answers, to give you ideas about how the answer should be, and also why he talks about computer program.
Try for yourself, download scheme or python and calculate, say some linear graph like y = 4x -2, with increments being 1.
And experiment with making it more and more general.
This is a basic problem, but getting it right means that you really have to understand how these types of equations work.
When effort is highest- real character is formed. When one develops character they do their best work.
I guess there is a part 2 somewhere in which he actually describes how to change school math.
Bryon Lape
If you purchase of copy of Wolfram Alpha you can prolly type that inquiry into the searchbar and get some pretty interesting algorithms. I'm gonna guess that the trajectory of change for schools will put this solution somewhere in the 35th century. :-/
+Jennifer Grove (Dark Moon) , this is not new in USA, it has been discussed for decades by NCTM, specially their document of 1980 Problem solving: an agenda for action , and the following discussion and additions.
Teaching math through programming is great..we have to do it, but its dumb to say the conventional approaches are irrelevant and dated. Computational approaches can only enrich the analytical methods. not replace them. For example how else can we develop the differential calculus if not by the ab initio methods that involve taking limits of the rate of change as independent variable tends to zero? Without an appreciation of such first principles , its impossible to learn math
Hi, I recognize this is an old response, but he has been working heavily with the government of Estonia (post-Soviet darling of the tech world) to reform their curriculum.
@@premprasad3511 yeah you have to know the algorithm to program the computer.
@chessfan6
i dont know about you but when i was taking calc we didnt just sit and cranked out graphs and equations. It was always learn to concept and then practice it by calculating it. the actual calculations are not hard if you know the concept but by doing them by hand you can see where the error was made while with a computer you often cant (depends on program of course)
What he's saying is what I've been saying since I was in junior high. They make math WAY harder than it actually has to be. They use the wrong type of language to describe what's going on, spend too much time on the tedious aspects and not enough time on building a perspective by explaining the symbolism of equations and the context of procedures. At its heart, math is just like doing a puzzle. It takes more logical computations to talk to people than it does to do calculus.
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.
He makes a compelling and well backed argument. The current way math is taught really is like trying to teach driving by showing how an engine works. Computers are now everywhere and can do many tedious tasks that are no longer necessary for humans do to, but the curriculum has not yet changed in response to this.
As mathematician Paul Erdos once said, mathematics is not about computation, it's about making connections. Let computers do the number crunching.
@anotherelvis if you teach your students the same problems, but allow them to use the computer instead of/in addition to paper, a lot of them may benefit.
If you f.ex. use MS word's integrated formula writer to write formulas and the calculator to do calculations, the students may simply formulate the algorithm (formula) necessary to solve a given problem once, copy it to where they are going to use it, and substitute the variables with their input.
The end result and thought process is the same
Since leaving school I've had two attempts (in my own time) at learning math. Both times I've got to differentiation, managed to do it from first principles, and then stalled and got no further. I think it was the sheer effort involved in the working out that made me lose momentum. I think he has a good point.
Worth remembring there might be a bias as he's got financial interests in Wolfram alpha and Mathematica.
So true. I remember in my HS calculus class, I literally came up to the front of the class a few times to show the teacher and the class why they were arriving at answers different from the answer key. My calculus teacher didn't even understand calculus.
I had a similar experience. I was failing calculus bad at first. I worked so hard. Class working on a big problem. I pointed out they were doing chain rule wrong. So many texts and professors have errors. It's sad we have to verify answers with the answer key. Maybe should have one real world problems that are verified by reality idk I'm not that smart lol
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.
Also, when he suggests writing computer programs, he means writing algorithms that would solve arithmetical problems. Surely, anyone who could write a function from scratch that correctly and efficiently factors any positive integer must have a clear understanding of factorization. I get your point, but writing completely unrelated code that just happens to use a mathematical equation is NOT what he is suggesting.
Continuing the below post....Exeter seems to encourage the use of technology in solving the nightly problem sets. Any and all resource usage is fully encouraged. Many of the problems don't have a "correct answer". HOW students present their solutions (in writing and orally) is just as important as whether their answer is correct (if there even IS a "corrrect answer"). The approach they take is called the Harkness Table method, and they certainly produce some extremely talented students.
