• 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.

• The Mathematical Education
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• v.58 no.3
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• pp.367-381
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• 2019

This investigation engaged elementary and middle school pre-service teachers in a task of modeling and explaining the magnitude of $0.14m^2$ and examined their responses. The study analyzed both successful and unsuccessful responses in order to reflect on the patterns of misconceptions relative to pre-service teachers' prior knowledge. The findings suggest a need to promote opportunities for pre-service teachers to make connections between different domains through meaningful tasks, to reason abstractly and quantitatively, to use proper language, and to refine conceptual understanding. While mathematics teacher educators (MTEs) could use such mathematical tasks to identify the mathematical content needs of pre-service teachers, MTEs generally use instructional time to connect content and pedagogy. More importantly, an early and consistent exposure to a combined experience of mathematics and pedagogy that connects and deepens key concepts in the program's curriculum is critical in defining the important content knowledge for K-8 mathematics teachers.

• The Mathematical Education
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• v.60 no.3
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• pp.281-295
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• 2021

This study examines the breadth and depth of knowledge of the teacher employment test for secondary mathematics. For the breadth of knowledge, we attempted to figure out the range of knowledge in terms of the content areas using the standards from the Korea Society Educational Studies in Mathematics[KSESM](2008). For the depth of knowledge, we chose Anderson & Krathwohl(2001) framework to analyze levels of each item in the test. The results from the analysis of 180 items in the teacher employment test between 2014 and 2021 show that while items in mathematics education have considerable variation in terms of range and levels of knowledge, those in some subjects of mathematics can be found only certain level of knowledge. i.e., merely certain topics or levels of knowledge have been heavily evaluated. Thus, considering the breadth and depth of knowledge teachers should have, the current exam needs to be improved in terms of teacher knowledge. It does not mean that every topic and every level of knowledge should be evaluated. However, it is a meaningful opportunity to think about what kinds of knowledge teachers should have in relation to K-12 mathematics curriculum and how we can evaluate the knowledge. More collaborative effort is inevitable for the improvement of teacher knowledge and teacher employment test.

• The Korean Journal of Community Living Science
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• v.22 no.4
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• pp.519-533
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• 2011

The objective of this study was to follow up changes in knowledge related to the mathematics education field work of preliminary early childhood teachers. The subjects of this research were 28 students who were taking mathematics education courses in early childhood education departments at various universities. This research ran for 15 weeks and was conducted through field work relating to mathematics education. The study collected data from pre-service teachers' knowledge, the diagram of concept, writing journals, interviews, and materials from the internet. Through this procedure, pre-service teachers' knowledge for mathematics education could later be expanded, ordered, and integrated. In addition, pre-service teachers not only understood the importance of contents and levels of lesson plans, but also learned how to utilize educational media to make effective lessons. Furthermore, pre-service teachers realized that the mathematical concepts of students could be expanded depending on the contents and methods of pre-service teachers' lesson plans and students could then apply these concepts into daily situations.

• Research in Mathematical Education
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• v.14 no.2
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• pp.173-194
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• 2010

This study examines the differences and similarities of mathematics teachers' subject matter knowledge among England, the Chinese mainland and Hong Kong. Data were collected from a ten-item test in the SKIMA subject matter audit instrument [Rowland, T.; Martyn, S.; Barber, P. & Heal, C. (2000). Primary teacher trainees' mathematics subject knowledge and classroom performance. In: T. Rowland & C. Morgan (eds.), Research in Mathematics Education, Volume 2 (pp.3-18). ME 2000e.03066] from over 500 participants. Results showed that participants from England performed consistently better, with those from Hong Kong being next and then followed by those from the Chinese mainland. The qualitative data revealed that participants from Hong Kong and the Chinese mainland were fluent in applying routines to solve problems, but had some difficulties in offering explanations or justifications.

