Conrad Wolfram

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Who could best contribute to the ideas of computer-based math education?

Based on the vision I set forth in my TED talk, we're hosting a key summit in London this November to drive a worldwide change to computer-based math education (http://www.computerbasedmath.org/events/londonsummit2011/index.html). Very interested in ideas of who could best contribute? And I'm not just talking educators but leaders who want radical change and have a stake in the future of STEM education. We've already got many countries, governments and quite a few fields represented but really want to make sure we don't miss key people out.

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    Sep 17 2011: To me it's not teaching maths at all. Maths is part of a toolkit for innovation and learning. It's very important but so are many other tools.

    I know many mathematicians and physicists, computer scientists who would struggle to change a car tyre or work out how to mend a broken pipe. The Engineering capability is lost when we dive straight in. Given this ability and then the extremely powerful tool that is computers we can make enormous differences. I believe it's before children can use computers, even before reading a writing the creative capability of using stuff around them as tools to get other stuff working is paramount, missing out this part is like putting a child in a fast car, they may get somewhere fast and not necessarily know how they did, i.e. they will struggle to make better cars or transport.

    So my opinion is teach problem solving pre-computer and with computers eventually (with reading and writing). This way people will understand at the deepest level.

    You can drive without really knowing how a clutch works or how to get around a faulty handbrake etc., you will just drive better when you do.
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      Sep 21 2011: I'd like to see schools use Chess as an alternative to mathematics.
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        Sep 25 2011: Chess as an alternative to Math? Or to teach math?

        I had a teacher use poker to teach statistics. It was the first time all term the light bulb went on for many of the students. The thought of using Chess would bring in logic and planninig. I like that.
    • Sep 29 2011: I'm not convinced that it's important enough to know how a clutch works to teach that to students who are learning to drive. Yes, you can argue that students would drive better if they understood the inner workings of a clutch but, how much better would students be and for how much effort? And, what would you replace in the curriculum to spend time on that skill?
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        Sep 29 2011: I agree to an extent but also think it's a failure to not teach to this level. Take for instance all the people taught about aerodynamics and lift and now we realise that was flawed, or perhaps if it transpires some particles break light speed. (we lost 600 years of maths from not believing in zero, were we right to do that or even to take on zero as existing at all ? we still cannot really answer this and yet rarely teach children about the serious issues of zero or infinity etc.)

        If these people were never taught first principles (or how a clutch works) then all their knowledge on these subjects is very much limited and taking on new ideas will be so much more difficult.

        It's a problem of progress, we leave behind many things (like ability to light fires or prepare and cook food in the wild etc.). When we expand these issues we leave behind to scientific and Engineering type subjects in particular then I believe there could be bad consequences.

        It's a balance to get right and no real right or wrong, just a balance and first we need to recodnise it.

        I take your point, perhaps everyone does not need to know everything, but it sure helps to know more that we sometimes do.
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    • Sep 29 2011: Agreed. The children are very important here. Not only should the children provide input on the value of already created computer-based learning modules but their input is also valuable to guide the development of new modules. And, in some cases, I can see students doing the module development themselves.
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    Oct 10 2011: As a student preparing to become a math teacher, I think it would be valuable to include teacher educators in the discussion. These are the people who are teaching tomorrow's teachers the methods behind mathematics instruction.

    I am currently working on my senior research paper, which is focused on using technology and project based mathematics (real world applications) to build student engagement and content retention. Through my various field experiences, I have seen teachers using projects to connect middle school students, and the results are incredible! Imagine if more teachers were taught to think of math this way! I applaud your efforts, Mr. Wolfram, and cannot wait to be involved in change!
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    Oct 6 2011: Why not invite someone from Apple to talk about how the iPad is being used in education? Speaking of which, how great wouldn't it be to have Mathematica running on it..?
  • Sep 26 2011: An important component of teaching is the interaction between teacher and student, and quite frankly, I do not see how this can be replicated in computer-based education.
    • Sep 29 2011: As I responded to Rudy below, we're not trying to replace the interaction between teacher and student. Here's what I wrote.