I find the approach interesting, as it somewhat forces a rethinking on how we teach math. Especially in a country where math is often regarded skeptically in the first place. I have had so many teachers and instructors that never truly understood the material, which ended up losing the other students. They wanted to learn, but didn't have the proper avenue to follow. Nice presentation, thanks
@Crazylalalalala Highschool went into memorization of formulas with no explanation. Being curious I figured out the reasons behind things on my own which is part of why I managed to get through the terrible system. Our teachers did not understand or have any curiosity beyond what formulas they needed to teach. Formulas with such simple explanations, such as the area of a triangle, were presented as one of a million things to memorize and not to understand the meaning of.
Not necessarily. In my high school calculus class, I was one of the only people who understood related rates. Turns out, it was because, since I had to draw derivative graphs BY HAND, I had a better intuitive understanding of what maximums and minimums meant, and therefore understood how to get the information I needed. (admittedly, this example does not a trend make, and is a correlation-causation case: it may be that because I'm good at math, I never got a calculator, rather than vice-versa)
@Nigrescence
I have to agree with you. Using computers can become a crutch for many people; just plugging a problem and hitting 'solve'.
But I think it is possible to have a curriculum which combines learning things by hand and programming what you learn to solve more difficult and complex problems.
I think it builds character to learn math by hand, but we can also use computers to take shortcuts so we can examine the meat of a problem rather than spending hours getting to that point by hand.
@HarveyMushman85 Programming is the same thing as writing it on paper, but with programming you also learn how to program. Given a word problem, you write down the variables and constants in the order and arrangement that will allow you to come to an answer. You do the same when programming. You must figure out how to arrange the information and determine what operations you do on that information and then you tell the computer how to do it. The student becomes the teacher.
Hobby programming on the old 8bit computers gave me a big head start in learning real Maths
I think what he's saying is valid to a point. If no one knows how to solve d[(x^2)/3x] then we cant create the program to solve it. It is essential to learn the fundamentals of each subset of mathematics (algebra calculus) so that people do know how to do it.
Once the student has those fundamentals, they shouldn't be forced into "grinding them out" them for every subject though. Learn algebra the hard way and when you get into calculus don't worry about the algebraic details as much.
@LeMegasandwich You missed the entire point of the presentation - we're not going to lose those people that go on to a deeper understanding of these concepts, just like not forcing everyone to be a mechanic before they drive a car hasn't limited the progress in developing new means of transportation.
The mechanics are still learning to be mechanics while the rest of us proceed with our lives using transportation in the way it's intended to serve us.
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.
It's been 10 years since this Ted Talk. Have schools made any progress on this? Genuine question. Please share examples.
Teaching calcculation is importat too. Calculating by hand helps us understand how it works, and if we understand how it works we can create new proofs->new rules->new, better methods
I think he has some really valid points here and I think that he's right in not calling this education math, but how to use math. I would have loved to learn math this way, applied concepts would have kept me more interested and focused
I'm sure there will be those that would still want to learn how to solve formulas by hand and that's great. We can driver cars, use computers, travel in planes, and talk on our cell phones without knowing how all the items inside work. They are means to the end
I wish this was the way of teaching maths when I was at school. Last year of school I got a D, retook maths at college, 1st year got an E, retook it again, got an F, took it again, finally pulled of a C. That is 4 years of maths education, the most challenging part of my education so far. Learning maths needs to be done when you are young, and done correctly, and excitingly. Its inspiring to see that those with a passion for teaching maths KNOW how it should be taught.
@digitalcrypt
well as i dont know what your education was like 20-30 years ago i can tell you that mine was not just about calculations. In fact students these days already use fairly advanced programmable calculators that allow you to do all of the time consuming calculations (deferential, integration, matrix, graphs) quickly.
And most of the questions are not just Solve this, the questions usually test your understanding of the math not just how to do it but what does it mean.
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!
An Indian script writer named Ravi Naik, told once that "there's a link between heart and books" when we were talking about the failure of eBook readers in India.
