[Maths-Education] use of counterexamples in primary classrooms

[Dylan Wiliam]

Interestingly the same "method" of division features in Abbott and
Costello's "In the Navy".


> From: <romlins at rc.unesp.br>
> Reply-To: Mathematics Education discussion forum
> <maths-education at lists.nottingham.ac.uk>
> Date: Thu, 17 May 2007 23:04:45 -0300 (BRT)
> To: Mathematics Education discussion forum
> <maths-education at lists.nottingham.ac.uk>
> Subject: Re: [Maths-Education] use of counterexamples in primary classrooms
> 
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> Dear Tim,
> 
> for some reason I got 'enchanted' by the clip on
> 
> http://youtube.com/watch?v=ieKTU94-BgI
> 
> If it is not propoerly what you were after, maybe it will give you ideas
> (as it gave to me!).
> 
> all the best
> Romulo
> 
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>> 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,
>> Tim
>> _______________________________
>> 
>> Dr Tim Rowland
>> Faculty of Education
>> University of Cambridge
>> 184 Hills Road
>> Cambridge CB2 8PQ
>> England
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