      "The conventional classroom is important in the computer-based math world. Teacher instruction, group discussions, and classroom exercises are all important."
  • Sep 21 2011: What I have been kicking around for a couple of years is that there needs to be an education marketplace. Given that content is cheep (MIT open courseware) and there is a trend to test via computers in private industry. The big gap validation of identity and storing transcripts.

    Maybe a e-bay for education content?

    One worry was will this take teachers out of the picture. It is my belief that it will create even more demand.

    Think of what could be done in a place like Haiti. Free education, and a system based on ability and desire.

    Just a though.
  • Sep 17 2011: I just watched your video, and I believe if you use computers for only step 3 of your four steps, you're eliminating the tedium, but not improving the learning. When mathematicians see a page filled with Greek letters and arcane symbols, they visualize the problem. For them those symbols are like words in a story. They instinctively make the connection between the symbols and their meaning. Now consider how language learning uses computers. The computer presents a sentence or plays the audio and the screen illustrates what is being said. Math needs to do that. Computers are great for visualization, and I don't mean with graphs and pie charts; I mean in terms of the real world. If students can be taught to make the connection between mathematical symbols and the real world, then they can use math to solve real world problems. I don't mean to suggest that this is easy. Even though "word problems" have been trying to make that connection for centuries, some students have particular difficulty with "word problems." For them, it's not a connection at all, because the pieces of the connection and how they are assembled together is a mystery to them. When I was learning math, I always though of it as a type of puzzle or a game. Computers are great at games. I think if you talk with the Serious Games community, you might get some ideas. Unfortunately, a lot of that keeps too much of the "game" and forgets that the technology is just the vehicle used to illustrate the principles, but you might get some useful ideas.
    • Oct 6 2011: Some students learn math for its own sake, via math puzzles and games. I was one of those students and today I still enjoy the recreational side of math. Most students, however, are preparing for a career where math is used but where it's not the major focus. Few students will become professional mathematicians although many will use math in engineering, finance, chemistry, architecture and other careers. At computerbasedmath.org we are trying to simultaneously teach conceptual learning and also learning to think the way professionals think about math. And we aim to teach students to use computers the way professionals use computers. Teaching students to read math the way musicians read music is something we need explore and see how we can fit it into the learning materials we are developing. Thanks for the ideas.
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    Oct 13 2011: I have waited to the end date to see all the other comments before I write my own. I have seen Conrad ted talk many times. Though some people were not interested,I have shared it with many people . I have seen more than 200 Ted talks ,but Conrad talk is by far the best one for me. That may be because I am a victim of bad math eduction .I remember during in mindless drills in elementary schools while I was in elementary school and junior high school.But my mind stopped accepting probably after I was grade 11.In my country Ethiopia ,most architects,engineers ,chemistry don't use math advanced than algebra.Students ,teaches fail to get the real purpose of mathematics.I remember once my highschool English teacher saying that the purpose of square roots and simultaneous equation is to broaden and exercise you mind. The thing that has kept from giving up on math education in my country is the excellent textbooks and nine resources out there. Modern textbooks like Stewart calculus have excellent content and projects to induce real math understanding.I have uploaded some pictures
    http://www.mypicx.com/uploadimg/522916619_10132011_1.png
    http://www.mypicx.com/uploadimg/1128109856_10132011_2.png
    http://www.mypicx.com/uploadimg/159747351_10132011_3.png
    http://www.mypicx.com/uploadimg/852067881_10132011_4.png
    Properly using this tools with the super tools like mathemaica and wolfram alpha can transform math from "following steps" subject" to a subject interesting ,applicable subject. Using computers properly one can focus its mind on the big picture . I think I can be a great help to the computer based math education . I can bring the perceptive from a developing country .
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    Oct 6 2011: I'd say you should invite her - http://www.youtube.com/user/Vihart

