id: 06297470
dt: a
an: 2014c.00626
au: Liu, Chunhua; Schliemann, Analúcia D.; Carraher, David W.
ti: Understanding proportionality: from children’s qualitative intuitions to
quantification.
so: Lindmeier, Anke M. (ed.) et al., Proceedings of the 37th conference of the
International Group for the Psychology of Mathematics Education
“Mathematics learning across the life span", PME 37, Kiel, Germany,
July 28‒August 2, 2013. Vol. 3. Kiel: IPN‒Leibniz Institute for
Science and Mathematics Education at the University of Kiel (ISBN
978-3-89088-289-5). 289-296 (2013).
py: 2013
pu: Kiel: IPN‒Leibniz Institute for Science and Mathematics Education at the
University of Kiel
la: EN
cc: F82 F72
ut: proportionality; qualitative intuitions; quantification; weight; volume;
density; proportional reasoning; ratio
ci:
li:
ab: Summary: We report on 20 elementary school children (ages from 8 to 11) who
made significant progress in understanding proportionality in the
context of quantifying relationships among weight, volume, and density.
We compare the pre- and post-performance for the whole sample and we
examine transcripts from two students whose responses typify those of
many of the participant children. We attempt to show how the particular
materials used (cylinders of different materials, an unconventional
scale, and an unconventional ruler) and the design of the tasks
supported the emergence of proportional reasoning based on ratios among
measures.
rv: