| Affiliation: | (1) Department of Mathematics, Joetsu University of Education, 1, Yamayashiki, Joetsu City 943-8512, Japan;(2) Department of Mathematics Education Graduate School of Education, Hiroshima University, 1-1-1, Kagamiyama, Higashi-Hiroshima City 739-8524, Japan |
| Abstract: | When we consider the gap between mathematics at elementary and secondary levels, and given the logical nature of mathematics at the latter level, it can be seen as important that the aspects of children's logical development in the upper grades in elementary school be clarified. In this study we focus on the teaching and learning of “division with decimals” in a 5th grade classroom, because it is well known to be difficult for children to understand the meaning of division with decimals, caused by certain conceptions which children have implicitly or explicitly. In this paper we discuss how children develop their logical reasoning beyond such difficulties/misconceptions in the process of making sense of division with decimals in the classroom setting. We then suggest that children's explanations based on two kinds of reversibility (inversion and reciprocity) are effective in overcoming the difficulties/misconceptions related to division with decimals, and that they enable children to conceive multiplication and division as a system of operations. |
