Margreet Vogelzang - ACT-R modeling to investigate the effect of multiple graphical representations in fractions

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, Bolyard, & Spikell, (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) did 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 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 an ACT-R model. The model is used to investigate the generality of students' knowledge when learning fractions, especially with MGRs. Different models are fit to the data, representing different generalizations. Based on students' correct strategies and error strategies, it compares whether students are more apt to generalize over GRs or over task types. The results show that the tutor changes the way children generalize over problems. Moreover, students in the SGR tutor condition sometimes generalize differently than students in the MGR conditions.