“Computation meets Knowledge”
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.