\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2008a.00052}
\itemau{Norton, Stephen}
\itemti{The construction of proportional reasoning.}
\itemso{Chick, H. L. (ed.) et al., Proceedings of the 29th annual conference of the International Group for the Psychology of Mathematics Education, PME 29, Melbourne, Australia, July 10--15, 2005. Vol 1-4. Melbourne: University of Melbourne, Dep. of Science and Mathematics Education. Part IV, 17-24 (2005).}
\itemab
Summary: The development of proportional reasoning has long been recognised as a central but problematic aspect of mathematics learning. In a Year 6 teaching intervention the part/whole notion of fractions was distinguished from the part:part notion of ratio, and the "between" and "within" relationships in ratio were emphasised. Numerous representations of fractions and ratio including LEGO construction activities were used to develop the multiplicative thinking associated with these concepts. The pre-post results indicated this integrated approach helped students to apply proportional reasoning and to enumerate their responses.
\itemrv{~}
\itemcc{C33 F83 F43}
\itemut{proportional reasoning; representations of fractions and ratio; arithmetic; cognitive development; multiplicative thinking; empirical investigations; grade 6; lower secondary; }
\itemli{emis:proceedings/PME29/PME29RRPapers/PME29Vol4Norton.pdf}
\end