An Analysis of Fraction Operation Sense to Enhance Early Algebraic Thinking
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While many studies on early algebra have been conducted, there have been only a few studies on the operation sense as the fundamental element of algebraic thinking, especially the fraction operation sense. This study explored the dimensions of fraction operation sense and then investigated students’ fraction operation sense. A total of 183 of sixth graders were surveyed and 5 students who showed high operation sense were clinically interviewed in order to analyze their algebraic thinking in detail. The results showed that students had a tendency to use direct calculation or employ inappropriate operation sense rather than to use the structure of operation or the relation between operations on the basis of algebraic thinking. This study implies that explicit instruction on early algebra is necessary from the elementary school years
Abstract
While many studies on early algebra have been conducted, there have been only a few studies on the operation sense as the fundamental element of algebraic thinking, especially the fraction operation sense. This study explored the dimensions of fraction operation sense and then investigated students’ fraction operation sense. A total of 183 of sixth graders were surveyed and 5 students who showed high operation sense were clinically interviewed in order to analyze their algebraic thinking in detail. The results showed that students had a tendency to use direct calculation or employ inappropriate operation sense rather than to use the structure of operation or the relation between operations on the basis of algebraic thinking. This study implies that explicit instruction on early algebra is necessary from the elementary school years
참고문헌 (19)
- Bastable, V, "Classroom stories: Examples of elementary students engaged in early algebra, In Algebra in the early grades", pp.165~184 (2008), Lawrence Erlbaum Associates
- Boester, T, "Visualizing algebraic reasoning, In Algebra in the early grades", pp.211~234 (2008), Lawrence Erlbaum Associates
- Carpenter, T. P, "Thinking mathematically: Integrating arithmetic and algebra in elementary school" (2003), Heinemann
- Carraher, D. W, "Early algebra and algebraic reasoning, In Second handbook of research on mathematics teaching and learning" (2007), Information Age Publishing
- Carraher, D. W, "Early algebra is not the same as algebra early, In Algebra in the early grades", pp.235~272 (2008), Lawrence Erlbaum Associates
- Huinker, D., "Examining dimensions of fraction operation sense, In Making sense of fractions, ratios, and proportions", pp.72~78 (2002), NCTM
- Kaput, J. J, "Algebra in the early grades", pp.5~17 (2008), Lawrence Erlbaum Associates
- Kaput, J. J, "from a symbolization point of view, In Algebra in the early grades", pp.19~56 (2008), Lawrence Erlbaum Associates
- Kilpatrick, J, "A history of algebra in the school curriculum, In Algebra and algebraic thinking in school mathematics", pp.3~18 (2008), NCTM
- Lee, J, "An analysis of fraction operation sense to enhance early algebraic thinking", the 12th International Congress on Mathematical Education (ICME-12) (2012)
- Markovits, Z, "The ability of sixth grade students in Korea and Israel to cope with number sense tasks", the 31st Conf. of the Int. Group for the Psychology of Mathematics Education (PME-31), (3), pp.241~248 (2007)
- Mason, J, "Making use of children's powers to produce algebraic thinking, In Algebra in the early grades", pp.19~41 (2008), Lawrence Erlbaum Associates
- Schifter, D, "Developing operation sense as a foundation for algebra. Paper presented at the annual meeting of the American Educational Research Association", the annual meeting of the American Educational Research Association (1997)
- Schifter, D, "Early algebra: What does understanding the laws of arithmetic mean in the elementary grades?, In Algebra in the early grades", pp.413~447 (2008), Lawrence Erlbaum Associates
- Schoenfeld, A. H, "Algebra in the early grades", pp.479~510 (2008), Lawrence Erlbaum Associates
- Slavit, D, "The role of operation sense in transitions from arithmetic to algebraic thought", Educational Studies in Mathematics, 37(3), pp.251~274 (1999)
- Smith, J. P, "Quantitative reasoning and the development of algebraic reasoning, In Algebra in the early grades" (2008), Lawrence Erlbaum Associates
- Verschaffel. L, "Whole number concepts and operations, In Second handbook of research on mathematics teaching and learning", pp.557~628 (2007), Information Age Publishing
- Wu. H. H, "How to prepare students for algebra", American Educator, 25(2), pp.10~17 (2001)