“Computation meets Knowledge”

Posted by Emma on Jan 2, 2016

Wolfram argues that mathematics has been “liberated from calculating” eliminating the need for step-by-step calculations by hand. He tackles the issue of understanding, stating that programming is an excellent way to illustrate an individual fully understands the procedures and processes behind mathematics. This proposal renders ideas from the likes of Skemp’s ‘instrumental and relational understanding’ and Dweck’s ‘fixed and growth mindset’ somewhat irrelevant. He is arguing that it is not the way in which mathematics is taught which is important but the mathematics itself which is unimportant, as we can get a computer to do that bit for us. He wants computers to take away the maths from education which programmes such as Khan Academy aim to teach us. Wolfram is using the computer technology to do Mathematics so we don’t have to and can concentrate on what comes after the maths while Khan Academy is hung up on us being able to do the calculations and computing tasks either by hand or with a calculator, with little worry or concern for what comes after.

Jo Boaler also criticises the way in which we teach children mathematics and the way we question them in lessons, that the mathematics we teach in classrooms is a distorted picture of what mathematics is in “real-life”. However Boaler argues that it is the questions which are unrealistic and not comparable to real life. Wolfram on the other hand goes one step further stating that an even more realistic mathematics is to get students to spend less time computing sums and calculations and more time posing questions, conceptualising and applying problems. In a way this is echoed by Blair who argues that in a level 4 Inquiry classrooms students should be posing their own problems, finding their own method and determining their own solution. I suppose the difference is that Wolfram would encourage the students to use the computer as the means to the solution.

On the whole, I can see the positives of Wolfram’s ideas however I can’t help finding him somewhat contradictory. He states that there is no need to be calculators that the computers can do this for us but at the same time advocates programming as a measure of a student’s understanding. Surely to have the knowledge and understanding of maths to be able to programme one would need to learn the mathematics he argues is wasting our time? I would add to this that perhaps the classroom should be a space where students are away from technology when young people are spending “more than 7.5 hours per day” on electronic devices (according to Willingham’s article). Daniel Willingham argues that technology should be used as a tool; it’s the way in which you implement the technology not just the fact that the technology exists which makes it useful and relevant in the classroom. He argues that for technology to be successful as a way of increasing student’s engagement it must present a problem as “both challenging and solvable”.

Whether we choose to accept Wolfram’s idea of using computers in the classroom and in exams or not, I think what is almost more important is the way in which we implement this, much as Willingham suggests. The education system should agree wholly to accept this as a means to educate students or not at all, because it would only work with complete enthusiasm and commitment from all.


  1. Glen
    4 January 2016

    Brilliant article! I loved the links to other pieces of work, and really liked the passing comment at the end, I agree without wholehearted acceptance, using technology in that manner would be difficult, however do you believe that the consensus will be difficult to achieve because some teachers are naturally more predisposed to not use technology?

  2. Stephen
    6 January 2016

    Interesting thoughts, I strongly agree that there is a risk of overuse of a techology and blindly using it “because it’s new!”. I feel you have touched upon removing the calculations, however have you considered the implications to the understanding of maths this provides. Would inputting numbers in to a computer to calculate the area be any better than understanding where this has come from. It seems to me if we do fully as Wolframm suggests we may merely be moving from one type of instrumental understanding to another. I wonder what you feel about this?

    I do believe that used correctly Wolframs ideals could go a long way to broadening relational understanding; the operative word being CORRECTLY.

  3. Dom
    9 January 2016

    Emma, your post is very interesting. I liked the way you linked together pieces of information from multiple sources and at the same time you kept the thread of Wolfram’s arguments about implementing technology at school.
    I also agree with you that, the most important thing should be the way in which technology is used rather than accepting it just for the sake of modernity and that maybe students should be spending less time with technology at school, since they already use it a lot during the day.

  4. Senay
    10 January 2016

    I agree with the last sentiment here Emma. What Wolfram is suggesting requires an all or nothing approach – it would be impossible to go down the path he is suggesting without a revolution in the classroom. I think that financial constraints and the current exam system are also important potential obstacles to this philosophy’s success.

    I understood Wolfram in the same way: the idea that computers (by doing the calculating for students) actually leave them free to do more true maths i.e. posing questions, real world application/verification etc. (stages 1,2 and 4 in his four stage description of what mathematics) is very clever.

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