Development of thirdgrade students’ combinative reasoning inscience context

Abstract

Combinative reasoning enables us to enumerate constructs from different elements, based on specific conditions. It is essential for applying higher order thinking skills such as scientific reasoning or problem solving. The development of combinatorial reasoning is usually a part of mathematics education, and there are only a limited number of examples of developmental programs targeting this skill in science context.The aim of our research was to test our six week program for developing six combinatorial operations of the reasoning of third grade students (9-10-year-old) in science context. The sample included seven classes of three elementary schools in Budapest (Nexperimental=92, Ncontrol=73). The developmental program was based on Csapó’stheoretical model (1988, 2003). It contained nine tasks for each operation, a total of 54 new combinatorial tasks. The tasks were distributed evenly, with students working on three tasks for each of three operations selected for every week. The developmental tasks had a story line embedded in a science context, and the program was taught as a part of regular curricular lessons. The skill was assessed in pre-and posttest with the digitalised version of Csapó’s combinative test (Csapó andPásztor,2015) through the eDia (Electronic Diagnostic Assessment) platform via internet in the schools’ ICT labs.Combinatorial reasoning developed significantly for both the experimental and the control group. However, the average development of the experimental group (17,9%) is almost the double of the development of the control group (8,2%). The effect size of the program is moderate (Cohen’s d=0,57). Improvement in performance was significantly higher for students who had lower scores on the pre-test, so the program proved to be more effective for children with lower initial levels of the skill. There were no significant gender differences in the pre-and posttest, either in the experimental or in the control group. Of the six operations targeted, the program was effective for the three that proved most difficult in the pretest, and the difference is significant regarding these operations compared to the control group. The relations between the tasks depended on the types of the operations. In the cluster analysis, variation and combination tasks were in the same cluster for both the experimental and the control group.The results showed that the program is effective: the combinative reasoning tasks embedded in science context can be effectively applied at early school age. However, further research is required to explore the long term and transfer effects of this short term developmental program.