We definitely are going to need some paperwork before we jump to the next level. Computer is about making things faster, and paperwork is about trying to inject the knowledge into ourselves.
Paperwork first, and then programming (same applies for learning basic programming, too). So I believe it would work after sufficient paperwork.
Ten years ago, university teachers were experimenting about how to do this using Wolfram's Mathematica. This stopped when their competitor Maple basically gave their software to bona fide students for their own use, probably reasoning that they would hack it anyway. It would be great to implement what Conrad is suggesting, but Wolfram has got to come up with a better licensing model to recapture this market.
It is important to know how solve mathematical problems without computers. This doesn't mean that the best way to teach people to do this is by teaching hand calculation particularly to the determent of other important aspects of math education. I think Wolfram is at correct in suggesting that the best way to do this is to increase our use of computers in teaching math. While any problem can be solved by hand given enough time we should be teaching efficiently.
I remember doing Calculus 1+2 via Woflram Mathematica and I really didn't gain much out of it, but that's simply because I didn't really find it interesting. When I got to Differential Equations and we did it by hand I learned the material very well and aced it... But that had more to do with the material being useful.
The biggest issue was that the problems they had us do in Calc 1+2 were all basically physics problems we could solve without doing any calculus :/.
@Phyrexious I completely agree with you. I am pretty good at "math", in the "school" sense. I can crunch my way through complex equations, differential equations and stuff, yet I couldn't "use" that skill. As far as 20 minutes ago, I had the concept that "math" was simply a series of calculations, at the end which we get a number or an exact answer. However, as this video explains, math is so much more than just that. Let's stop teaching "math" as we knew it, and focus on the "real" math!
Thesis, although thought-provoking, has at least one problem: there is a difference between analytics and numerical simulation, i.e., going logically through all the steps and just computing. And you need both.
@jamma246, there's no one "correct version" of the abbreviation, only what your ears are used to hearing. The UK says "maths" and the US says "math". They're simply two different abbreviations for the same word, mathematics. I'm guessing that Wolfram probably says "maths" by convention, but since he was doing this presentation in (I think) California, he said "math".
I wish i had learned math this way. The old academic way of math teaching bored me in school since i got the concepts the first lecture, and then spent a lot of time doing mindless repetition. I actually made programs on my calculator in basic to solve the equations because i was so bored with calculating on paper. If i had learned programming + conceptual computational math instead, i'd be a lot better at math. I've been using math in hobby projects since, and learned a lot there.
@zipporapper Me being an engineer and very often requiering some computational muscle, I can't just put the numbers in and expect result, the computer doesn't even know what the hell do you want to do with them. What I allways invariably endout doing is to "teach" the computer how to do what it is that I want to do and then let it crunch the numbers (and sometimes it is faster to just do it by hand).
Source? As a veteran AP Calculus teacher, I'm pretty confident that my colleagues know quite a bit more about math that you do. Most math teachers are required to take several classes of advanced mathematics beyond calculus for their endorsement. And the statement "apply calculus to real life" is about as inane as expecting organic chemistry be taught to "apply to real life". Both are far more useful in a specialized career setting than a mundane one.
Agreed. I tutor students in algebra at my university and they have a computer program that they use. They all start off hating me because I won't let them use a calculator until they've shown they can do the work by hand, but the first time that they catch a mistake (from punching the wrong button on a calculator) before they put it into the program, they feel so powerful. Then they realize they can actually do the stuff and really take the reins because they aren't using computers as crutches.
about time... used LOGO in my classes to encourage programming because the IT subject didn't teach it... BUT the shift that is required, imho, is not technological but social: schools are still factories rather than nexi for genuine enriching engagement whether maths or any other subject...
1 That 17 min talk felt like 5 mins. Really interesting to listen to.
2 From UK, shame we haven't had this new approach to teaching maths trialled in schools.
@Demagogue88, personally I wish I learned calculus before I took physics, because I thought calculus simplified a lot of it. Sure, you can memorize 20 different already-derived formulas and doing a "plug 'n chug" on the right one, but with calculus you can usually just do integrations on ONE formula (e.g., v = ds/dt) to derive what you have to use. Likewise, Diff Eq'ns saved me from having to memorize a lot in thermodynamics classes.
