for the learning of mathematics

an international journal of mathematics education

Sean Larsen - Vol. 30 Num. 1 (2010)
 Struggling to untangle the associative and commutative properties


In the context of a teaching experiment in elementary group theory, interesting difficulties arose as undergraduate students struggled to make sense of the meaning of the associative property as they reinvented the group concept. A subsequent exploration of the research literature revealed similar difficulties have been observed in research with teachers and middle school children. Drawing on this literature and the theory of Realistic Mathematics Education, an analysis of these difficulties is presented in order to develop an explanation.