Problem solving in Chinese mathematics education: research and practice

In this study, we used problem posing as a measure of the effect of middle-school curriculum on students' learning in high school. Students using a Standards-based curriculum in middle school performed equally well or better than students who used more traditional curricula in high school. The findings from this study not only show evidence of strengths one might expect of students who used the Standards-based reform curriculum, but also bolster the feasibility and validity of problem posing as a measure of curriculum effect on student learning. In addition, the findings of this study demonstrate the usefulness of employing a qualitative rubric to assess different characteristics of students' responses to the posing tasks. Instructional and methodological implications of this study, as well as future directions for research are discussed.

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“…Student performance was improved by engaging in the problem-posing activities (Cai & Nie, 2007;Lu & Wang, 2006). …”

Section: Problem Posing In the Curriculummentioning

confidence: 99%

Mathematical problem posing as a measure of curricular effect on students' learning

et al. 2012

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“…Our view is that both have served those ends well, enabling the construction of detailed narratives for each of teacher in which could be seen the complex relationship between how teachers think and act (Cohen 1990;Skott 2009Skott , 2013Wilkins 2008). For example, and acknowledging that teachers are conditioned by the cultures in which they work (Andrews 2007;Cai & Nie 2007), it was reassuring to find substantial similarities in the problem-related beliefs, solution procedures and teaching practices of the three teachers that are, we suggest, reflective of a Cypriot perspective on mathematics education in general and problem solving in particular.…”

Section: Discussionmentioning

confidence: 98%

“…For example, Cai and Nie (2007) found significant differences in the beliefs about mathematical problems of Chinese and America teachers, typically deriving from their experiences as learners of mathematics. In similar vein, Andrews' (2007) interview study found Hungarian teachers describing mathematics as a subject based on intellectually challenging problems, which was a perspective largely unrecognised by his English informants, while others have identified substantial culturally constructed differences in the problem solving-related beliefs of preservice primary teachers in Cyprus and England (Xenofontos & Andrews 2012).…”

Section: Teachers' Problem Solving-related Beliefsmentioning

confidence: 99%

Analysing the relationship between the problem-solving-related beliefs, competence and teaching of three Cypriot primary teachers

Andrews

Xenofontos

2014

J Math Teacher Educ

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In this paper we analyse the problem solving-related beliefs, competence and classroom practice of three Cypriot upper-primary teachers. Data derived from semi-structured interviews focused on teachers' beliefs about the nature of mathematical problems, problem solving, and their competence as both problem solvers and teachers of problem solving; clinical interviews during which teachers solved a context-free geometrical problem; and observations of a lesson during which teachers introduced the same geometrical problem to their grade 6 students. Analyses, which were structured by a framework derived from key problem solving literature, indicated firstly, that the framework was an effective tool, being sensitive to variation both within and across the data from the three teachers, and secondly that all three teachers, in largely explicable ways, exhibited both consistency and inconsistency in the ways in which their beliefs, competence and practice interacted. Some implications for further research are discussed.

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“…Some have aimed to provide an account of mathematical problem-solving in Chinese mathematics teaching (e.g., Cai & Nie, 2007;Wong, 2002), while others utilise teaching with variation when accounting for the classroom teaching of 267 mathematics (e.g., Huang & Li, 2009;Park & Leung, 2006). Some research is beginning to use the theory of variation to research the teaching and learning of proof and proving.…”

Section: The Theory Of Teaching With Variationmentioning

confidence: 99%

Proof, Proving, and Teacher-Student Interaction: Theories and Contexts

Jones

Herbst

2012

New ICMI Study Series

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Abstract. This chapter focuses on the teachers' role in teaching proof and proving in the mathematics classroom. Within an over-arching theme of diversity (of countries, curricula, student age-levels, teachers' knowledge), the chapter presents a review of three carefully-selected theories: the theory of socio-mathematical norms, the theory of teaching with variation, and the theory of instructional exchanges. We argue that each theory starts by abstracting from observations of school mathematics classrooms. Each then uses those observations to probe into the teachers' rationality in order to understand what sustains those classroom contexts and how these might be changed. Here, we relate each theory to relevant research on the role of the teacher in the teaching and learning of proof and proving. Our review offers evidence and support for mathematics educators meeting the challenge of theorising about proof and proving in mathematics classrooms across diverse contexts worldwide.

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Problem solving in Chinese mathematics education: research and practice

Cited by 107 publications

References 20 publications

Mathematical problem posing as a measure of curricular effect on students' learning

Mathematical problem posing as a measure of curricular effect on students' learning

Analysing the relationship between the problem-solving-related beliefs, competence and teaching of three Cypriot primary teachers

Proof, Proving, and Teacher-Student Interaction: Theories and Contexts

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