Characteristics of 5th graders' logical development through learning division with decimals

Masakazu Okazaki, Masataka Koyama

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)217-251
Number of pages35
JournalEducational Studies in Mathematics
Issue number2
Publication statusPublished - Oct 2005
Externally publishedYes


  • Cognitive conflict
  • Division with decimals
  • Equilibration
  • Formal operational thinking
  • Implicit model
  • Misconception

ASJC Scopus subject areas

  • Mathematics(all)
  • Education


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