Abstract
This thesis reports the findings of a three-year longitudinal research project set up to investigate the effectiveness of employing online mini-games for the learning of multiplication and division, including multiplicative fact knowledge (declarative knowledge), multiplicative operation skills (procedural knowledge), and insight in multiplicative number relations (conceptual knowledge). A large number
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of primary school students was followed from end Grade 1 to end Grade 4. The first study in this thesis examined the students’ initial multiplicative ability at the end of Grade 1, just before multiplication and division were formally introduced. It was found that the students could already solve quite some multiplicative problems (58% correct). Especially problems involving equal groups and problems including pictures with countable objects were often solved correctly. Furthermore, students’ performance was influenced by parental education and by the mathematics textbook used. The second study was on the effects of multiplicative mini-games in Grade 2. A cluster randomized experiment was used, with four conditions: playing multiplicative mini-games at school, integrated in a lesson (E1), playing multiplicative mini-games at home without attention at school (E2), playing multiplicative mini-games at home with debriefing at school (E3), and a control group (C) in which mini-games on other mathematics domains were played at school. Learning effects were investigated using a pre- and posttest including multiplicative operation skills and insight. When comparing each experimental condition to the control group, a marginally significant effect was found for the E3 condition (p = .07, d = 0.23); for the other conditions no effects were found. The third study investigated the effects of the mini-games in both Grade 2 and Grade 3. Effects were examined on multiplicative fact knowledge, operation skills, and insight in multiplicative number relations. The games were found to be effective both in condition E1 and E3 in enhancing insight, and in condition E3 also in enhancing operation skills (ds ranging from 0.22 to 0.35). In the E2 condition the games were only effective for students with above-average prior mathematics ability. Time and effort spent on the games was in some cases, but not always, related to learning outcomes. Furthermore, in Grade 2 the games were more effective for boys than for girls. The fourth study examined the effectiveness of the mini-games in special primary education (Grade 2). Here, only the E1 and C condition were included. It was found that the multiplicative mini-games positively affected students’ multiplicative fact knowledge as compared to the control group (d = 0.39). For multiplicative operation skills and insight (measured with a combined test) there was no difference with the control group. The fifth study investigated the development of regular primary education students’ attitude towards mathematics, from end Grade 1 to end Grade 4. In accordance with earlier studies, mathematics attitude was found to decrease over the years. Girls had a more positive mathematics attitude than boys, and relations were found between mathematics attitude and mathematics achievement. Finally, time and effort spent on the mini-games was a significant, but weak, predictor of later mathematics attitude.
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