• The Mathematical Education
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• v.52 no.4
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• pp.567-586
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• 2013

The purpose of this study was to introduce the Knowledge Quartet (KQ) framework by which we can analyze teacher knowledge revealed in teaching mathematics. Specifically, this paper addressed how the KQ framework has been developed and employed in the context of research on teacher knowledge. In order to make the framework accessible, this paper analyzed an elementary school teacher's knowledge in teaching her fifth grade students how to figure out the area of a trapezoid using the four dimensions of the KQ (i.e., foundation, transformation, connection, and contingency). This paper is expected to provide mathematics educators with a basis of understanding the nature of teacher knowledge in teaching mathematics and to induce further detailed analyses of teacher knowledge using some dimensions of the KQ framework.

• Journal of the Korean School Mathematics Society
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• v.16 no.4
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• pp.695-717
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• 2013

Teacher knowledge needed for teaching is bound to be revealed in teaching the subject matter in relation to the given instructional context. Given this, recent studies on mathematics teacher knowledge tend to analyze actual Mathematical Knowledge in Teaching [MKiT]. This study focused on the dimension of transformation and its related codes in Knowledge Quartet, which has been recognized as a MKiT framework, and analyzed a Korean teacher's transformation knowledge revealed in her elementary mathematics teaching. The analysis showed that the codes related to the dimension of transformation were useful in analyzing teacher knowledge in the Korean context. However, a few codes need to be revised or added for more suitability. On the basis of these results, this paper closes with implications for analyzing teacher knowledge in mathematics teaching.

• Journal of Educational Research in Mathematics
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• v.26 no.3
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• pp.421-442
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• 2016

This study analyzed characteristics which emerged while 38 secondary school teachers observed a video clip about a centroid of triangles instruction. The aim of this study based on the analysis was to deduce implications in terms of the various means which would enhance teachers' knowledge in teaching mathematics and assist in designing mathematics education programs for teachers and professional development initiatives. To achieve this goal, this research firstly reviewed previous studies relevant to the 'Knowledge Quartet' as a framework of analyzing teachers' knowledge in mathematics instructions. Secondly, this study probed the observation results from the teachers in the light of the KQ. Therefore, some issues in the teacher education program for teaching mathematics were thirdly identified in the categories of 'Foundation', 'Transformation', 'Connection', and 'Contingency' based on the analysis. This research inspires the elaboration of what features have with regard to effective teachers' knowledge in teaching mathematics through the analyzing process and additionally the elucidation of essential matters related to mathematics education on the basis of the analyzed results.