• Journal of Elementary Mathematics Education in Korea
• /
• v.21 no.1
• /
• pp.215-241
• /
• 2017

This study analyzed teachers' Pedagogical Content Knowledge (PCK) regarding the pedagogical aspect of the instruction of ratio and rate in order to look into teachers' problems during the process of teaching ratio and rate. This study aims to clarify problems in teachers' PCK and promote the consideration of the materialization of an effective and practical class in teaching ratio and rate by identifying the improvements based on problems indicated in PCK. We subdivided teachers' PCK into four areas: mathematical content knowledge, teaching method and evaluation knowledge, understanding knowledge about students' learning, and class situation knowledge. The conclusion of this study based on analysis of the results is as follows. First, in the 'mathematical content knowledge' aspect of PCK, teachers need to understand the concept of ratio from the perspective of multiplicative comparison of two quantities, and the concept of rate based on understanding of two quantities that are related proportionally. Also, teachers need to introduce ratio and rate by providing students with real-life context, differentiate ratios from fractions, and teach the usefulness of percentage in real life. Second, in the 'teaching method and evaluation knowledge' aspect of PCK, teachers need to establish teaching goals about the students' comprehension of the concept of ratio and rate and need to operate performance evaluation of the students' understanding of ratio and rate. Also, teachers need to improve their teaching methods such as discovery learning, research study and activity oriented methods. Third, in the 'understanding knowledge about students' learning' aspect of PCK, teachers need to diversify their teaching methods for correcting errors by suggesting activities to explore students' own errors rather than using explanation oriented correction. Also, teachers need to reflect students' affective aspects in mathematics class. Fourth, in the 'class situation knowledge' aspect of PCK, teachers need to supplement textbook activities with independent consciousness and need to diversify the form of class groups according to the character of the activities.

• Communications of Mathematical Education
• /
• v.21 no.4
• /
• pp.575-596
• /
• 2007

This study investigates preservice teachers' development of subject-matter knowledge and pedagogical content knowledge in teaching function concept. This development takes place in the pedagogical mathematics courses in which the theory of constructivism and cooperative learning theory are aligned. Pre and post courses test were administered to examine the development and the follow-up interviews were conducted to gain more details. Analysis of the written questionnaire results and interview transcripts reveal that their limited concept image can be extended and developed in depth through pedagogical mathematics courses that apply reformed teaching methods.

• The Mathematical Education
• /
• v.41 no.2
• /
• pp.173-187
• /
• 2002

The purpose of this study through ethnographic inquiry is to describe how an elementary teacher teaches mathematics with understanding. The ways that teachers'beliefs affect instructional activities, what means understanding from the view of cognitive psychology, and ethnographic research tradition were reviewed to anchor theoretical background of this study. A third-grade teacher and his 45 students were selected in order to capture vivid and thick descriptions of the teaching and learning activities of mathematics. Three major sources of data, that is, participant-observation with video taping, formal and informal interviews with the teacher and his students, and a variety of official documents were collected. These data were analyzed through two phases: data analysis in the field and after the fieldwork. According to data analysis, ‘teaching mathematics with understanding’ was identified as the teachers central belief of teaching mathematics. In order to implement his belief in teaching practices, the teacher made use of three strategies: ⑴ valuing individual student's own way of understanding, ⑵ bring students' everyday experiences into mathematics classroom, and ⑶ lesson objectivies stated by students. It is suggested for future research that concrete and specific norms of mathematics classroom for the improvement of mathematics understanding are needed to be identified and that experienced and skillful teachers' practical knowledge should be incorporated with theories of teaching mathematics and necessarily paid more attention by mathematics educators.

• Korean Journal of Child Studies
• /
• v.35 no.2
• /
• pp.137-156
• /
• 2014

The purpose of this study was to better understand the tendencies and general distributive features of mathematical educational activities which are presented in the Nuri Curriculum Teaching Guidebooks. This was done by analysis of 628 mathematical activities suggested in those guidebooks, the total number of which was thirty-two. The results of this study can be summarized as follows: First, the number of activities for mathematical education was 204 for the age of three, 223 for the age of four, and 201 for the age of five. Second, these mathematical educational activities are aimed mainly for developing positive attitudes toward mathematics rather than the delivery of mathematical knowledge and skills. Third, the number of activities for developing mathematical inquiry skills was greater than that of activities for developing of inquiry attitudes. Furthermore, the characteristic of understanding the basic concepts of space and figures can be found most frequently in five kinds of activities for mathematical inquiry. Last, the activities for mathematical education are more frequently found in free choice activities rather than group activities. The results of this study also suggest that checking the current status of mathematical education for young children and the Nuri Curriculum Teaching Guidebooks can be utilized for creating teachers' manuals.

