
05240173
a
2008a.00052
Norton, Stephen
The construction of proportional reasoning.
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 1015, 2005. Vol 14. Melbourne: University of Melbourne, Dep. of Science and Mathematics Education. Part IV, 1724 (2005).
2005
Melbourne: University of Melbourne, Dep. of Science and Mathematics Education
EN
C33
F83
F43
proportional reasoning
representations of fractions and ratio
arithmetic
cognitive development
multiplicative thinking
empirical investigations
grade 6
lower secondary
emis:proceedings/PME29/PME29RRPapers/PME29Vol4Norton.pdf
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 prepost results indicated this integrated approach helped students to apply proportional reasoning and to enumerate their responses.