• Education of Primary School Mathematics
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• v.18 no.2
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• pp.61-75
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• 2015

This study analyzed the characteristics of mathematical tasks including the level of cognitive demands set up by pre-service elementary school teachers. 50 pre-service teachers in G university of education who participated in their 4 weeks teaching practicum were selected as subjects. They planned and implemented mathematics lesson with their lesson plans. Lesson plans, video of their lessons, transcript of video were gathered and analyzed the characteristics of mathematical tasks used in their lesson. Through the analysis, several conclusions were drawn as follow. First, 78% of the subjects modified tasks in mathematics textbooks. Since modification or construction of mathematical tasks gives good chance for constructing mathematical task knowledge for teaching, more chance should be given to pre-service teachers to construct new tasks or modify tasks in mathematics textbooks. Second, types of modification done by pre-service teachers were categorized as number change(15.6%), situation change(78.1%) and material change(6.3%). As Chapman(2013) emphasized the importance of MtKT, pre-service teachers must have more MtKT by understanding the characteristics of mathematical tasks. Third, the level of cognitive demands required by mathematical tasks were relatively low. 74% of mathematical tasks was lower cognitive demands and only 26% was higher cognitive demands. The level of cognitive demands of tasks in mathematics textbooks tended to be lowered by the directions given right after the tasks were given. In this respect, the structure of mathematics textbooks need to be changed.

• Research in Mathematical Education
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• v.24 no.3
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• pp.229-254
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• 2021

Students' participation in epistemic practices, which are related to knowledge construction on the part of students, is becoming a crucial part of learning (Goizueta, 2019). Research on epistemic practices in science education draws attention to teachers' support of students to engage in epistemic practices in mathematics instruction. The research highlights a need for incorporating epistemic goals, along with conceptual and social goals, into instruction to promote students' epistemic practices. In this paper, I investigate how teachers interact with students to integrate epistemic goals. I examined 24 interaction excerpts that I identified from six interview transcripts of two beginning teachers' mathematics instruction. Each excerpt was related to the teachers' talk about their specific interaction(s) in a small group. I explored how each teacher's discursive moves and goals were conceptual, social, and epistemic-related as they intervened in small groups. I found that both teachers used conceptual, social, and epistemic discursive move but their discursive moves were related only to social and social goals. This paper suggests supporting teachers to develop epistemic goals in mathematics instruction, particularly in relation to small groups.

• Journal of Educational Research in Mathematics
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• v.26 no.2
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• pp.269-285
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• 2016

PCK(pedagogical content knowledge) has been frequently discussed in the field of subject matter education as well as education in general. Considering the fact that PCK characterizes teacher professionalism, and the distinction of mathematics education from neighboring disciplines, PCK is one of the core concepts in the discourse of mathematics education. This study focused on KCS(knowledge of content and students) among the areas of PCK. The purpose of this study to investigate the KCS of pre-service teachers attending a private university located in Seoul. An in-depth interview with 30 pre-service teachers was conducted in a semi-structured manner, using four questions dealing with common student errors, students' understanding of content, and student developmental sequences. The pre-service teachers gave mathematical answers while in others they gave priority to pedagogical considerations. The implication drawn from the interview data is that the teacher training program should fully reflect the complexity of mathematical concepts which appeared in school mathematics over several grade levels and content areas.

• Communications of Mathematical Education
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• v.30 no.1
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• pp.101-120
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• 2016

The purposes of the study were to analyze pre-service mathematics teachers' MKT and to examine the perceptions of MKT to find implications for the improvement of pre-service mathematics teacher education program in the aspect of teachers' content knowledge. Twenty-six pre-service mathematics teachers participated in the survey to examine the perceptions of MKT and they also finished two MKT tasks which focused on a specific area of middle school geometry. According to the survey results, the participants thought that they have enough knowledge in all categories of MKT except KCT-2 and they appreciated the importance of MKT education in pre-service mathematics teacher education program. However, the participants showed difficulties in MKT task items which required SCK, KCS, KCT, especially, the proportions of those who showed appropriate knowledge on the items required SCK and KCT was less than 50%. These results show disagreement between the perceptions of pre-service mathematics teachers' MKT and practice of MKT.

• The Mathematical Education
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• v.42 no.5
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• pp.647-672
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• 2003

This study sought to determine the impact of the graphing calculator on prospective math-teachers' mathematical thinking while they engaged in the exploratory tasks. To understand students' thinking processes, two groups of three students enrolled in the college of education program participated in the study and their performances were audio-taped and described in the observers' notebooks. The results indicated that the prospective teachers got the clues in recalling the prior memory, adapting the algebraic knowledge to given problems, and finding the patterns related to data, to solve the tasks based on inductive, deductive, and creative thinking. The graphing calculator amplified the speed and accuracy of problem-solving strategies and resulted partly in students' progress to the creative thinking by their concept development.