• Journal of the Korean School Mathematics Society
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• v.16 no.1
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• pp.187-200
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• 2013

This study, as part of the research on mathematics teacher knowledge analyzed the differences in understanding and familiarity on geometric knowledge of middle-high school teachers. Through this study, survey was carried out using a questionnaire and examination for 80 middle-high school teachers. As the result, differences between familiarities about believing in knowing about the proposition, and actually understanding why the proposition is established, was big. These results can provide us implications on the education of teachers and pre-service teachers of middle-high school.

• Journal for History of Mathematics
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• v.27 no.3
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• pp.211-231
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• 2014

Although Monty Hall dilemma is used in many areas including philosophy, economics, and psychology, it is used in the current mathematics textbooks only as a material for reading or one of probability questions. The present study tries to explore students' understanding of Monty Hall dilemma through a class case. In this study, a group of high-school students participated in group activities, in which they read an argument about Monty Hall dilemma, and tried to resolve it through small-group and whole-class discussions, and then studied the conditional probability. The analysis supports the studies in psychology that intuitive understandings on probability do not change easily, and that counter-intuitivity in Monty Hall dilemma induces confusion and offers a basis for discussions among students. Similar results are anticipated when other dilemmas on probability are used.

• East Asian mathematical journal
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• v.36 no.2
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• pp.173-201
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• 2020

Mathematical modeling has been emphasized because it offers important opportunities for students to both apply their learning of mathematics to a situation and to explore the mathematics involved in the context of the situation. However, unlike its importance, mathematical modeling has not been grounded in typical mathematics classes because teachers do not have enough understanding of mathematical modeling and they are skeptical to implement it in their lessons. The current study analyzed the data, such as video recordings, slides, and surveys for teachers, collected in four lessons of teacher education in terms of mathematical modeling. The study reported different kinds of tasks that are authentic with regards to mathematical modeling. Furthermore, in teacher education, teachers' identities have separated a mode as learners and a mode as teachers and conflicts and intentional transition were observed. Analysis of the surveys shows what teachers think about mathematical modeling with their understanding of it. In teacher education, teachers achieved different kinds of modeling tasks and experience them which are helpful to enact mathematical modeling in their lessons. However, teacher education also needs to specifically offer what to do and how to do it for their lessons.

• Research in Mathematical Education
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• v.23 no.4
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• pp.219-233
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• 2020

Teachers' intervention in small groups is a research area that needs more research attention. Ehrenfeld and Horn (2020) identified teachers' group work monitoring routines that consist of four recurrent talk moves: 1) Initiation, 2) Entry, 3) Focus, and 4) Exit. To better understand prospective teachers' (PTs) intervention in small groups in mathematics classrooms, I investigated how PTs' intervention actions and purposes are related to the monitoring routines, particularly, in terms of Focus moves. I analyzed 26 PTs' responses to four written scenarios, each of which depicts interactions among students in a small group. I identified 1) types of PTs' math talk, 2) types of PTs' non-math talk, 3) types of intervention purposes, and 4) patterns of intervention actions and purposes by scenario. This study contributes to understanding PTs' intervention actions and purposes in mathematics instruction.

• Journal of the Korean School Mathematics Society
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• v.24 no.4
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• pp.327-348
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• 2021

This study examines the effects of mathematics learning mentoring activities on mathematical knowledge for teaching (MKT) of pre-service mathematics teachers. We choose six pre-service mathematics teachers in the department of mathematics education at M University. The pre-service mathematics teachers conducted 1:1 mathematics learning mentoring for two hours at a times and twice a week for 15 weeks. The pre-service mathematics teachers submitted the mentor log, which recorded weekly learning and emotional observations. We collected the mentor log and the reflection log of pre-service mathematics teachers and the interviews with pre-service mathematics teachers. Based on the collected data, we analyzed the effects of MKT, the understanding of students, and pre-service mathematics teachers' introspection by mathematics learning mentoring. We obtained conclusions as follows. First, mathematics learning mentoring provides an opportunity for pre-service mathematics teachers to apply the theory of mathematical education to schools. Thus pre-service mathematics teachers express theoretical knowledge as practical knowledge. Second, mathematics learning mentoring helps pre-service mathematics teachers have the ability to understand students and provide opportunities to reflect on their attitudes as learners. Third, mathematics learning mentoring helps advance teaching activities by providing pre-service mathematics teachers with opportunities to reflect on their teaching activities. Finally, mathematics learning mentoring has positively influenced the change in pre-service mathematics teachers' beliefs and teaching intuition.