    Vi may not be a specialist in math software, but she definitely knows how to make understanding math interesting and fun.
  • Sep 29 2011: I work for Conrad Wolfram, supporting computerbasedmath.org. Both Conrad and I are grateful for all of your comments. I've replied to a number of them.
  • Sep 25 2011: No one better than Sal Kahn. See him on TED, youtube or khanacadamy.org.
  • Sep 25 2011: I think tapping the collective body of knowledge from parents, math teachers, and perhaps gifted students that are close to the age of those forming the target learning population. Here are some ideas:
    1. Computer games where increased advantage in play could be achieved by applying age appropriate math techniques. Not equations, but scenarios where how to apply the math was part of the puzzle. Tapping the competitive nature of kids might be a good motivator for on-line competition. Make new math knowledge like a new toy. We just need to provide applications and games that are a playground to show off the new toy and enjoy it.
    2. Perhaps have contests for best child developed game, learning technique, or applications.
    3. Work with Scouting organizations to integrate math projects in the programs.
    4. If you could earn the scholastic equivalent of “frequent flyer miles” on-line for extra age appropriate math work accomplished, sort of earning points or “education dollars” honored by academic institutions and perhaps co-subsidized by industry and government, that might be an immediate and progressive positive feedback mechanism that would appeal to kids.
    5. Industry adding some cool perks to the existing scholastic mathematics competitions, like meeting Bill Gates, Conrad Wolfram, key Scientists, Mathematicians, Nobel laureates, etc.
    6. Kids like catching adults making mistakes. Perhaps we offer so many of the points from 4 above for the first one to identify a mistake in any published document.
    7. Personalize great math discoveries. Talk about the lives of great mathematicians. Put in perspective the inovativeness of the time.
    8. Have a design completion where communication of design decisions using math was the key factor.
    9. Per Bloom, we need to inject knowledge, comprehension, application, analysis, synthesis and evaluation to the critical thinking process. Teachers need to make math learning a critical thinking process.
    10. Motivate thinking adults.
    • Sep 29 2011: Robert, excellent suggestions. Thank you. I'll respond in more detail when I respond to the next batch of comments.
  • Sep 25 2011: Ever since I saw this TED video a few months ago, I've felt like I was training to be a menial worker, learning in school how to compute integral problems which could easily be solved by a computer, but not thoroughly learning the concept of derivatives or integrals and not learning at all how to map a problem to an equation. There is some computer-based problem solving in computer programming classes, but it is rather limited, and one is only expected to employ logic, not other mathematics. I wish my school had already adopted your suggestions.
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    Sep 23 2011: second post

    ...continued
    You see I am not all together certain that “better tools or models” is the answer, maybe one answer but not the answer. In my experience those that do very well in math are in a minority while those that do ok are the majority, those that don’t do well at all are also in a minority, albeit a far less glorious one. I wonder if more work and research should be done on those that don’t get it instead of those that do. It seems likely to me and something that you have stated in your video, that it may indeed be a conceptual predilection.
    Personally I am beginning to think the problem with math is not the model. Rather another communication tool that is severely limiting and interfering with the conceptual structure tools needed to “get” maths….that is human language and not just spoken. It is finite but inaccurate, wonderfully expressive but imprecise. It is absolutely the tool that is used to construct conceptual structures yet the tool is hopelessly inadequate to the task. The sooner we turn from alphabetical to numerical communication the better.

