don steward
mathematics teaching 10 ~ 16

Saturday, 5 March 2016


this idea was researched by G Noelting (1980) ' the development of proportional reasoning and the ratio concept'

students should be given the opportunity (i.e. time) to debate
with the teacher remaining silent or encouraging other views to be aired, "I wonder if that is right?"
"anyone disagree?"

at some stage techniques will need to be considered though...

reversing the question could include:
can you devise proportions where
the concentrations are the same?
where A is slightly more concentrated than B?
where A is twice as concentrated as B?

there is much interesting analysis of the development of multiplicative reasoning available

I particularly like the account of strategies adopted by two 11 to 12 year old students, Karen and Alice,  written about by Parmjit Singh
Karen is more confidently (flexibly) able to unitise and then compose these, iteratively, to a result

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