• The Mathematical Education
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• v.61 no.1
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• pp.157-178
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• 2022

Mathematics teachers' content knowledge is an important asset for effective teaching. To enhance this asset, teacher's knowledge is required to be diagnosed and developed. In this study, we employed problem-posing and problem-solving tasks to diagnose preservice teachers' understanding of fraction multiplication. We recruited 41 elementary preservice teachers who were taking elementary mathematics methods courses in Korea and the United States and gave the tasks in their final exam. The collected data was analyzed in terms of interpreting, understanding, model, and representing of fraction multiplication. The results of the study show that preservice teachers tended to interpret (fraction)×(fraction) more correctly than (whole number)×(fraction). Especially, all US preservice teachers reversed the meanings of the fraction multiplier as well as the whole number multiplicand. In addition, preservice teachers frequently used 'part of part' for posing problems and solving posed problems for (fraction)×(fraction) problems. While preservice teachers preferred to a area model to solve (fraction)×(fraction) problems, many Korean preservice teachers selected a length model for (whole number)×(fraction). Lastly, preservice teachers showed their ability to make a conceptual connection between their models and the process of fraction multiplication. This study provided specific implications for preservice teacher education in relation to the meaning of fraction multiplication, visual representations, and the purposes of using representations.

• Education of Primary School Mathematics
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• v.27 no.1
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• pp.1-18
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• 2024

Teachers' ability to notice is a crucial indicator of their instructional expertise. Despite the significance of this ability, research in mathematics teacher education has predominantly focused on the noticing of preservice teachers, with limited exploration into the noticing abilities of experienced in-service teachers. This study addresses this gap by examining the noticing characteristics of in-service elementary teachers actively developing their competency in elementary mathematics education. For this purpose, 23 elementary school teachers were asked to complete an analysis sheet while viewing the mathematics lesson video depicting on the concept of (fraction)÷(natural number), allowing us to scrutinize their attending, interpreting, and responding skills in detail. The study's results revealed that teachers demonstrated a tendency to attend mathematically significant aspects related to the teaching of fraction division. They interpreted the observed phenomena through the lens of fraction division's instructional principles, proposing specific pedagogical alternatives. These findings offer valuable insights for mathematics teacher education research.

• School Mathematics
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• v.13 no.4
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• pp.543-562
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• 2011

In this research, the PBL program was developed in terms of 'classroom practice ability', 'self-develop ability', and 'teaching profession character' which classroom friendly teachers get ready and was applied to the classroom friendly elementary mathematics teachers for studying the effectiveness of the program. From the result elementary preservice teachers' disposition in terms of thought about mathematics, mathematics learning, and mathematics teaching was changed to the positive direction through the PBL. They could developed their classroom practice ability, self-develop ability, and teaching profession character through application of new knowledge and plan for problem solving and reflection after solving the problems.

• Communications of Mathematical Education
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• v.19 no.1 s.21
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• pp.317-318
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• 2005

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.2
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• pp.333-359
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• 2011

The purpose of this study was to investigate the teaching activities of guidance teachers in student teachers' planning mathematics lesson and the role of guidance teachers in teaching practicum. To fulfill the purpose, 54 student teachers participated in teaching practicum in G university of education located in G city were selected as subjects and gathered data by asking student teachers to record the interaction process with guidance teachers in detail. By analyzing the teaching activities, the conclusions were drawn as follows: First, guidance teachers' teaching activities in student teachers' planning a lesson were focused on the strategies of teaching and organizing activities according to the ability level of students in the classroom. Second, four types of guidance teachers were identified by analyzing teaching activities as noninterference, supervision, guidance, cooperation. Most of guidance teachers can be indexed as guidance. Third, more effective teaching practicum, guidance teachers need to understand the role of guidance teacher in teaching practicum and systemic program for teaching practicum should be developed.