    So, in this sense…
    I believe what you are suggesting is crucial to the continued evolutional advancement of humanity.
    • Sep 29 2011: I don't think the point of computerbasedmath.org is to build a better model. We're looking at how professionals (not just mathematicians but engineers, economists, architects, medical researchers, and many others) use math in the careers and creating the kinds of learning experiences that will prepare students to think like these professionals and to use computers the way professionals use them in the real world. Math has advanced tremendously in the last 50 years but if you look at what's taught in text books, especially for young learners, the content hasn't changed. We're drilling kids to death and having them perform tedious calculations by hand that no professional today would do by hand. So, if we're creating a model I guess the model is "learn how professionals think and use math and teach that."
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    Sep 23 2011: two posts.
    Conrad Wolfram,
    I have seen your video and applaud your model. Is it the right model? Who can know…but certainly it appears a greater (dare I say it) “holistic” model that has been delivered before and delivers hope.

    My math skills are appalling; in fact it remains an embarrassment to me on a personal level. I don’t mind that other people know that I don’t get math… but I feel embarrassed for myself. I am not an unintelligent person, I am no Einstein either. I am a creative individual, an accomplished professional musician and can do most things I put my mind too. Yet I have a block to math.

    It may be an emotional knee-jerk reaction but I do get a sense of “it’s easy for you to say” when I hear people stating that the answer to the problem of math in education is a better model. As an example; Being a musician I find it amazing that some people have such a hard time learning music, while those that haven’t a clue at all (in moments of shameful weakness) I wonder if they just didn’t try hard enough. But it doesn’t stop there. There is another side to professional musicians where some can read (music) and perform but not create spontaneously, where others can perform and create spontaneously but cannot read. Could they all learn to read and create…in most cases I believe so… but the divide is there in the first place not because they did not possess a better model, but because it was conceptually hard for them to learn that particular skill set....continued
  • Sep 22 2011: I guess not all children will appreciate the idea nor understand math through simulations and graphic representations. however, using such technology to aide in understanding the complex behaviour of math equations would somehow add value to the conventional classroom setting. I gues both should work together.
    • Sep 29 2011: Simulations and graphic representations are just two ways of learning that use computers. Among other things students can program computers, they can perform research with them, they can synthesize information based on their research, and they can analyze and verify data provided by computer programs. And, yes, the conventional classroom is important in the computer-based math world. Teacher instruction, group discussions, and classroom exercises are all important.
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    • Sep 29 2011: Yes, video games and math can be a nice combination and, yes, visualizing Calculus concepts is a great use of computers. And, thanks for the link to the protein folding article. I'm very excited about the integration of social networking with math education. Crowd-sourcing, citizen science, and other ways that people connect on the Web are great ways for our social natures to be a key part of the learning process.
  • Sep 21 2011: *The Quest to Learn team: http://q2l.org/team
    *The many people setting up charter schools in the UK
    *University teachers and students of game design.
    *The Dyson foundation
    *Sudhir Karandikar

    I hope this hellps. Best of luck with this worthy project!
  • Sep 17 2011: Unfortunately, a lot of teachers (and other key professions) don't have the programming skills to understand the difference IT can really make. Once a child has learnt some basic programming skills, he/she will not require any further description of what a variable is and why you need it. It becomes obvious. I think programming would be a huge step forward to help children really understand maths. Even better if it's also connected to science.

    I think you need people who use this in their everyday life. Engineers and programmers. E.g. Simulation programs are amazing tools to develop and improve technology. A lot of things that can be computed now were not possible in the past. I could imagine people in that sector could help with the 'convincing educators' bit.

    I remember being at school and just not realising what the hell maths is for and how it is used (apart from giving the right amount of change at a shopping till). It was once I realised that it is a short cut und incredibly powerful that I got interested. Computing helped me get decent maths A-levels in a fraction of the time you would usually require. I was almost angry afterwards. I remember thinking, "that was really easy and I can't believe they (and I) wasted so much time".

    I'm not going to wait for teachers to catch up. My daughter is starting programming next week. The only difficulty I face is getting a teenager to do something that is just so 'uncool'. If I can get her through the first weeks/months - and she starts really understanding - then we've made it and the rest will be a breeze. Hopefully, she'll then have more time to go to the cinema or lie around in a hammock - because we can make the whole process quicker and more efficient - which I think is really cool.

