• Journal of Educational Research in Mathematics
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• v.22 no.1
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• pp.39-52
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• 2012

Research in teachers' knowledge for teaching mathematics (KTM) has been gradually growing for the past several years. With various conceptualizations about what teachers need to teach mathematics, there have been studies to find out the relationship between teachers' KTM and their students' achievement. In this paper, I reviewed various conceptualizations of teacher's mathematical knowledge for teaching, and existing qualitative and quantitative studies about this relationship. Based on the review, I identified the challenges to studying this relationship mainly focusing on the existence of a phase-teaching practice-between teachers' KTM and students' learning. Considering the challenges that have been identified in the literature review, I proposed topics for future studies that would contribute to our understanding how the teachers' KTMare related to their students' achievement, and investigate further about whether and how teacher-student interaction in classroom is related to changes in teachers' KTM.

• School Mathematics
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• v.13 no.4
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• pp.615-632
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• 2011

The purpose of the study was to investigate the mathematical knowledge for teaching (MKT) of pre-service and in-service mathematics teachers on the concept of vector. 80 pre-service and 124 in-service mathematics teachers were asked to perform three questions based on MKT's subdomain. The results show that pre-service teachers have stronger common content knowledge(CCK). On the other hand, in-service teachers have stronger specialized content knowledge(SCK), knowledge of content and teaching(KCT) compared to those of pre-service teachers. The paper proposes CCK, SCK and KCT about the concept of vector and discusses the relationships between subdomains of MKT.

• School Mathematics
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• v.17 no.2
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• pp.179-202
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• 2015

In this research, I explored how to apply the history of mathematics in teacher education and investigated the applicability of Chosun Sanhak (mathematics of Chosun Dynasty) as the program that enriched the mathematical knowledge for teaching of prospective elementary school teachers. This program included not only mathematical knowledge but also socio-cultural knowledge and connection knowledge. Prospective teachers participated in various mathematical activities such as explaining, reasoning and problem solving in this program. The effects of this program are as follows. Prospective teachers learned the subject matter knowledge(SMK) which was helpful in teaching basic concepts and skills of elementary mathematics. Next, this program produced the pedagogical content knowledge(PCK) to prospective teachers by giving ideas how to teach.

• The Mathematical Education
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• v.55 no.3
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• pp.317-334
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• 2016

Knowledge and data interpretation on statistical estimation was important to have statistical literacy that current curriculum was said not to satisfy. The author investigated mathematics teachers' MKT on statistical estimation concerning interpretation of confidence interval by using questionnaire and interview. SMK of teachers' confidence was limited to the area of textbooks to be difficult to interpret data of real life context. Most of teachers wrongly understood SMK of interpretation of confidence interval to have influence upon PCK making correction of students' wrong concept. SMK of samples and sampling distribution that were basic concept of reliability and confidence interval cognized representation of samples rather exactly not to understand importance and value of not only variability but also size of the sample exactly, and not to cognize appropriateness and needs of each stage from sampling to confidence interval estimation to have great difficulty at proper teaching of statistical estimation. PCK that had teaching method had problem of a lot of misconception. MKT of sample and sampling distribution that interpreted confidence interval had almost no relation with teachers' experience to require opportunity for development of teacher professionalism. Therefore, teachers were asked to estimate statistic and to get confidence interval and to understand concept of the sample and think much of not only relationship of each concept but also validity of estimated values, and to have knowledge enough to interpret data of real life contexts, and to think and discuss students' concepts. So, textbooks should introduce actual concepts at real life context to make use of exact orthography and to let teachers be reeducated for development of professionalism.

• Journal of Educational Research in Mathematics
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• v.17 no.2
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• pp.147-162
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• 2007

This paper reports an analysis of 19 Chinese and Korean middles school mathematics teachers' understanding of division by fractions. The study analyzes the teachers' responses to the teaching task of generating a real-world situation representing the meaning of division by fractions. The findings of this study suggests that the teachers' conceptual models of division are dominated by the partitive model of division with whole numbers as equal sharing. The dominance of partitive model of division constraints the teachers' ability to generate real-world representations of the meaning of division by fractions, such that they are able to teach only the rule-based algorithm (invert-and-multiply) for handling division by fractions.

• The Mathematical Education
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• v.60 no.3
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• pp.297-319
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• 2021

The present study explored a relationship between mathematical understandings of teachers and ways in which their knowledge transferred in designing lessons for hypothetical students from Gess-Newsome (1999)'s transformative perspective of pedagogical content knowledge. To this end, we conducted clinical interviews with four secondary mathematics teachers of their solving and teaching of equation writing. After analyzing the teacher participants' attention to Key Developmental Understandings (Simon, 2007) in solving equation writing, we sought to understand the relationship between their mathematical knowledge of the problems and mathematical knowledge in teaching the problems to hypothetical students. Two of the four teachers who attended the key developmental understandings solved the problems more successfully than those who did not. The other two teachers had trouble representing and explaining the problems, which involved reasoning with improper fractions or reciprocal relationships between quantities. The key developmental understandings of all four teachers were reflected in their pedagogical actions for teaching the equation writing problems. The findings contribute to teacher education by providing empirical data on the relationship between teachers' mathematical knowledge and their knowledge for teaching particular mathematics.

• Journal of the Korean School Mathematics Society
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• v.18 no.4
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• pp.431-448
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• 2015

Elementary school teacher selection test has to be implemented for knowledge(MKT) to estimate and to be a step in the expansionary direction. For this, It has to be analyzed closely in terms of teacher's MKT first that questions set from selection tests until now. In this research, some standards were established by type of question, grade, contents field and subject from 84 mathematics questions set at examinations. And it was analyzed concretely by general tendency and produced the results of analysis related to elementary teacher's MKT in elementary school teacher selection test since year 2000. The results showed that descriptive and short answer type was mostly set(71.4%) in type of question and integrated grade type was mostly set(41.7%) in type of grade in elementary school teacher selection test. And in type of contents field, rated from highest to lowest, number and operations(31.0%), measurement(23.8%), figure(15.5%) were set. Textbook/manual(34.5%), solution of problem(26.2%), learning psychology(13.1%) in status of subject were followed in order, but there's no relationship with estimation. This research was based on a standard of precedent study and made an analysis of elementary mathematics questions of selection test since year 2000. Therefore, it has a meaning because of produced results from analysis related to elementary teacher's MKT.