• The Mathematical Education
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• v.53 no.2
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• pp.185-200
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• 2014

교사의 자기 효능감은 그 교사가 실제로 잘 가르칠지를 예측하는 매우 강력한 구인이다. 본 연구는 우리나라의 초등 예비교사들이 수학을 가르치는데 대한 효능감을 측정하는 정당한 척도를 개발하는 것이다. 먼저, 문헌조사로부터 개인효능감과 결과기대감의 두 개 변인에서 58개의 문항을 개발하였고, 표본 크기 919인 자료 위에서 정규성 검사를 실시하였다. 다음에 전체 자료를 크기가 각각 419와 500인 두 개의 표본으로 나누었고, 첫째 표본에서 신뢰도 검사 및 탐색적 요인 분석을, 둘째 표본에서 확인적 요인 분석을 실시하였다. 최종적으로 개인효능감 변인에서 12 문항, 결과기대감 변인에서 6 문항 등 총 18개의 문항으로 구성된 수학교수효능감척도(MTES)를 개발하였다.

• Communications of Mathematical Education
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• v.36 no.2
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• pp.287-311
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• 2022

This study was related to the cases in which pre-service elementary teachers designed math lessons tailored to math underachievers with learning trajectories and universal design for learning. Learning trajectories can be a basis to identify students' current state of understanding and development, and make a lesson plan responsively tailored to underachievers' state. And universal design for learning is a framework that removes potential barriers that may exist in math lessons from the time the lessons are planned, and guides the rich learning environment accessible to all learners. In order to provide an experience of designing math lessons considering the characteristics of math underachievers, this study required pre-service elementary teachers to create learning trajectories and make lesson plans with the principles of universal design for learning. The characteristics of the learning trajectories shown in the lesson plans and the results of applying the principles of universal design for learning were analyzed. By discussing the results, implications were derived regarding the necessity of lesson planning for math underachievers and the development of lesson planning competency of pre-service elementary mathematics teachers in teacher education.

• Communications of Mathematical Education
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• v.31 no.2
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• pp.153-166
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• 2017

164 preservice elementary teachers' decision and enactment of their knowledge of fraction multiplication were examined in a context where they were asked to write a story problem for a multiplication problem with two proper fractions. Participants were selected from an entry level course and an exit level course of their teacher preparation program to reveal any differences between the groups as well as any recognizable patterns within each group and overall. Patterns and tendencies in writing story problems were identified and analyzed. Implications of the findings for teaching and teacher education are discussed.

• The Mathematical Education
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• v.53 no.1
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• pp.147-162
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• 2014

The purpose of this study was to investigate the nature of pre-service elementary teachers' metaphors on mathematics textbooks. Their metaphors describe individual and collective patterns of thinking and action on mathematics teaching and learning. To analyze their metaphors, qualitative analysis method based on Lakoff and Johnson's theory of metaphor (1980) was adopted. Metaphors on mathematics textbooks were elicited from 161 pre-service elementary school teachers through writing prompts. The writing prompt responses revealed three types and thirteen categories: As Type I, there were (1) 'Principles', (2) 'Summary', (3) 'Manual', (4) 'Encyclopedia', (5) 'Code', (6) 'Guidelines', and (7) 'Example'. As TypeII, there were (9) 'Assistant', (10) 'Friend', (11) 'Scale', and (12) 'Ongoing'. As TypeIII, there was (13) 'Trap'. Among these categories, 'Guidelines', 'Assistant', and 'Ongoing' were the most frequently revealed. These results indicate that the relations of mathematics curriculum, textbooks, and classrooms are not a unilateral way but should communicate with each other.

• Education of Primary School Mathematics
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• v.26 no.1
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• pp.65-82
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• 2023

The purpose of this study is to examine how pre-service teachers' digital capabilities and content knowledge for teaching pi appear and are strengthened in the process of developing digital-based teaching and learning materials of pi, and to derive implications for pre-service teacher education. To this end, the researchers analyzed the process of two pre-service teachers developing exploratory activity materials for teaching pi using block coding of AlgeoMath program. Through the analysis results, it was confirmed that AlgeoMath' block coding activities provided an experience of expressing and expanding the digital capabilities of pre-service teachers, an opportunity to deepen the content knowledge of pi, and to recognize the problems and limitations of the digital learning environment. It was also suggested that the development of digital materials using block coding needs to be used to strengthen digital capabilities of pre-service teachers, and that the curriculum knowledge needs to be emphasized as knowledge necessary for the development of digital teaching and learning materials in pre-service teacher education.