Tracing the development of representational flexibility and problem solving in fraction addition: A longitudinal study
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The study models the development of students' multiple-representation flexibility and the use of problem-solving strategies and representations in fraction addition. A test administered three times, with breaks of 3-4 months between successive measurements to 108 students at a transition within primary school (Grade 5-6), 132 students at a transition from primary to secondary education (Grade 6-7) and 148 students at a transition within secondary school (Grade 7-8). Multivariate analysis of variance for repeated measures and dynamic structural equation modelling were carried out in order to analyse the data. Findings suggested that students' performance improve through measurements. Dynamic modelling provided evidence for the strong interrelation between representational flexibility and problem solving at the three measurements. The results indicated the students' established pre-existent knowledge and the important role the initial state of the aforementioned cognitive parameters plays on their advancement. Didactical implications are discussed. © 2013 © 2013 Taylor and Francis Group, LLC.