• School Mathematics
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• v.14 no.2
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• pp.233-253
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• 2012

The purpose of the study investigate mathematics content knowledge(MCK) of prospective teachers in differential area. 70 prospective teachers were asked to perform six questions based on Cho's MCK (2010, 2011). The results show that depending on whether they experience any teacher education program, the level of prospective teachers' mathematics content knowledge may vary. In particular, prospective teachers struggled with an unfamiliar problem situations. We also found that prospective mathematics teachers have some difficulty in solving problem about the use of mean value theorem and derivative.

• The Mathematical Education
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• v.54 no.3
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• pp.207-222
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• 2015

Mathematics preservice teachers' Mathematical Content Knowledge ("MCK") includes not only knowledge for mathematics, but also academic knowledge for school mathematics and mathematical process knowledge. We can consider the items in PISA 2012 as suitable tools to assess process knowledge as well as mathematical content knowledge because these items are developed by competent international educational experts. Therefore, the responses to items with the low percentage of correct answers in conjunction with the mathematical contents were analyzed with focus on FMC. The results showed the reasoning competency in responses using the conditions of the problem and of understanding the conditions after reading the complex problems within the context (i.e. the reasoning and argumentation competency, and communication competency) requires improvements. Furthermore the results indicated the errors due to a lack of ability of devising strategies for problem solving. Based on the foregoing results, the implications towards the directions of the education for the preservice mathematics teachers have been derived.

• School Mathematics
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• v.13 no.2
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• pp.345-362
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• 2011

This paper addresses mathematics content knowledge required for teaching in secondary school. Three components of mathematical knowledge are needed for teaching: (i) knowing school mathematics, (ii) knowing process of school mathematics, (iii) making connections between school mathematics and advanced mathematics. We investigated mathematics content knowledge of secondary teachers. We found that secondary mathematics teachers have a lack of understanding in solving realistic problem, reasoning and proof, and making connections between school mathematics and advanced mathematics.

• School Mathematics
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• v.16 no.4
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• pp.763-782
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• 2014

The purpose of this study is to investigate mathematics content knowledge(MCK) of pre-service teachers about the area of a circle. 53 pre-service teachers were asked to perform four tasks based on the central ideas of measurement for the area of a circle. The results of this study are as follows. First, pre-service teachers had some difficulty in describing the meaning of the area of a circle. Quite a few of them didn't recognize the necessity of counting the number of area units. Secondly, pre-service teachers had insufficient content knowledge about the central ideas of measurement for the area of a circle such as partitioning, unit iteration, rearranging, structuring an array and approximation. Lastly, few pre-service teachers understood the concept of actual infinity. Most students regarded the rectangle as the figure having the approximation error instead of the limitation from rearranging the parts of a circle.

• School Mathematics
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• v.15 no.4
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• pp.995-1013
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• 2013

The purpose of this paper was to investigate mathematics teachers' mathematical content knowledge about quadratic curves. Three components of mathematical knowledge are needed for teaching: (i) knowing school mathematics, (ii) knowing process of school mathematics, (iii) making connections between school mathematics and advanced mathematics. 24 mathematics teachers were asked to perform 10 questions based on mathematics curriculum. The results showed that mathematics teachers had some difficulties in conic section definitions and eccentricity definitions of ellipse and hyperbola. And they also got difficulty in Dandellin sphere proof of the equivalence of conic section definitions and quadratic curve definitions. Especially, no one answered correctly to the question about the definition of eccentricity. The ratio of correct answer for the question about constructing tangent lines of quadratic curves is less than that for the question about the applications of the properties of tangent lines. These findings suggests that it is needed that to provide plenty of opportunities to learn mathematical content knowledge in teacher education programs.