Cross-National Comparison of Representational Competence

Brenner, Mary E.; Herman, Sally J.; Ho, Hsiu‐Zu; Zimmer, Jules M.

doi:10.2307/749773

Cited by 42 publications

(38 citation statements)

References 20 publications

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“…For example, TIMSS data showed that rational number reasoning is a weakness in US students' performance whereas it is a strength in Asian students' performance (Mullis, Martin, Beaton, Gonzalez, Kelley & Smith, 1997). Differences in performance in rational numbers apparently mirror variations in the types of representation skills that students in the US and Asian nations demonstrate (Brenner, Herman, Ho & Zimmer, 1999). The reasons for why these differences exist remain unclear at present.…”

Section: Comparing Us and Japanese Elementary School Teachers' Facilimentioning

confidence: 84%

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

Moseley

Okamoto

Ishida

2006

Int J Sci Math Educ

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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.

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Section: Comparing Us and Japanese Elementary School Teachers' Facilimentioning

confidence: 84%

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

Moseley

Okamoto

Ishida

2006

Int J Sci Math Educ

View full text Add to dashboard Cite

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“…Alternatively, analysis of the Japanese mathematics curriculum reveals that students there receive a wider range of rational number representations and that they are more often asked to translate between these representations than their US peers (Stevenson, 1985). This suggests that US students, when compared to their Japanese peers, are more highly focused on the features of the part-whole perspective of rational numbers rather than the mathematical relations that compare quantities (Brenner et al, 1999;Mullis et al, 1997). Further, it is important to note that these effects need not be great at any one time, but if constantly applied over extended periods of time could lead to profound differences in the types of mathematical knowledge that students in different nations possess.…”

Section: Discussionmentioning

confidence: 95%

“…Research has indicated that US students' performance is largely dependent on items grounded in this perspective due to the fact that they tend to score more successfully on these items than those based on other perspectives. Even deviations from commonly used part-whole representations are often very difficult for US students (Brenner et al, 1999). In this study the part-whole perspective is identified as a part of a quantity related to its total amount.…”

Section: The Part-whole Perspectivementioning

confidence: 99%

“…However, research in this area has indicated that US students lag behind their peers in other nations in terms of their facility for linking representations of quantity to notation (Brenner et al, 1999). It has also been shown that students' knowledge of rational number concepts is often highly compartmentalized, and not linked to their broader mathematical knowledge (Kerslake, 1991).…”

Section: Introductionmentioning

confidence: 98%

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Students' Early Mathematical Representation Knowledge: The Effects of Emphasizing Single or Multiple Perspectives of the Rational Number Domain in Problem Solving

Moseley

2005

Educ Stud Math

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This study examined changes in 26 fourth-grade students' early conceptions of rational number representations as a function of receiving one of two curricular interventions. The first group of 12 students received a curriculum that emphasized constructing knowledge through extended problem solving with a single perspective of the rational number domain based on part-whole relations. A second group of 14 students received a curriculum that emphasized a more conceptually diverse multiple perspective view of the domain through problem solving with operator and ratio relations. Analyses of the students' rational number knowledge before and after the interventions indicated that students in the single perspective group produced organizations of knowledge that more frequently diverged from a formal domain analysis than those produced by students in the multiple perspective group. Further, students in the single perspective group increased their focus on superficial surface features. Alternatively, students in the multiple perspective group demonstrated an increased focus on operations that more frequently reflected the underlying mathematical relation conveyed by the representation. The findings indicate that an early exposure to more diverse perspectives of rational numbers assists students in developing more interconnected and viable representation knowledge for rational numbers.KEY WORDS: constructivist curricula, early rational number knowledge, elementary students, mathematical representation, problem solving, rational number perspectives Educational Studies in Mathematics (2005) 60: 37-69

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“…For instance, Cai (1995) found that US students compared to their Chinese peers preferred to use visual-related representations in problem-solving, 13 vs. 0%. Brenner et al's (1999) study reported that the Chinese students appeared relatively weak on some visual representation items, on which the US students performed well. It seems to us from this textbook analysis that the US students likely have more experience with the visual-related representations as well as heuristics, which is positively associated with their problem-solving behavior.…”

Section: Illustration Of Problem-solving Heuristics In the Representamentioning

confidence: 94%

Representation of problem-solving procedures: A comparative look at China, Singapore, and US mathematics textbooks

2007

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This study examined how selected school mathematics textbooks in China, Singapore, and USA at the lower secondary grade level represent problem-solving procedures. The analysis of problem-solving procedures was carried out in two layersgeneral strategies, which adopted Pólya's four-stage problem-solving model, and specific strategies, which consisted of 17 different problem-solving heuristics such as 'acting it out,' 'looking for a pattern,' 'working backwards,' etc. Both similarities and differences in the representation of problem-solving procedures in the textbooks across the three countries were revealed and compared. The possible reasons for the similarities and especially for the differences were explored. Suggestions about how to improve the representation of problem-solving in mathematics textbooks were provided at the end of the study.

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Cross-National Comparison of Representational Competence

Cited by 42 publications

References 20 publications

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

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

Students' Early Mathematical Representation Knowledge: The Effects of Emphasizing Single or Multiple Perspectives of the Rational Number Domain in Problem Solving

Representation of problem-solving procedures: A comparative look at China, Singapore, and US mathematics textbooks

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