• Journal of the Korean School Mathematics Society
• /
• v.9 no.3
• /
• pp.317-345
• /
• 2006

The purpose of this paper is to provide readers related to mathematics education with information and guidelines on 'Teaching and Learning Materials for Differentiated Instruction in Mathematics'. This paper is generally comprised of two parts. The one part is basically focused on understanding the meaning of differentiated education. The focus of the other part is on developing differentiated instructional materials for mathematics, according to the following procedures: 1. Analyzing the current differentiated mathematics curriculum and textbooks 2. Drawing a framework for developing the differentiated teaching and learning materials, and planning the procedure of developing the materials in detail. 3. Developing, checking, and revising the materials 4. Proposing how to utilize the materials effciently and effectively in class

• Journal of The Korean Association For Science Education
• /
• v.34 no.3
• /
• pp.295-301
• /
• 2014

The purpose of this study is to investigate the difficulties of teachers and students on the unit about 'measuring weight.' In this research, we have acquired data about teachers through survey, interview, and self-reflection journals, at the same time we have collected information on the students through survey, assessment test, and interview. We have extracted the difficulties from analysis with constant comparison method. In addition, we have analysed the curriculum of science and mathematics to know the leaning sequence. The analysis had been checked up by experts in science education. The result of the study is as follows: The difficulties of teachers are from the lack of teachers' descriptive knowledge, disorder of conceptual hierarchy in the curriculum, poor experimental instruments, and low psychomotor skill of students. The difficulties of students are from common misconceptions, opaque concepts, lack of manipulation skill, insufficiency of mathematical ability, difficulty of application of principles to the real situation, and lack of problem-solving ability. In addition, teachers have recognized that students face more difficulties in experiment class, while students think that they face more difficulties in conceptual understanding class.

• Journal of Educational Research in Mathematics
• /
• v.27 no.3
• /
• pp.511-536
• /
• 2017

The present study aims to investigate ways in which pre-service secondary mathematics teachers anticipate 1) students' responses to specific mathematical tasks which are chosen or devised by the participating pre-service teachers as requiring students' higher cognitive demand and, 2) their roles as math teachers to scaffold students' mathematical thinking. To achieve the goal, we had our pre-service teachers to engage in an adapted version of Spangler & Hallman-Thrasher(2014)'s Task Dialogue writing activity whose focus was to develop pre-service elementary teachers' ability to orchestrate mathematical discussion. 14 pre-service teachers who were junior at the time enrolled in the Mathematics Teaching Method Course were subjects of the current study. In-depth analysis of both Task Dialogues which pre-service secondary mathematics teachers wrote and audiotapes of the group discussions while they wrote the dialogues suggests the following results: First, the pre-service secondary teachers anticipated how students would approach a task based on their own teaching experiences. Second, they were challenged not only to anticipate more than one correct students' responses but to generate questions for the predicted correct-responses to bring forth students' divergent thinking. Finally, although they were aware that students' knowledge should be the crucial element guiding their decision-making process in teaching, they tended to lower the cognitive demands of tasks by providing students with too much guidance which brought forth the use of procedural knowledge. The study contributes to the field as it provides insights as to what to attend in designing teacher education course whose goal is to provide a foundation for developing pre-service teachers' ability to effectively orchestrate mathematical discussion.

• Journal of the Korean School Mathematics Society
• /
• v.21 no.2
• /
• pp.91-111
• /
• 2018

Junior college students in located Eup-Myeon areas commonly fail to meet the basic standards of mathematics. This leads students to lack basic knowledge and to have difficulties in studying their majors. In addition, students often lose their interest in the study and eventually leave school or drop out, while some have difficulties in their life at work. To remedy and solve these problems, the country proposes National Competency Standards(NCS). The basic occupational competencies proposed in NCS are essential occupational abilities required to successfully perform the job. I want to apply mathematical ability, which is one of the basic occupational competencies, to mathematics education of junior college. Applying NCS mathematical ability to junior college students, I would like to examine the effectiveness of the NCS mathematical ability course. The purpose of this study is to find out the way of education of desirable mathematical ability and to raise basic academic ability and interest in mathematics.

• School Mathematics
• /
• v.18 no.2
• /
• pp.323-348
• /
• 2016

The 2009 revised national mathematics curriculum have inserted mathematical 'linking cube' activities in the 6th grade math classes to improve students' spatial problem solving abilities and communication skills. However, we found that it was hard for teachers to teach problem solving and communication skills due to the absence of mathematical way of representing linking cubes in the classroom. In this paper, we propose 3D 'turtle representation system' as teaching and learning tools for linking cube activities. After using turtle representation system for linking cube activities, teachers responded that turtle representation system is a valuable problem solving and communication tools for the linking cube mathematics classes. We conclude that turtle representation system is a well designed teaching and learning tools for linking cube activities, and there are lots of educational meanings in the 3D turtle representation system.

