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Topic: Concept Inventories in Mathematics
Replies: 16   Last Post: Sep 28, 2010 9:30 PM

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GS Chandy

Posts: 8,307
From: Hyderabad, Mumbai/Bangalore, India
Registered: 9/29/05
Re: Concept Inventories in Mathematics
Posted: Sep 21, 2010 10:04 PM
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The concept inventory idea would, I believe, be an excellent tool to enable monitoring (including self-monitoring) of progress of learning in math - it could also turn out to be an 'active aid' to learning (see ii below). If, as Richard Hake shows, such constructs are not readily available to the math educator/learner, they should be - a most worthwhile project indeed for some math teachers and educators? See, for instance, 'Concept Inventory' at Wikipedia -

I observe that the OPMS process, about which I have written here, could:

i) Enable concept inventories to be created where they do not exist; and

ii) (Possibly) Lead to a rather more sophisticated type of concept inventory, including an ontology and maps showing how the understanding of one concept could contribute to (/enhance/ support) the understanding of other(s). These maps could, with some small effort, be personalized to suit the abilities/ learning styles* of specific students or groups of students.

I recall that the late John N. Warfield - inventor of the modeling processes underlying the OPMS - had done some exercises with mathematicians and math teachers at George Mason University that foreshadowed the ideas of Concept Inventories as discussed here at ii) above. The "John N. Warfield Collection" held at the library of George Mason University (see should be able to provide access to the related documents.

(*Yes - I do know that some of us think 'learning styles' is not a valid concept. I happen to feel it is - though I have no detailed evidence to support this feeling - however, plenty of references to 'learning styles' do come up via Google).


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