• Journal of Educational Research in Mathematics
• /
• v.11 no.2
• /
• pp.239-256
• /
• 2001

The notion of metaphor has been increasingly popular in research of mathematics education. In particular, metaphor becomes a useful unit for analysis to provide a profound insight into mathematical reasoning and problem solving. In this context, this paper takes metaphor as an analytic unit to examine the relationship between objectivity and subjectivity in mathematical reasoning. Specifically, the discourse analysis focuses on the code switching between literal language and metaphor in mathematical discourse. It is shown that the linguistic code switching is parallel with the switching between two different kinds of mathematical knowledge, that is, factual knowledge and mathematical imagination, which constitute objectivity and subjectivity in mathematical reasoning. Furthermore, the pattern of the linguistic code switching reveals the dialectical relationship between the two poles of mathematical reasoning. Based on the understanding of the dialectical relationship, this paper provides some educational implications. First, the code-switching highlights diverse aspects of mathematics learning. Learning mathematics is concerned with developing not only technicality but also mathematical creativity. Second, the dialectical relationship between objectivity and subjectivity suggests that teaching and teaming mathematics is socioculturally constructed. Indeed, it is shown that not all metaphors are mathematically appropriated. They should be consistent with the cultural model of a mathematical concept under discussion. In general, this sociocultural perspective on mathematical metaphor highlights the sociocultural organization of teaching and loaming mathematics and provides a theoretical viewpoint to understand epistemological diversities in mathematics classroom.

• School Mathematics
• /
• v.7 no.3
• /
• pp.303-318
• /
• 2005

If students can use mathematics to solve their problems and learn the mathematical knowledge through it, they may think mathematics useful and valuable. This study is for the teaching through problem solving in mathematics education, which I consider in terms of the problem-based learning and mathematical modeling. 1 think mathematical modeling is applied to teaching mathematics as a problem-based learning. So I developed the teaching model, and showed the example that students learn the formal and hierarchic mathematics through mathematical modeling.

• East Asian mathematical journal
• /
• v.25 no.3
• /
• pp.247-262
• /
• 2009

Permutation and combination are the part of mathematics which can be introduced the pliability and diversity of thought. In prior studies of permutation and combination, there treated difficulties of learning, strategy of problem solving, and errors that students might come up with. This paper provides the method so that meaningful teaching and learning might occur through the systematic approach of permutation and combination. But there were little prior studies treated counting numbers that basic of mathematics' action. Therefore this paper tries to help the understanding of permutation and combination with the process of changing from informal knowledge to formal knowledge.

• Research in Mathematical Education
• /
• v.18 no.1
• /
• pp.55-74
• /
• 2014

This study examined the potential teaching strategies of prospective elementary teachers and their perceptions of the procedural/conceptual nature of examples. Fifty-four prospective teachers participated in this study, engaging in two-phase tasks. Analysis of data indicated that: (a) Overall, the participants' perceptions were geared toward putting emphasis on conceptual understanding rather than procedural understanding; but (b) Generally, procedure-oriented strategies were more frequently incorporated in participants' potential teaching plans. This implied that participants' preconceived ideas regarding math examples were not always reliable indicators of their potential teaching strategies. Implications and suggestions for mathematics teacher preparation are discussed.

• The Mathematical Education
• /
• v.55 no.2
• /
• pp.171-192
• /
• 2016

As teachers' competency is evaluated based on their teaching performance. pre-service teachers need to have an opportunity to reflect on themselves by systematically analyzing and evaluating their own lesson planning and teaching performance through self-assessment. In this study, we aimed to examine what evaluation criteria for lesson planning and teaching performance pre-service mathematics teachers consider in the process of self-assessment. This study used a mixed-methods research design. To draw the self-evaluation criteria for lesson planning and teaching performance, pre-service self-reported assessments were analyzed using qualitative analyses. In addition, descriptive statistics were used to investigate the pre-service teachers' distribution across the criteria and check the ratio of pre-service mathematics teachers for each element. As a result, it was disclosed that pre-service mathematics teachers considered eight elements in self evaluating their own lesson planning and teaching performance. In addition, we found that pre-service mathematics teachers tended to consider Pedagogical Content Knowledge (PCK) more than Subject-Matter Knowledge (SMK). Moreover, the results of this study provide educational implications for the curriculum in the pre-service teacher's education program.

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