• Journal of Gifted/Talented Education
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• v.23 no.6
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• pp.1077-1098
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• 2013

Science gifted students enrolled in a program, where classes had either explicit or implicit instruction about self-directed learning, were asked to write what was satisfying after each class. This process was part of the evaluation of the program. Students' descriptions related to self-directed learning are compared in these two classes, one with explicit instruction and the other with implicit instruction. First, most of the components related to self-directed learning, which were reported in the previous research articles, were mentioned in students evaluation. If there was any specific description regarding what was satisfying, there were components of self-directed learning. Students descriptions were consistent with list of self-directed learning components, which was constructed based on the previous research. Therefore it may be concluded that students recognized most of the reported self-directed learning components and satisfied with them. Second, There were differences in the evaluation of two types of classes. The evaluation of class with explicit instruction contained more self-directed learning components more frequently. For example, students worked in small groups in both classes. However more students mentioned small groups in classes with explicit instruction. As a result the explicit instruction appears to be more effective for students to recognize the self-directed learning components. However some of the components mentioned in classes with implicit instruction were not mentioned in the classes with explicit instruction. Therefore classes with explicit and implicit instructions are complimentary with each other and both instructions are necessary.

• Journal for History of Mathematics
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• v.20 no.4
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• pp.23-48
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• 2007

This study begins from posing a problem, 'formal introduction of mathematical induction in school mathematics'. Most students may learn the mathematical induction at the level of instrumental understanding without meaningful understanding about its meaning and structure. To improve this didactical situation, we research on the historical progress of mathematical induction from implicit use in greek mathematics to formalization by Pascal and Fermat. And we identify various types of thinking included in the developmental process: recursion, regression, analytic thinking, synthetic thinking. In special, we focused on the role of regression in mathematical induction, and then from that role we induce the implications for teaching mathematical induction in school mathematics.

• Journal of the Korean School Mathematics Society
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• v.9 no.3
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• pp.265-286
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• 2006

Given that less attention has been paid to teachers than students in mathematics education, this study attempted to provide theoretical foundations to understand better mathematics teacher learning and teaching practice in transition. First, this paper summarized three conceptions of teacher learning on the basis of the relationships of knowledge and practice followed by several implications to mathematics teacher education. Second, this paper provided a brief overview of cognition as situated, social, and distributed. This paper then explored new implications and issues about mathematics teacher learning that the overview brought to light. It is expected for teacher educators and researchers to participate in rich discussion of many implicit issues about teacher learning that this paper begins to raise.

• School Mathematics
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• v.11 no.1
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• pp.111-129
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• 2009

This paper is about didactical transposition, which is to transpose academic knowledge into practical knowledge intended to teach. The research questions are addressed as follows. 1. Are the 13 mathematics textbooks of the 10-Na level indisputable regarding with the didactical transposition, in terms that the order of arrangement and the way of explaining the knowledge of trigonometric functions being analyzed and that its logical construction and students' understandings are considered? 2. Can some transpositions for easier use of didactical manipulative, for more practical and for more principle based be proposed? To answer these questions, this research examined previous studies of mathematics education, specifically the organization of the textbook and the trigonometric functions, and also compared orders of arranging and ways of explaining trigonometric functions from the perspective of didactical transposition of 13 versions of the 10-Na level reorganized under the 7th curriculum. The paper investigated what lacks in the present textbook and sought a teaching guideline of trigonometric functions(especially about sector and graph, period, characters of trigonometric function, and sine rule).