Conceptual and procedural knowledge of fractions are improved but not integrated by instruction. In Drew H. Bailey (Chair), Advances in research on fraction learning: from cognitive processes to mathematical achievement. Symposium conducted at the biennial meeting of the European Association for Research on Learning and Instruction (EARLI)

Studies from several decades and continents showed that fraction arithmetic is a particularly difficult subdomain of mathematics for students. Students’ procedural knowledge about fraction arithmetic is oftentimes incomplete and includes faulty strategies. Several authors suggested that a lack of conceptual understanding might underlie students’ problems with acquiring and using the correct computational procedures. The integration of fraction concepts and fraction procedures might help students to better understand which procedural strategies are correct and when they can be applied. In the current study, we investigated with 193 students how the absolute amounts of conceptual and procedural knowledge as well as their intercorrelations vary between Grade 5 and Grade 7 as well as between three regions with different curricula (Flanders in Belgium, Baden-Wurttemberg and Brandenburg in Germany). The results indicate strong main effects for grade level and region along with substantial interaction effects on the amounts of knowledge. All forms of instruction provided in the three regions improved students’ fraction concepts and procedures but differed in when and how strongly they did. In contrast, the correlations between conceptual and procedural knowledge were small and not significantly different from zero for almost all combinations of grade level and region. Instruction in all three regions increased knowledge without integrating it. Even students with high conceptual knowledge were apparently not able to apply this knowledge on procedural tasks. The results demonstrate the need for experiments and field studies into how instructional strategies can foster the integration of fraction concepts and procedures.status: publishe