TY - JOUR
T1 - Characteristics of 5th graders' logical development through learning division with decimals
AU - Okazaki, Masakazu
AU - Koyama, Masataka
N1 - Funding Information:
This paper is the elaboration of Okazaki (2003) presented at the PME 27 conference as a Research Report. We would like to thank the referees for their insightful and helpful comments on this paper in the process of reviewing. We also thank the school staff and children who participated in the teaching experiment. This research was funded by the Grant-in-Aid for Scientific Research in Japan Society for the Promotion of Science (No. 14780097 and No. 16700539).
PY - 2005/10
Y1 - 2005/10
N2 - 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.
AB - 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.
KW - Cognitive conflict
KW - Division with decimals
KW - Equilibration
KW - Formal operational thinking
KW - Implicit model
KW - Misconception
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U2 - 10.1007/s10649-005-8123-0
DO - 10.1007/s10649-005-8123-0
M3 - Article
AN - SCOPUS:27944484522
SN - 0013-1954
VL - 60
SP - 217
EP - 251
JO - Educational Studies in Mathematics
JF - Educational Studies in Mathematics
IS - 2
ER -