id: 06434113
dt: a
an: 2015c.00639
au: Beckmann, Sybilla; Izsák, Andrew
ti: Variable parts: a new perspective on proportional relationships and linear
functions.
so: Nicol, Cynthia (ed.) et al., Proceedings of the 38th conference of the
International Group for the Psychology of Mathematics Education
“Mathematics education at the edge", PME 38 held jointly with the
36th conference of PME-NA, Vancouver, Canada, July 15‒20, 2014, Vol.
2. [s. l.]: International Group for the Psychology of Mathematics
Education (ISBN 978-0-86491-360-9/set; 978-0-86491-362-3/v.2). 113-120
(2014).
py: 2014
pu: [s. l.]: International Group for the Psychology of Mathematics Education
la: EN
cc: F80 I20
ut: proportional relationships; multiplicative relationship; linear functions;
ratio
ci:
li:
ab: Summary: We present a mathematical analysis that distinguishes two
quantitative perspectives on ratios and proportional relationships:
Multiple batches and variable parts. We argue that (a) existing
research on proportional relationships has addressed multiple batches
but has largely overlooked variable parts, (b) multiple batches makes
the co-variation aspect of proportional relationships more explicit,
while variable parts makes the fixed multiplicative relationship
between two quantities more explicit, (c) the distinction between
multiple batches and variable parts is orthogonal to the
within-measure-space versus between-measure-space ratio distinction,
and (d) variable parts affords promising new approaches for addressing
linear relationships.
rv: