
06647468
j
2016f.01086
Wilkie, Karina J.
Students' use of variables and multiple representations in generalizing functional relationships prior to secondary school.
Educ. Stud. Math. 93, No. 3, 333361 (2016).
2016
Springer Netherlands, Dordrecht
EN
H23
H33
C33
algebra teaching and learning
functional thinking
multiple representations
variables
middle years of schooling
doi:10.1007/s106490169703x
Summary: Algebra has been explicit in many school curriculum programs from the early years but there are competing views on what content and approaches are appropriate for different levels of schooling. This study investigated 1213yearold Australian students' algebraic thinking in a hybrid environment of functional and equationbased approaches to learning algebra. This article reports on a survey of 102 students examining their generalization ability and knowledge of multiple representations and variables prior to formal study of algebraic expressions and equations at secondary school. Nearly half of the students demonstrated the ability to generalize explicitly with one fifth able to construct a symbolic functional rule. Nearly half were able to represent a reallife scenario of a linear relationship algebraically. There was little evidence yet of connecting a growing pattern or reallife scenario to an appropriate graphical representation. Level of pattern generalization ability was found to be associated with flexible thinking for exploring functional relationships in reverse and with explaining the inappropriateness of proportional reasoning for linear functions with a constant. Implications for the teaching and learning of algebra are presented.