• Research in Mathematical Education
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• v.13 no.2
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• pp.91-101
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• 2009

The mathematics curriculum reform has been carried out for almost five years (2004-2008) in the mainland China. But the teaching and learning in mathematics classrooms still are traditional in nature. Analyzing from the cultural angle, some reasons can be found: the orientation of teachers' role, teaching, and learning, the relationships between a teacher and the students, understanding the mathematics, and examination.

• School Mathematics
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• v.10 no.2
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• pp.199-222
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• 2008

The present study was conducted to review the definitions and methods of teaching reflection and then suggest the criteria for analyzing mathematics teaching reflection. The reason for addressing the teaching reflection, which recently attracts considerable attention, was that it would enhance the professional growth of mathematics teachers. The review of the prior studies shows that the hitherto proposed criteria which could be used for analyzing mathematics teaching reflection are inadequate and unsystematic. Further, it was revealed that the self-assessment checklists put forward by previous studies were overly ramified, and thus it seems that an integrative approach should be taken in order to establish the relevant criteria for analyzing mathematics teaching reflection. Considering these findings, the present study suggests the pre-lesson, in-lesson, and post-lesson criteria for analyzing leaching reflection for the subject of mathematics and the attendant questions posed to teachers.

• Journal for History of Mathematics
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• v.14 no.2
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• pp.61-68
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• 2001

Rationality in mathematics is discussed by analyzing historical facts concerning infinitesimality. Several views containing Platonism, formalism and falsificationism are suggested to analyze rationality.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.1
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• pp.55-78
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• 2001

Given the anisotropic Poisson equation $-{\nabla}{\cdot}{\mathcal{K}}{\nabla}p=f$, one can convert it into a system of two first order PDEs: the Darcy law for the flux $u=-{\mathcal{K}{\nabla}p$ and conservation of mass ${\nabla}{\cdot}u=f$. A very natural mixed finite volume method for this system is to seek the pressure in the nonconforming P1 space and the Darcy velocity in the lowest order Raviart-Thomas space. The equations for these variables are obtained by integrating the two first order systems over the triangular volumes. In this paper we show that such a method is really a standard finite element method with local recovery of the flux in disguise. As a consequence, we compare two approaches in analyzing finite volume methods (FVM) and shed light on the proper way of analyzing non co-volume type of FVM. Numerical results for Dirichlet and Neumann problems are included.

• Research in Mathematical Education
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• v.8 no.1
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• pp.1-18
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• 2004

Current interest in mathematics learning that focuses on understanding, mathematical reasoning and meaning making underscores the need to develop ways of analyzing classrooms that foster these types of learning. In this paper, the author show that the constructs of social and socio-mathematical norms, which grew out of taking a symbolic interactionist perspective, and Toulmins scheme for argumentation, as elaborated for mathematics education by Krummheuer [The ethnology of argumentation. In: The emergence of mathematical meaning: Interaction in classroom cultures (1995, pp. 229-269). Hillsdale, NJ: Erlbaum], provide us with means to analyze aspects of explanation, justification and argumentation in mathematics classrooms, including means through which they can be fostered. Examples from a variety of classrooms are used to clarify how these notions can inform instruction at all levels, from the elementary grades through university-level mathematics.

• Communications of Mathematical Education
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• v.18 no.1 s.18
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• pp.1-18
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• 2004

Current interest in mathematics learning that focuses on understanding, mathematical reasoning and meaning making underscores the need to develop ways of analyzing classrooms that foster these types of learning. In this paper, I show that the constructs of social and sociomathematical norms, which grew out of taking a symbolic interactionist perspective, and Toulmins scheme for argumentation as elaborated for mathematics education by Krummheuer, provide us with means to analyze aspects of explanation justification and argumentation in mathematics classrooms, including means through which they can be fostered. Examples from a variety of classrooms are used to clarify how these notions can inform instruction at all levels, from the elementary grades through university-level mathematics.

• The Mathematical Education
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• v.43 no.1
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• pp.97-107
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• 2004

Current interest in mathematics learning that focuses on understanding, mathematical reasoning and meaning making underscores the need to develop ways of analyzing classrooms that foster these types of learning. In this paper, I show that the constructs of social and sociomathematical norms, which grew out of taking a symbolic interactionist perspective, and Toulmin's scheme for argumentation, as elaborated for mathematics education by Kummheuer, provide us with means to analyze aspects of explanation, justification and argumentation in mathematics classrooms, including means through which they can be fostered. Examples from a variety of classrooms are used to clarify how these notions can inform instruction at all levels, from the elementary grades through university-level mathematics.

• Journal of Elementary Mathematics Education in Korea
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• v.5 no.1
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• pp.121-142
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• 2001

The purpose of this study is to investigate elementary teacher's beliefs and attitudes about mathematics and how those reflect their teaching practices. For this goal : (1) Designing questionnaire to measure elementary teachers' beliefs and attitudes about mathematics (2) Inquiring into character of elementary teacher's beliefs and attitudes about mathematics after analyzing questionnaire (3) Analyzing two teachers' mathematics teaching practices to understand how teacher's beliefs and attitudes affect mathematics teaching practices.

• Research in Mathematical Education
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• v.11 no.1
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• pp.53-63
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• 2007

Mathematics curriculum reform is very important, and it can be understood well by power. This paper uses the extended Foucault's power theory as foundations to view mathematics curriculum reform. The research's case is China's ongoing mathematics curriculum reform. Through analyzing the power relationships in China's ongoing mathematics curriculum reform, the paper thinks that power's balance is very important in mathematics curriculum design, because it will affect the designed curriculum.

• The Mathematical Education
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• v.42 no.2
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• pp.111-119
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• 2003

This research discussed a general concept on the qualitative research methods in mathematics education. It provided a classification of research methods in mathematics education. It also described research trends in mathematics education. It addressed how research design facilitates formulating a research problem, selecting a research design, choosing who and what to study, deciding how to approach Participants, selecting means to collect data choosing how to analyzing data, and interpreting data and applying the analysis. This study addressed the issues involved in choosing relevant populations and in selecting and sampling qualitative data. It described how populations are conceptualized and distinguished between probability sampling and criterion based selection. It discussed not only data arrangement such as, cross-sectional and categorical indexing, non-cross- sectional data organization, but also diagram flow chart matrix, cognitive map, family tree to facilitate analyzing data.