@KawallaBair I implore you to not make assumptions about my abilities or my personal biases against programs for calculations.
I suggest a happy medium because not everyone gets true understanding without the calculations behind a concept. It's 2 fold. The calculations help us check ourselves and avoid automatic assumptions that something is always true. Dynamics are not linear and there is no such thing as "always"
Hand computation is an end in itself since, by virtue of being rational beings, we may derive intrinsic value for computation. Also, even if a majority may believe computation is unpleasant and thus simply a means to an end does not justify that mastering hand computation is unnecessary to the art of problem-solving. Although posing proper questions is essential to problem-solving, working directly with numbers is too. Think of a builder who builds using a computer but never picks up a hammer.
@FmMan33 Solar flares don't affect textbooks nor would it destroy all our electronics. At worst, it would blow out any electronics running at the time in one region of the world. The other side of the world would be just fine.
In any case, any extremely unlikely and limited occurance such as a solar flare is nothing to base a policy around.
Completely agree. Calculating is a right brain activity that develops more than mere methods that will never be applied in the real world. Incoorporating programming and mathematics is a great idea, however, it would limit the accessibility of mathematics education.
as long as the people knows how to do it manually, they can be taught to program it. so this has a point and the only problem to get through is making the children learn the process itself.
You need to do some computation. If you've ever done regression analysis in Stata, Sas, etc, you know what it's like to have no idea why standard errors are changing based on what dependent variables you use, what it means when your computer is complaining about multicolinearity, etc. In higher math, I never fully got the concept of a vector space, topological space, metric space, etc until I went through the routine calculation once or twice of checking the axioms. Point valid but 2 strong.
@Crazylalalalala College improved upon this hugely, because suddenly our instructors were (mostly) people who had the curiosity to be able to explore questions they were asked, they had put a lot of thought into the material, they hadn't just memorized all of the formulas in the world - that kind of lack of understanding we are taught with would never get someone past maybe a bachelors degree in math at best.
he told everything as i really thought of education
i am an engineering student(computer science). im messed up with computer programming. i have back in my c,c++,java subjects. but ive interest in Nature of nature and now i am gonna make them true using real math(PROGRAMMING) jsk
You don't need programming to know that. n^2 = (n+a)(n-a) +a^2 = n^2-a^2+a^2. I know a few other ways squaring numbers. n^2 = (n-a)^2+a(n+a) is another way. Another way is to treat it as a quadratic. For example (10 2)^2 = 100 +40 +4 (put an extra 0 for 10s place and two 0 for 100s place) so it becomes 10000+400+4 = 10404. No programming is necessary.
Using a calculator is exactly like programming, except that usually with the calculator you're still doing part of the algorithm in your head or on paper. Either way you are using an algorithm, if you're solving it correctly. In fact, it's pretty common for us to solve problems on paper before write programs.
@Crazylalalalala I know that is a simple example but in the real world, nobody ever sits down and does calculus. They have computers. The thing calculus gives us is accuracy, but our job (the job of the humans) in the real world is to understand what to calculate, ask the questions. That takes an understanding of the concepts, not the inner workings of equations.
@hypermath
Wolfram Research has, for many years now, provided site licenses to universities and schools that cover all students for their personal computers. If your students don't have access, then talk to your site administrator.
It is certainly our aim that schools that want to use Mathematica for teaching face no practical licensing or deployment barriers.
TO use calculators or not to use is not important. Important is to teach kids to think. Which can be done by :
* asking children questions instead of providing them with the answers
* guiding children to the right solution instead of telling them what to do
* involving children in non-standard and inquiry-based problem solving
* showing children different methods and approaches to solving a problem
* simply asking children “Why do you think this way?”
Yasmina, math4u.ca
@digitalcrypt
sure if you ignore the part that i said that our schools are already focusing on the understanding the meaning and purpose of math and how it applies to eveyone's lives and less on doing by-hand calculations.
our schools are already doing this. It is not a new idea that he presents.