• School Mathematics
• /
• v.16 no.3
• /
• pp.445-469
• /
• 2014

This study aims to examine secondary mathematics teachers' understanding of the levels of cognitive demand on mathematical tasks suggested in mathematics textbooks. The study also attempts to investigate whether the teachers are able to characterize the tasks accordingly and to change low level tasks to high level ones. For this purpose, we developed a survey and 50 secondary mathematics teachers participated in the survey. The findings from the data analysis suggest that 59 percent of the teachers selected high level tasks as appropriate for achieving the national curricular goals, but about 1/3 of the teachers identified PNC tasks as high level ones. The results also reveal that more than half of the teachers were not able to transform low level into high level tasks and only 4 teachers out of 50 were able to transform successfully. The teachers seem to find difficulty in transforming low level tasks into high level ones.

• Communications of Mathematical Education
• /
• v.34 no.3
• /
• pp.235-256
• /
• 2020

The purpose of this study was to investigate the experience of pre-service mathematics teachers who attended at a university course combined with teaching practicum based on design thinking process to identify the change of their awareness of its activities. For the research, 8 pre-service mathematics teachers participated in a mathematics major course, consisting of 5 phases of design thinking formed by Stanford d.school. In the end of the course, qualitative data were collected through individual and focus group interviews and the course activities. By data analysis, the results of this study were as follows. Firstly, the participants' perspectives of design thinking activities were changed from the difficulty and ambiguity of its activity in the beginning of the process to positiveness with competence of solving authentic problem in terms of teaching practicum over time. Secondly, the participating pre-service teachers emphasized that design thinking activities helped them prepare well teaching practicum and raise understanding of students they met in the school fields. Thirdly, some research participants went through the difficulty in utilizing their products drawn from 4th phase (prototyping) of design thinking process depending on the acceptance of their guidance teachers. Fourthly, the research participants also pointed out that the design thinking was a significant activity in that they learned how to understand and communicate with their students and how to collaborate with team members and it gave an insight about the preparation for a class. Through these results, this study identified the possibility of using the design thinking process for pre-service mathematics teachers' teaching practicum. In addition, the research put forward some implications for better use of design thinking in teacher education.

• Communications of Mathematical Education
• /
• v.13 no.2
• /
• pp.563-589
• /
• 2002

