Computers Vs (Mathematical) Wrestlers
Is maths just finding an answer?
Should we be allowed to wrestle with the numbers and fight our way through to the answer, Jo Boaler suggest that the harder the challenge of the problem the more successful the reward. It is difficult to define what hard is, for any individual, Conrad Wolfram believes it is the concepts that are to be the most challenging things going forward. Why bother wasting much needed space on trivial calculations that most smartphones can compute for us? I feel the point he is aiming towards is perhaps similar to Dan Meyers ideas of allowing more freedom for students to ask their own questions and learning what Jo Boaler suggest to be real maths, patterns and problem solving.
I do feel tha perhaps there is some merit to Wolframs ideas in presenting “calculus” early, whilst the topic shown was nothing to complex the way it was presented and the idea of linking it does seem to be similar to the idea of relational understanding.
When I was taught maths I was always asked, when are you ever going to have a calculator in your everyday life? Hindsight would imply my teachers were shortsighted in the way technology has developed. I do wonder however if as Willingham suggested that given specialists in different areas are capable of chunking and are therefore able to process larger parts of information that to non specialists are complex situations. Does having and understanding basic calculations remove some of the much lauded relational understanding, Skemp, and therefore our ability to “chunk” effectively?
My largest fear is that there will be an over reliance on what Wolfram suggests, why teach effectively when the computer can do it for us? As Willingham suggests in his article merely having the technology does little to nothing to improve teaching practice. If a chalkboard and abacus is all that Japan requires then do we really need some amazing site that can pop out answers at a moments notice? They are after all high up on the PISA ratings.
However it must be said that moderation is key, clearly there are some incredible benefits from using Wolframs site and other new technologies, Virtual Reality?, yet it is only as useful as the context of its use.
I feel perhaps Wolfram could and should listen to some of what I have been taught over the past few months. Multiple methods and representations are a large part of better understanding, not necessarily removing a whole part of maths. I wrote about how instrumental and relational understanding could act synergistically to improve maths skills. Is removing part of this really necessary?
Perhaps there are more uses for Maths than high level concepts. Making sure you aren’t being scammed by doing some maths in your head?
Maybe wrestling with basic concepts has more merit than Wolfram believes, maybe the future is as always a balance between what we have done and what we can do?