[Maths-Education] use of counterexamples in primary classrooms

tr202 at cam.ac.uk tr202 at cam.ac.uk
Thu May 17 17:19:45 BST 2007

I'm interested in the use of examples in mathematics teaching, and have a 
collection of examples of such uses, especially in the teaching of concepts 
and procedures.

What I don't have is much in the way of 'real' examples of the use of 
counterexamples in primary (say, grades K to 6) mathematics teaching. I'm 
looking for situation where someone makes a claim, or a conjecture, and a 
counterexample is offered (by the teacher, or by a student) intended to 
refute the claim. A case in point would be Chapter 4 of Liping Ma's 
'Knowing and teaching elementary mathematics', where teachers offer 
counterexamples to refute a claim about a connection between perimeter and 
area. But that was an interview situation, whereas I'm looking for examples 
from 'live' classrooms.

I'd be grateful if anyone would share an anecdote or recollection of such 
an example, with me or the list.

Many thanks,

Dr Tim Rowland
Faculty of Education
University of Cambridge
184 Hills Road
Cambridge CB2 8PQ

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