고학년으로 갈수록 지필 환경에만 머무르는 현실 속에서 생활 및 예술 작품 등에서 수학적 원리와 개념을 발견하도록 하는 테셀레이션 수업은 학생들의 흥미와 호기심을 유발하고 수학의 아름다움을 느끼게 하는 것 이상으로 기하학적 사고의 기초를 학습하는데 도움을 줄 수 있다. 이에 본 연구는 4학년까지 적용되고 있는 7차 교육과정을 중심으로 새롭게 등장하고 있는 테셀레이션에 대한 이해 및 교수 학습 자료가 체계적으로 정비되어 있지 못한 현실적인 문제의 해결 방안으로서 테셀레이션을 활용한 수학 학습의 내용을 분석하여 교사들에게는 테셀레이션의 이해 및 교수 학습 자료로서 , 학생들에게는 수학의 기하적 개념들을 쉽고 재미있게 학습할 수 있는 학습도구로서 활용할 수 있도록 하는 것을 목적으로 테셀레이션을 구현할 수 있는 컴퓨터 소프트웨어를 활용하여 테셀레이션 교수 학습 자료를 개발하였고 이를 위해 다음과 같은 연구 내용을 설정하였다. 가. 테셀레이션의 정의와 예 그리고 종류를 알아보고 테셀레이션 속의 수학적 개념을 활용방법과 함께 제시한다. 나. 제7차 초등 수학 교육과정 중 도형 영역과 규칙성과 함수 영역을 중심으로 테셀레이션을 적용할 수 있는 내용영역을 분석하고 컴퓨터 소프트웨어를 활용한 테셀레이션 자료를 제시한다. 다. 제작된 테셀레이션 교수 학습 자료의 효과적 활용을 위한 활용 방안을 탐색한다. 라. 제작된 테셀레이션 교수 학습 자료의 활용 효과를 알아보기 위해 적용 실험을 하고 이에 대한 학생들의 반응을 분석하여 학습의 효과를 밝힌다. 제작된 테셀레이션 교수 학습 자료의 적용 실험을 위하여 광주대성초등학교 6학년 한 반을 선정하였고 약 4주에 걸쳐 컴퓨터 소프트웨어를 활용한 테셀레이션 교수 학습 자료를 투입하여 4번의 활동수업을 실시하였다. 수업 후 작성된 학습지와 소감문 및 연구자에 의해 관찰된 수업내용을 바탕으로 다음과 같은 연구 결과를 얻을 수 있었다. 첫째, 제7차 초등 수학 교육과정 중 도형 영역과 규칙성과 함수 영역을 중심으로 컴퓨터 소프트웨어를 활용한 테셀레이션 자료를 제시한 결과 지필적 환경에서 제한적이었던 탐구하고 조작해보는 활동을 할 수 있는 역동적인 수학 실험실 환경이 제공됨으로써 도구적 이해가 아닌 관계적 이해를 하는 것을 확인할 수 있었다. 수학적 개념을 암기하는 것에서 벗어나 자연스런 조작을 통해 학생들이 개념을 이해하고 탐구하는 과정 속에서 학생들은 수학을 공부한다기 보다는 수학 속에서 재미있게 놀이한다는 생각을 가지고 수업에 참여하였고 배우는 즐거움을 알고 자신감을 가지며 더 나아가 창의적인 생각을 하도록 하는 기회를 줄 수 있었다. 둘째, 테셀레이션은 우리 생활 속에서 쉽게 발견할 수 있는 것으로 수학이 단순히 책에서만 한정되지 않고 다양한 분야 즉 디자인, 생활 속에서의 벽지문양과 포장지, 예술작품 등에 활용되고 있음을 체험함으로써 수학이 실생활에 광범위하게 활용되고 있음을 알게 하였다. 역으로 생활 속에서의 테셀레이션을 통해 수학적 개념을 찾는 과정을 통해 수학이 아름다우면서도 실용적이라는 생각을 심어줄 수 있었다. 셋째, 테셀매니아, GSP, 캐브리, 거북기하 등 평소 수업에서는 활용도가 적은 컴퓨터 소프트웨어를 활용함으로써 컴퓨터 소프트웨어 자체에서 오는 호기심뿐만이 아니라 직접 조작하여 테셀레이션 작품과 개념을 익히고 새로운 작품과 학습을 해 내는 과정을 통해 자신감과 성취감 등에 있어 큰 변화가 있음을 발견할 수 있었다. 컴퓨터 기능이 미숙한 학생의 경우 처음에는 당황해 하고 어려워하는 부분도 있었으나 조작할 시간적 여유를 주고 교사와 우수한 학생들이 도우미로서 역할을 잘해내어 나중에는 큰 어려움 없이 마칠 수 있었다. 테셀레이션이라는 용어가 아직은 생소한 현장에서 교수 학습 자료가 부족하고 그에 따른 이해도 부족한 현실 속에서 컴퓨터 소프트웨어를 활용한 테셀레이션 교수 학습 자료가 교수 학습 현장에 투입되어 유용하게 사용될 수 있는지 그 가능성을 조사한 것을 목적으로 한 본 연구의 결과로서 테셀레이션이라는 주제는 도형 영역과 규칙성과 함수 영역에서 평면 도형의 각과 모양 등의 성질을 탐구하게 하고, 대칭변환의 개념을 효율적으로 학습하게 할 수 있고, 반복되는 모양에서 규칙성을 발견하고 부분과 전체를 파악하여 패턴을 인지할 수 있게 하며 제작하고 분석하는 과정을 통해 여러 가지 수학적 개념과 수학적 창의성, 수학적인 아름다움을 느끼게 할 수 있음을 발견할 수 있었다. 또한 테셀레이션은 수학적 개념은 물론 수학과 미술, 수학과 일상 생활과의 연결성을 논의하고 확인하는 데 흥미로운 주제가 될 수 있다. 초등학교 교육과정에서 새롭게 도입되고 있는 테셀레이션을 활용하여 지도하기 위한 교수 학습 자료로 유용하게 사용될 수 있고 앞으로는 테셀레이션과 관련된 내용이 직접적으로 교육과정 내에서 다루어지고, 또한 테셀레이션을 적용한 수업이 학생들의 기하학적 사고 및 수학적 태도에 미치는 영향과 관련한 연구가 뒤따라야 할 것으로 본다.

• Journal of Elementary Mathematics Education in Korea
• /
• v.4 no.1
• /
• pp.1-19
• /
• 2000

This paper aims to enhance students' interest in the use of calculators in mathematics education and promote their use of calculators in real-life situations. Towards these ends, problem types and instructional models developed for the efficient utilization of calculators. The instructional models focus on teaching mathematics relying on the path through which expert teachers have gone through to gain relevant knowledge. By developing problem types and instructional models suitable for calculator use, We can contribute to a better attainment of instructional goals in mathematics education. The instructional models and problem types will aid teachers in making decisions about instructional development plan and basic features of instructional activities. The use of a new medium will also lead to increased interest and confidence in learning, thus contributing to the enhancement of students' ego.

• Education of Primary School Mathematics
• /
• v.25 no.1
• /
• pp.101-123
• /
• 2022

Recently, as the educational paradigm shifts from teacher-centered to learner-centered, the active construction of knowledge of learners is becoming more important. Accordingly, classes using mathematical modeling are receiving attention. However, existing research is focused on teachers or middle and high school students, so it is difficult to apply the contents and results of the research to preservice teachers. Therefore, in this study, the experience of mathematical modeling was examined for elementary school preservice teachers. And we looked at how positive experiences of mathematical modeling change their perceptions. As a result of the study, elementary school preservice teachers had very little experience in mathematical modeling during their school days. In addition, it was found that the perceptions changed more positively than when a theoretical class on mathematical modeling was conducted, rather than when the experience of mathematical modeling was actually shared. Based on the results of this study, implications were suggested in the course of training preservice teachers.