    I'm cheesed off that I have to do that. I'd rather do other things after work. I'm paying tax for an education system that is still stuck in the last century. Maybe you also need some parents with IT skills to move this on.
    • Sep 29 2011: Yes, programming is an important skill especially for solving math problems that are procedure oriented. Problems related to counting things or to simulating events, for example, lend themselves very well to programming. Probability and statistics classes are particularly well-suited to programming exercises.
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      Oct 12 2011: One of the most powerful tools I had for learning mathematics was a programmable computer. This was the age of the Apple II (with BASIC-in-ROM), and you had to write (or at least copy) almost all the software you used.Seeing how algorithms worked from the "ground up" by learning to program in a simple language like BASIC was tremendously useful. Like Christine says, concepts like variables become crystal-clear in any form of programming. Matrices are another mathematical concept that becomes clear once you've used an array in a programming language.

      On a similar theme, I now use Excel spreadsheets to teach simple mathematical modeling to 2-year college students. It's really neat to see the students become empowered to analyze real-world data using such a ubiquitous tool. It's also another way computers could be used to help students grasp concepts like variables (every variable in Excel is a box on the screen referenced by a column/row address).

      I think a critically important concept when applying computers to math education is to make sure students *understand* the how and the why of what the software shows them on the screen. Software developers tend to be in the habit of shielding all the messy details from the user in deference to a polished presentation, but when you're using computers to teach math, the students really need to see what's going on "inside" so to speak. Programming the computer to do a specific mathematical task addresses this need nicely.
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    Sep 14 2011: Richard Rusczyk of Art of Problem Solving would be my first choice.
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    Sep 13 2011: Salman Khan would be my first choice. I would also suggest major players in the gaming industry because in terms of engagement with technology there is no tech-sector that is better. Try people from World of Warcraft, Zynga, or Sony because they all have games that have the models that are appropriate for math education.
    • Sep 29 2011: Thanks for the suggestions. Regarding Salman Khan - we'd be happy to welcome him because it would be nice to see his methodologies applied to computerbasedmath.org rather than just traditional math.

      Regarding the game community -- I do believe that there is much we can learn from how video games engage students but I'm not impressed by how most video games are too focused on mindless drilling.
      • Sep 30 2011: It's not clear to me what you mean by applying his methods to computerbasedmath.org. I don't find much on that website other than a link to the Wolfram Demonstration Project and some examples of using Mathematica from the Wolfram blog. While Mathematica is useful for running simulations, it is not a teaching metholodogy.

        I disagree with the theme of Conrad Wolfram's talk, that the teaching of math should be replaced with the teaching of computer programming. The two fields overlap in many ways, but their fundamental concepts are quite different. The mathematical concepts have to be understood before they can be implemented as a computer program.

        A good computer programmer is one who understands the domain to which the programming is being applied: engineering, finance, meteorology, music, and so on. To say that one could learn math by programming it, is equivalent to saying one could learn music by programming it. The fact that computers use binary arithmetic in their implementation is irrelevant. They use electric signals and solid state physics as well, but it would be folly to suggest that one could learn band theory simply by programming, without the background physics.

        Salman Khan uses computers in a very different way. He uses computers as his medium, as a time machine for his lectures. He uses it for analysis of the students progress. I think Wolfram is held back by his view of computers as just powerful calculators. TED itself is an example that computers are much more than that.

        I think to improve the teaching of math, you must first understand what the current problems are. Khan uses computers to fix the problem that one pace of teaching does not fit all. If that were the only problem, we'd be done now. Wolfram didn't really outline the problem that he was trying to fix, he just said that learning to calculate is a waste of time.

        So what are the specific problems?
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    Sep 13 2011: After completing the Irish leaving certificate, i believe that many students and teachers of math at both 2nd and 3rd levee would be there best people to contribute to ideas of computer based math education, I for one believe that it would have been a massive help as the computer system could test and teach the student, helping them strengthening their weak points