ACT-­‐R modeling to investigate the effect of multiple graphical representations on fraction learning

To improve children's understanding of fractions, many curricula have started to use graphical representations (GRs). These would help children to relate to the problem more than when only a symbolic representation is shown. Moyer et al. (2002) state that the use of GRs can be especially helpful in a computer tutor, because of the interactions that are not possible on paper. The Rational Number Project (RNP, Cramer et al., 1997) recommends using multiple GRs (MGRs) in one curriculum: potentially children could then combine the benefits of the separate GRs. Rau et al. (in press) performed a classroom study with an intelligent tutoring system for fraction learning with 4th and 5th grade students. The study had a between-­‐subjects design with one single GR (SGR) condition and multiple MGR conditions. The MGR conditions tested which pattern of presentation (schedule of practice) of GRs in an MGR tutor is optimal for learning. The results show that the MGR tutor improves children’s knowledge more than the SGR tutor. Furthermore, small differences between the MGR conditions were found. This project used the data from the experiment of Rau et al. (in press) for the development of three ACT-­‐R models. The models are used to investigate the specificity of students' knowledge when learning fractions, especially when using MGRs. It is expected that before using the tutor children have a few general strategies they apply to many different problems, and after the tutor children learned more specific strategies. The different models that are fit to the data represent different levels and types of specialization. Based on students' correct strategies and error strategies, the models compare whether students are more apt to use specific strategies per GR or per problem type. The results show that the tutor increases the number of specific strategies children use per problem type. Moreover, students in the SGR tutor condition sometimes generalize different from students in the MGR conditions.