Fraction calculation—A didactic approach to constructing mathematical networks

Two groups totalling 76 sixth graders (two classes, 38 students each) were trained in fraction calculation by their teachers. The treatment group was trained by means of PT (progressive transformation) didactics, based on semantic memory theory and developed in close cooperation with the math teachers. The main goal was to induce a special disposition in the studentsʹ mathematical thinking while dealing with fractions. The control group was taught within a traditional math education framework. Training in the treatment group always started with a well-understood base problem that was then progressively transformed (PT didactics), having the students focus primarily on relational aspects between the elements and the operations of the series of transformed problems, thereby leading them to construct network-type knowledge representations. PT didactics was supposed to foster conceptual mathematical thinking such that the treatment group should be superior in dealing with fraction problems that require more than mere algorithmic operations. The data supported the hypothesis. Further support for network-type knowledge representation stems from extensive thinking-aloud tests with a subsample of the two groups. Moreover, PT didactics led high-IQ students to exploit their intellectual potential to a greater degree in conceptual problem solving than low-IQ students. This was not the case with mere procedural fraction problems.