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\input zb-matheduc
\iteman{ZMATH 2015c.00639}
\itemau{Beckmann, Sybilla; Izs\'ak, Andrew}
\itemti{Variable parts: a new perspective on proportional relationships and linear functions.}
\itemso{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).}
\itemab
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.
\itemrv{~}
\itemcc{F80 I20}
\itemut{proportional relationships; multiplicative relationship; linear functions; ratio}
\itemli{}
\end