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11 June 2015 - question three: Concepts

In this issue


The recent question about general statements of mathematical ability produced some helpful replies. In his response comparing the learning of language and maths, Ken Ruthven posed an additional question about receptive and productive competence and the relationship between them. Take a look at his reply, and if you have any knowledge of whether there is any research on this I’d be pleased to hear.

As before, previous questions and conversations are still open to responses, so if you have second or even third thoughts, or want to reply to a posted comment, please do. Please do share these with potentially interested colleagues.

Best wishes

Question 3 - concepts

‘A threshold concept can be considered as akin to a portal,  opening up a new and previously inaccessible way of thinking about something. It represents a transformed way of understanding, or interpreting, or viewing something without which the learner cannot progress’

Meyer and Land (eds) (2006) Overcoming Barriers to Student Understanding: threshold concepts and troublesome knowledge. Routledge.

The new questions have arisen from the reading I’ve been doing about how to populate the framework. In the launch version I used 'threshold tasks' – those that a student would have to be able to do in order to ensure progression to the next ‘stage’. I also included, in the appropriate position, where new concepts would first be introduced. But my reading of Meyer and Land, and others, has focused my thinking on threshold concepts. This links back to Question 2 and mathematical behaviour. I would be really interested on your views about threshold concepts in maths, and whether they are a useful way of defining a framework?

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