Comparing US and Japanese Elementary School Teachers' Facility for Linking Rational Number Representations

Abstract

Using cognitive ethnography as a guiding framework, we investigated US and Japanese fourth-grade teachers' domain knowledge of key fraction representations in individual interviews. The framework focused on revealing cultural trends in participants' organization of knowledge and their interpretations of that organization. Our analyses of the interviews, which included a representation sorting task, indicated three major differences that defined US and Japanese teachers' approaches to rational number representation: (1) Japanese teachers interpreted all rational number representations as conveying primarily mathematical information, whereas US teachers interpreted only some representations as conveying primarily mathematical information;(2) the US teachers focused more intently on part-whole relations than Japanese in their interpretations; and (3) Japanese teachers more easily linked rational number representations to more advanced upcoming content in the curriculum. A review of US textbooks used by the teachers reflected their consistency with US teachers' interpretations of the representations. These findings imply that strong cultural differences underlay the approaches that teachers in both nations take to rational number representation and that these differences may help explain established crossnational differences in student reasoning.It has been demonstrated that US teachers are less successful than their Asian counterparts in computing correct values as well as providing indepth explanations when given tasks that involve rational number relations (Ma, 1999). A logical extension of Ma's work is to examine the possibility that differences between US and Asian teachers may, in part, be due to the ways they conceive of the various meanings of rational number representations (e.g., part-whole and ratios). We believe that these differences are more accurately interpreted as representative of cultural approaches to rational numbers in the two nations than simply reflecting individual differences in teachers' cognitive capabilities. In this study we adopted a cognitive ethnography framework to study the knowledge that US and Japanese teachers access when working to organize representations for rational numbers.

Preservice elementary school teachers’ knowledge of fractions: a mirror of students’ knowledge?

“…Compared to the large amount of research that focuses on students' knowledge of fractions, little is known, however, about both inservice and preservice teachers' knowledge of fractions (Moseley, et al, 2007;Newton, 2008). This is a critical observation since particularly in elementary education, it is a common misconception that school mathematics is fully understood by the teachers and that it is easy to teach NCTM, 1991;.…”

“…However, constructing a correct and clear conceptual framework is far from trouble-free because of the multifaceted nature of interpretations and representations of fractions . Research more particularly distinguishes five sub-constructs to be mastered by students in order to develop a full understanding of fractions Moseley, Okamoto, & Ishida, 2007). The 'part-whole' sub-construct refers to a continuous quantity, a set or an object divided into parts of equal size Lamon, 97 1999).…”

“…teachers Moseley, et al, 2007;. A cross-cultural study focusing on the division of fractions is the well-known study of Liping .…”

“…We further pointed at the need for more studies focusing on preservice and inservice teachers' knowledge of fractions (Moseley, Okamoto, & Ishida, 2007;Newton, 2008). Given that teacher education is considered to be crucial for teachers to develop a deep understanding of fractions Newton, 2008;Toluk-Ucar, 2009;, and that a major concern related to increasing the mathematics standards expected of students should be teachers' preparation to address these standards Siegler et al, 2010;, we analyzed Flemish preservice teachers' knowledge of fractions in Chapter 4 of this dissertation.…”

“…The review revealed a gap between students' procedural and conceptual knowledge of fractions Post, Cramer, Behr, Lesh, & Harel, 1993;Prediger, 2008), resulting in a rather instrumental understanding of the procedures Prediger, 2008). Regarding the conceptual understanding of fractions, research pointed at a multifaceted nature of fractions ) and distinguished five sub-constructs to be mastered by students in order to develop a full understanding of fractions Moseley et al, 2007). Related sudies revealed that students were most successful in assignments regarding the part-whole sub-construct, and that in general, they had too less knowledge of the other sub-constructs; especially knowledge regarding the measure subconstruct seemed to be lacking .…”