id: 06145635
dt: j
an: 2013b.00502
au: Simon, Martin A.; Placa, Nicora
ti: Reasoning about intensive quantities in whole-number multiplication? A
    possible basis for ratio understanding.
so: Learn. Math. 32, No. 2, 35-41 (2012).
py: 2012
pu: FLM Publishing Association, Fredericton, NB
la: EN
cc: F30 F40 F70 F80
ut: multiplication; numbers; mathematical concepts; logical thinking;
    instructional design; ratio; fractions; measurement; quantities
ci: 
li: http://flm-journal.org/index.php?do=details&lang=en&vol=32&num=2&pages=35-41
ab: Summary: One of the challenges of learning ratio concepts is that it
    involves intensive quantities, a type of quantity that is more
    conceptually demanding than those that are evaluated by counting or
    measuring (extensive quantities). In this paper, we engage in an
    exploration of the possibility of developing reasoning about intensive
    quantities during the teaching of whole-number multiplication. The
    investigation is grounded in a measurement-based instructional design
    attempt that built on the Elkonyn-Davydov curricular approach. We
    report on this investigation and resulting implications for learning to
    reason about intensive quantities and understanding ratio concepts.
rv: