Time, Space and Mathematics……….The final frontier?
The Khan Academy, introduced to us by Sal Khan, is not an unfamiliar resource. I have on occasion found it extremely useful when investigating and exploring mathematical problems. The subjects covered being diverse and invariably covered in an intuitive and user friendly way. I did therefore find it extremely interesting that it has been developed and adopted as a tool for teaching Mathematics and would be fascinated to discover whether four or five years later the results are as impressive as early signs indicate they may be. (The Tedtalk looked to be recorded in 2011.)*
Unsurprisingly both Khan and Daniel Willingham suggest that a child learns best when they can progress at a speed that is suitable to them, which was also argued by both Skemp and Meyer previously. Furthermore the idea’s inherent in the articles and the videos have been taken further, particularly by Khan, who at least offered a dynamic alternative to standardised testing.
However, once again I was challenged by Willingham’s argument regarding the three levels of knowledge, factual, procedural and conceptual. I believe that procedural and conceptual lie very closely with Skemp’s ideas of relational and instrumental understanding and it is very likely that we can’t have one without the other. The links between the two being far more intricate than I have previously given them credit for.
It also made me ponder whether factual knowledge is often misconstrued as ‘instinct’. I will give you an example. ‘Instinct’ dictates to us that touching something that is hot will hurt, however toddlers have to be constantly reminded until they ‘instinctively’ know that they will undoubtedly hurt themselves if they try to touch something deemed hot. Isn’t this why we teach children the times tables constantly until they can answer without thought? Isn’t this perhaps the foundation for ‘brain training’, an awakening of the synapses within our brains that eventually lead to a better understanding of the foundations of mathematics? I don’t know, but perhaps it is worth considering.
I also find it very interesting that a Professor of Cognitive Science, a study of the mind and intelligence, generates similar arguments to others involved in the practice of teaching maths as to how the subject can be best taught. That the psychological limitations that we place upon ourselves can be reversed, that ability measured, whether gifted or not, could come down to timing! (Khan) and that we are all born with the ‘equipment’ to be fairly proficient at maths.
This suggests to me that at a fundamental level we need to get those we are teaching into the right mind set before attempting basic principles, that a ‘can do’ attitude is at least as important as ability and that a ‘one-size’ fits all approach could in fact end up alienating more students than teaching.
*perhaps something that needs further investigation.