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'

the powerpoint is here

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 available for the emergent development of multiplicative reasoning

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