@SuperiorApostate : Except for the fact that it's "Maths". The word is a shortened version of "Mathematics"... not "Mathematic". It's a shortened version of a plural, and hence should also be plural. Ergo : "Maths".
@LilSnyperX
to be honest i did not pay much attention at middle school. mostly because i moved to the USA at that time and didnt know English too well and in general i was not very enthusiastic about leaving Israel. So i cant tell you much about that.
in elementy school in Israel the only thing i do remember specifically is that we work with blocks and other visual tools to learn what the math represents and i do believe that was useful for me. We also competed back then just to show off.
I love wolframalpha, it is a brilliant, brilliant website and one of the most powerfull free tools on the internet! But i have to disagree with the idea of teaching programming rather than learning how to solve maths by hand. You need to know what the machine does, so you can trust the outcome. We have enough blinkered specialists already!
@TheBoneLESS Well, as he points out, part of the problem is that real world problems are often vastly more complex. Of course, if you mean by concrete, a well constructed, highly interactive computer demo of how the integral or derivative of a function relate to the graphs various functions, then we're on the same page. I think you might enjoy a BBC series called "The History of Maths", and if you're really curious, google "MIT ocw" and look at all the stuff they have for math.
@MarkVanDerVoort The steping on Shoulders of giants is only find and dandy if you can climb them to the top.
I loved this. I'm in graduate school, and at the point where the math is so complex no one does it by hand because it would take an extremely long time to do a basic task. So...we don't learn anything by hand. No basics. It works, we may trust it, it has been proven. Instead, we learn what the professor calls "math appreciation". We understand what the computer is doing, and we learn how to do everything but the tedious week-long paper calculation...steps 1, 2, and 4.
Thats so true! School makes you pretty good at calculating stuff absolutely irrelevant to the reality, instead of actually making you understand the processes.
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
As much as I hate calculating things manually, and as much as I love to use wolfram alpha to quickly solve improper integrals, check series convergence or find limits, I don't think that this is the solution to the problem. I don't even think boring computation is the problem with math education. I think he's right that we should focus on the real-world to math (and back) conversion of problems, but I don't think that means we need to eliminate manual computation.
I understood his point to be exactly as you have explained it. I think it will work for the kids who would get the math anyway. I'm skeptical how well it would work with kids who are not already mathematically gifted.
Dumbing down problems so that they can be reasonably solved by hand always bothered me in school. We weren't learning skills we would need in the real world. Real world problems have messy calculations. This guy is right on.
@Scottium
True that.. However, there is a limit to which computers can be trusted, I am an engineer, and yup, I trust computers almost completely, but a computer does not give the full picture ever. For example, if we want roots to a polynomial, using newton's method, we can never converge at the right answers but we can get close.. Close is not good enough to mathematicians.
You may not use calculus in the grocery store but an intuitive understanding of it shows a person that it is present in all of reality, and can be used to solve an incredible range of problems if applied correctly. Mathematicians are biased in their view of this because mathematics is a subject so pure in its objectives that it is not concerned with reality, only with which realities are conceptually possible. If we're to teach math to the general public, "reality" is far more relevant.
As a 10 year old, and currently learning calculus & linear algebra for my Cambridge International Math Exam at the end of this year (2011), I do use Maple math software in my learning. Its important to understand how to solve problems by hand first, b4 using computer. Check out my channel web-page, which I have 4 short videos for solving polynomial identities (algebra), differentiation & indefinite integration (calculus) & also 1 for solving 2-variable linear simultaneous equations (algebra).
Wait calculus at 10. If only I had been as smart as you
This is what i've been thinking like for ever!!!!
I want kids learning game programing real early ot go hand in hand with physics and math... also kids have way more creativity and energy.. give them the tools and help they need and they can soar... all i had as a kid was delphi and my own bloody minder persistance... sadly i coud only do so much without a good graphical library... but today i have XNA and C# imagine if i had started out with that! and help!
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.
