• The Mathematical Education
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• v.51 no.1
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• pp.77-88
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• 2012

This qualitative research provides a situation model, which is designed for promoting learning of eigenvalue and eigenvector. This study also demonstrates the usefulness of the model through a small groups discussion. Particularly, participants of the discussion were asked to decide the numbers of milk cows in order to make constant amounts of cheese production. Through such discussions, subjects understood the notion of eigenvalue and eigenvector. This study has following implications. First of all, the present research finds significance of situation model. A situation model is useful to promote learning of mathematical notions. Subjects learn the notion of eigenvalue and eigenvector through the situation model without difficulty. In addition, this research demonstrates potentials of small groups discussion. Learners participate in discussion more actively under small group debates. Such active interaction is necessary for situation model. Moreover, this study emphasizes the role of teachers by showing that patience and encouragement of teachers promote students' feeling of achievement. The role of teachers are also important in conveying a meaning of eigenvalue and eigenvector. Therefore, this study concludes that experience of learning the notion of eigenvalue and eigenvector thorough situation model is important for teachers in future.

• Research in Mathematical Education
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• v.19 no.2
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• pp.101-115
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• 2015

In the present paper, we argue any research concerning human knowledge construction, components, or types needs to clarify its epistemological stance regarding 'knowledge' in that such viewpoint might have much influence on the nature of knowledge the researcher sees and the way in which evidence for knowledge development is gathered. Thus, we suggest two alternative research groups who conducted their studies on mathematical knowledge for teaching with an explicit epistemological standpoint. We finalize our discussion by reviewing concrete examples in the previous literature on teacher knowledge of fraction conducted by the two groups.

• Journal of Educational Research in Mathematics
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• v.23 no.4
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• pp.449-466
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• 2013

Mathematical discussion has been highlighted so that what students do actually guides their learning of mathematics and mathematical practice. However, the work of leading mathematical discussions has not yet been specified in such a way that it can be adequately studied and taught to teachers. This study analyzes a teacher's lessons that show full engagement in leading discussions, and examines the work of leading mathematical discussions in elementary classrooms. It identifies and illustrates the central tasks of leading mathematical discussions with single case questions with five steps. This article argues several key issues in leading mathematical discussions: helping students engage in struggling with important mathematical ideas, treating mathematical connections in an explicit and public way to have coherent and structured discussions, and parsing the work of teaching at a grain size that is usable in educating teachers.

• Journal of Educational Research in Mathematics
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• v.24 no.2
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• pp.125-143
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• 2014

In this study, we analyzed a mathematical discussion in the Calculus II course of the Gifted Science Academy and individual interviews to determine the relationship between cognitive conflicts and commognitive conflicts. The mathematical discussion began with a question from a student who seemed to have a cognitive conflict about the osculating plane of a space curve. The results indicated that the commognitive conflicts were resolved by ritualizing and using the socially constructed knowledge, but cognitive conflicts were not resolved. Furthermore, we found that the cause of the cognitive conflict resulted from the student's imperfect analogical reasoning and the reflective discourse about it could be a learning opportunity for overcoming the conflict. These findings imply that cognitive conflicts can trigger the appearance of commognitive conflicts, but the elimination of commognitive conflicts does not imply that cognitive conflicts are resolved.

• Journal of the Chungcheong Mathematical Society
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• v.11 no.1
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• pp.185-192
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• 1998

We briefly review the $S^1$-equivariant cohomology theory of a finite dimensional compact oriented $S^1$-manifold and extend our discussion in infinite dimensional case.

• Research in Mathematical Education
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• v.7 no.1
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• pp.11-24
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• 2003

The key features of our integrated approach to teaching and loaming college mathematics include interactive and discussion-based teaching, small group work, computer as a tool, problem solving approach, open approach, mathematics in context, emphasis on mathematical thinking and creativity, and writing/communicating about mathematics. In this paper we report a few examples to illustrate the type of problems we use in our integrated approach.

• The Mathematical Education
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• v.49 no.3
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• pp.343-351
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• 2010

In this paper, we take the survey through both papers and recent reports to investigate points to be considered in developing the national mathematical curriculum. Then we suggest that to prepare the next national mathematical curriculum, we consider the method to deduce the math-dislike, the method to increase the power of problem solving etc. and also we construct a compact curriculum which contains most of important math items. In the process of developing the curriculum, we must have lively discussion with mathematicians, and especially with teachers.

• Journal of the Korean School Mathematics Society
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• v.20 no.2
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• pp.187-210
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• 2017

The animated discussion about mathematical modeling that had studied consistently in Korea since 1990s has flourished, because mathematical modeling was involved in the teaching-learning method to improve problem solving competency on 2015 reformed mathematics curriculum. In an attempt to re-examine the educational value and necessity of application to school education field, this study was to review the literature of mathematical modeling in mathematical competencies perspective. As a result, mathematical modeling could not only be involved the components of problem solving competency, but also support other competencies; reasoning, creativity-amalgamation, data-processing, communication, and attitude -practice. In this regard, This paper suggested the necessity of the discussion about the position of mathematical modeling in mathematical competencies and the active use of mathematical modeling tasks in mathematics textbook or school classes.

• Research in Mathematical Education
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• v.15 no.4
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• pp.327-340
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• 2011

In this paper we propose an inquiry task on the subject of congruent triangles. The task deals with conditions that are sufficient for congruency, and conditions that are insufficient. The aim of the task is to find the minimal number of identical components in two triangles that is sufficient to ensure congruency.

• Bulletin of the Korean Mathematical Society
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• v.35 no.3
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• pp.421-431
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• 1998

We characterize real 4-dimensional Kahler metrices which are critical for natural quadratic Riemannian functionals defined on the space of all Riemannian metrics. In particular we show that such critical Kahler surfaces are either Einstein or have zero scalar curvature. We also make some discussion on criticality in the space of Kahler metrics.