COMPUTER IN MATHS: FRIEND OR FOE
Both article and talk pose some very interesting questions in relation to the use of technology in the teaching of mathematics. Conrad Wolfram critiques the traditional arguments used to prevent the overuse of technology in mathematics towards the end of his talk and this was critical to the arguments put forward. These are views which are often heard and which I myself had a degree of sympathy with (before watching the talk). The notion that people should learn the “basics” before using computers or that computers some how “dumb down” mathematics are very intelligently disected and shown to be effectively nonsense. His challenge to consider what the “basics” really are made me think and I liked his four point definition/summary of what exactly mathematics is (a question not considered enough it would seem). The obsession with computation (stage 3 in Wolfram’s list) is one of the biggest difficulties with the way mathematics is now taught in schools. The point is made very strongly that computation is a means to an end and only part of the mathematical process that students need to understand and be able to utilise. Furthermore, Wolfram puts the whole subject in context by raising important questions about why mathematics is so important and the conundrum that we are now faced with the growing importance of mathematics to the economy (and therefore society) and falling standards in schools. The importance of the education system producing individuals which are of actual use to the economy is a subject that I have touched on previously. The only major problems with the very strong arguments put forward by Wolfram are that we are currently confined by our traditional system of exams (which are not currently planned with computers or their use in mind) and the clear cost implications of providing more computers/technology to schools.
Willingham’s article compliments Wolfram’s talk by considering the detail surrounding the use of technology in teaching. It is clear that Willingham is far less prepared to blindly accept that technolgy is necessarily always a positive for students. He seems to reject the ideas that young people all engage better with the subject matter because of technology or that it is necessarily a good thing that they seem to exist in a permanent state of self-imposed multitasking. I think it is clear that the latter is a negative when deep concentration on one task is required and Willingham seems to suggest that the difference in achievement is stark. This has challenged my opinions in that people of my generation are often in awe at the younger generation’s use of technology, but I think it is now clear that some depth of understanding/engagement may be sacrificed by the fleeting nature of interaction with various modern gadgets: can you really have a conversation with someone, text on a phone and watch television/listen to music and apply yourself to all three/four in equal measure?
A comparison with the Khan Academy is interesting. I think the Khan Academy concept whilst making use of technology is in fact only a platform upon which traditional teaching concepts (not methods) can continue. This is different to Wolfram’s idea that the technology should be used to do the computation part of mathematics, leaving students to concentrate on stages 1, 2 and 4 (in his scheme). In this sense Wolfram’s proposition is far more revolutionary and would require a complete overhall of the way teaching is currently conducted in schools. Khan Academy on the other hand can be used as a tool to complement the status quo without necessarily challenging the key issues of examination and curriculum and the other issues raised by Wolfram.
I have already downloaded and used the Wolfram Alpha app. This is such a clever and practical use of mathematics and far more scientific than a search engine. Rather than being thrown up various websites and invited to find information yourself, the Wolfram Alpha website/app pulls in data and uses algorithms to produce calculation based results for certain questions. This is an excellent tool for objective, yes/no, quantifiable subject matter, but clearly has its limitations with more subjective material.