Some kind of balance gotta be struck. I started learning programming when I was 13. I am now 17 and in my first year for Diploma in Electrical and Electronic Engineering. I must say that it was my exposure to computer mathematics that ignited the passion for math in me and it has really helped me a lot more than just doing dumbed down math at the middle/high school level. In fact, I find my math classes right now boring still and make it fun with code. :P
@anotherelvis the best math teacher in ireland teaches all his students to use a slide rule
@TheBoneLESS He's not talking about abolishing calculation, just not cramming it down every throat. Even people who are in math heavy industries and have degrees that required years of courses in calculation don't use it the way it was taught, and have forgotten the rest.
Think of it this way. Before writing was widespread, bards and troubadours were trained to memorize hundreds of lines of song at a single hearing, because it was needed. Do you really think we ALL still need that skill?
Would be interesting to have a debate between Wolfram and Stoll.
He's so right, to think we used to use log tables just a few short years ago...
@Martyj2009 The programmers definitely need to learn all the calculating. But not everyone needs to know, just like the car engineering example given in the video.
@Powervids123 There are some things it's valuable to learn by hand, but take a classic example: Long division. Should we be good at long division? I think not. We have calculators that can do it far better than any human. And being good at long division doesn't increase our capacity to form mathematical models of reality. It's all of the things like that that need to be computerized.
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.
THANK YOU!!! This is why I was thinking about this! I just didn't know the problem.
Asking kids to select life insurance would be pretty funny. 14:30
So if this idea is applied, then it's learning how to use the "calculating" device that needs to be taught. Try learning to use a scientific calculator, or a complex computer program. In my opinion, it may not be any easier than learning to do math by hand. But I do agree that being able to articulate complex problems and figure out the answers would push us faster in an advantageous direction. I'm just not sure that eliminating the "calculation" stage is how to do it.
@g0m99 But I think he's right in that how we're framing Math is incorrect, and it's conducive to kids not enjoying Math & Sciences. But I think this has a lot to do with Parenting as well.
My key takeaways:
Mathematics involves four steps:
1. Posing the right question
2. Translating the real world problem into a mathematical formulation
3. Performing the computation
4. Interpreting the mathematical result in the real world context and verifying its validity
Schools focus too much on step 3, which computers can do better than humans, and neglect the other steps, which computers cannot do well and require human creativity and intuition.
Finally! I've always believed the brain should be used for higher order thinking & computers for computation. If we could implant or integrate (including instant connection between the web and the brain), we can get to the next level.
But.. i realise my reference is from the other side of really understanding math and application. Given the shortcut, i might only have developed to learn "moving the slider does x" and nothing more.
And program procedures can ALSO be learnt without understanding.
@LilSnyperX
the grading curve is one of the real problem i think.
i understand what you are saying but even in school i did not do RREF or almost any complex calculations after they were first introduced because we already were using TI-83 as well as software like MatchCAD and MATlab which all do that on their own and the instructors encouraged that.
this is obviously still a very new and imature idea, but it shows great potential. the key point is to understand that we have to be more practical in education yet stimulating and make education the reflection of what actually happens in the world. its silly really to cram our brains with so much unecessary information
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.
as a 4th year student for mechanical engineer and math minor i can not even begin to explain my complete agreement with wolfram. I am going to graduate soon and at this moment i feel like i have very little knowledge on anything outside of writing math formulas down and solving them, but dont ask me how any of it relates to the real world. outside of arithmatic, algebra and geometry everything else to do by hand is a frivalous waste of time.
I don't see how what he's saying is different than how math is taught now in HS and College. I used calculators to calculate. I only did things by hand the 1st time we learned them. Math and Computers are how we are being educated today.
I used a TI-93 in AP Calculus, on the AP exam there is a section with a calculator and a section without. The section without asks you to solve real word problems. In college we used the Calculator, Maple & Matlab.
This guy really hits the bulls eye. I hope this message gets heard by people.
@iamwhoiamnow42 I'd actually go a step further, as the speaker does. Basic concepts that are vital to higher math are not all that hard to understand, and some of them can be easily integrated into either math or science classes at a very early level. You could easily integrate basic set theory and propositional logic into existing curriculum wholesale, and there are dozens of easy to understand ideas used in subjects as advanced as vector geometry that don't even require algebra to explain.
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.
@Ruxistico :-) glad to be of help best thing about KA is that its free