• Journal of the Korean School Mathematics Society
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• v.21 no.1
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• pp.63-89
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• 2018

In this study, the researcher developed a course integrated mathematical problem posing activities in order to enhance pre-service mathematics teachers' ability to carry out problem posing activities in mathematics classroom, and examined the changes of pre-service mathematics teachers' perceptions about problem posing through the course. The problem posing course developed in this study consisted of three stages: education on the theories regarding problem posing; activities with problem posing; development and implementation of problem posing tasks. According to the results of the questionnaires, interviews, and class journals data analysis, the problem posing experiences provided in this study were very effective in improving pre-service mathematics teachers' understanding of the problem posing strategies and the benefit of problem posing activities to student learning. Particularly, the experience in various problem posing activities and the implementation experience of problem posing provided in the course played a key role in the improvement of pre-service mathematics teachers' understanding of problem posing and PCK.

• Research in Mathematical Education
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• v.16 no.2
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• pp.91-106
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• 2012

Spatial ability has been valued as a talent domain and important skill in mathematics education because it enhanced an intuitive view and an understanding in many areas of mathematic. In addition, spatial ability highly correlates with mathematics achievement, indicating its crucial role in success in mathematics education. Some researchers founded gender differences in mathematics and spatial ability, and indicated that spatial ability served as a mediator of gender difference in mathematics. This study explored the spatial ability of 349 Korean middle school students (Grade 7-9), and investigated the association among students' spatial ability and their mathematics achievement, gender, and grade. The result of this study shows that spatial ability correlates positively with mathematics achievement. While gender difference did not exist in mathematics, significant gender difference existed in spatial ability favoring male students.

• Journal of Engineering Education Research
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• v.20 no.2
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• pp.50-56
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• 2017

Because all areas of mechanical engineering involves the use of mathematics, mechanical engineers need mathematical understanding and skill enhancement. To achieve the effective mathematics education for mechanical undergraduate students, it should reorganize the important subtopics of mathematics. In this paper, we explore the direction of the development of mathematics education for mechanical engineers by analyzing the teaching hours of each topics in the mathematics and by comparing the results with significance analysis of expert survey. To do so, syllabuses of mathematics courses of the selected mechanical engineering departments were analyzed and the survey responses of professionals in the Korean Society of Mechanical Engineers were also investigated. Finally, the revision of mathematics curriculum in the mechanical engineering was proposed.

• Journal of The Korean Association For Science Education
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• v.32 no.8
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• pp.1318-1332
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• 2012

This paper takes another approach in assessing students' perception of mathematics. Instead of asking for verbal description of the students' perception of mathematics, we asked the respondents who were all college students to draw their perception of mathematics. This relatively new approach enabled students to take a second look of how they perceived math and, at the same time, explored students' creativity and provided a less austere appearance to mathematics which was taken usually in a more formal and severe manner. This approach of assessing students' perception of mathematics generated new information that could not be normally gleaned from other approaches like Likert Scale. Some drawings of mathematics of the respondents reinforced their math affect towards mathematics. For those who hated math, their drawings revealed so the same is true with those who loved mathematics. Examining the visual representations of mathematics and looking for commonalities, the researcher found a number of interesting themes that may shed some light to educators' understanding of students' math affect.

• Education of Primary School Mathematics
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• v.10 no.1 s.19
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• pp.29-39
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• 2007

This paper is to give a brief introduction to a new discipline called 'conceptual metaphor' and 'mathematical metaphor(Lakoff & Nunez, 2000) from the viewpoint of mathematics education and to analyze the metaphors at 4th graders' mathematics classroom as a case of conceptual metaphors. First, contemporary conception on metaphors is reviewed. Second, it is discussed on the effects and defaults of metaphors in teaching and learning mathematics. Finally, as a case study of mathematical metaphors, conceptual metaphors on the concepts of triangles at 4th graders' mathematics classrooms are analyzed. Students may reason metaphorically to understand mathematical concepts. Conceptual metaphor makes mathematics enormously rich, but it also brings confusion and paradox. Digging out the metaphors may lighten both our spontaneous everyday conceptions and scientific theorizing(Sfard, 1998). Studies of metaphors give us the power of understanding the culture of mathematics classroom and also generate it.