• Research in Mathematical Education
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• v.24 no.4
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• pp.279-311
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• 2021

In this paper, we report the types of teaching moves a mathematics teacher educator attempted in his teaching of third-grade students at an urban elementary school in South Korea over two months. We analyze the lesson videos to find the patterns of teaching moves and speculate the link between the teaching and students' mathematical proficiencies recommended in the Common Core State Standards for Mathematical Practices. Closely related teaching moves to the students' development of a certain mathematical proficiency would imply the exemplary practices that teachers-both inservice and preservice teachers-can implement in their classrooms.

• Communications of Mathematical Education
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• v.20 no.1 s.25
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• pp.117-145
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• 2006

Mathematically gifted children have creative curiosity about novel tasks deriving from their natural mathematical talents, aptitudes, intellectual abilities and creativities. More effect in nurturing the creative thinking found in brilliant children, letting them approach problem solving in various ways and make strategic attempts is needed. Given this perspective, it is desirable to select open-ended and atypical problems as a task for educational program for gifted children. In this paper, various types of open-ended problems were framed and based on these, teaming activities were adapted into gifted children's class. Then in the problem solving process, the characteristic of bright children's mathematical thinking ability and examples of problem solving strategies were analyzed so that suggestions about classes for bright children utilizing open-ended tasks at elementary schools could be achieved. For this, an open-ended task made of 24 inquiries was structured, the teaching procedure was made of three steps properly transforming Renzulli's Enrichment Triad Model, and 24 periods of classes were progressed according to the teaching plan. One period of class for each subcategories of mathematical thinking ability; ability of intuitional insight, systematizing information, space formation/visualization, mathematical abstraction, mathematical reasoning, and reflective thinking were chosen and analyzed regarding teaching, teaming process and products. Problem solving examples that could be anticipated through teaching and teaming process and products analysis, and creative problem solving examples were suggested, and suggestions about teaching bright children using open-ended tasks were deduced based on the analysis of the characteristic of tasks, role of the teacher, impartiality and probability of approaching through reflecting the classes. Through the case study of a mathematics class for bright children making use of open-ended tasks proved to satisfy the curiosity of the students, and was proved to be effective for providing and forming a habit of various mathematical thinking experiences by establishing atypical mathematical problem solving strategies. This study is meaningful in that it provided mathematically gifted children's problem solving procedures about open-ended problems and it made an attempt at concrete and practical case study about classes fur gifted children while most of studies on education for gifted children in this country focus on the studies on basic theories or quantitative studies.

• The Mathematical Education
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• v.27 no.1
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• pp.15-23
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• 1988

We are at the onset of a major revolution in education, a revolution unparalleled since the invention of the printing press. The computer will be the instrument of this revolution. Computers and computer application are everywhere these days. Everyone can't avoid the influence of the computer in today's world. The computer is no longer a magical, unfamiliar tool that is used only by researchers or scholars or scientists. The computer helps us do our jobs and even routine tasks more effectively and efficiently. More importantly, it gives us power never before available to solve complex problems. Mathematics instruction in secondary schools is frequently perceived to be more a amendable to the use of computers than are other areas of the school curriculum. This is based on the perception of mathematics as a subject with clearly defined objectives and outcomes that can be reliably measured by devices readily at hand or easily constructed by teachers or researchers. Because of this reason, the first large-scale computerized curriculum projects were in mathematics, and the first educational computer games were mathematics games. And now, the entire mathematics curriculum appears to be the first of the traditional school curriculum areas to be undergoing substantial trasformation because of computers. Recently, many research-Institutes of our country are going to study on computers in orders to use it in mathematics education, but the study is still start ing-step. In order to keep abreast of this trend necessity, and to enhance mathematics teaching/learning which is instructed lecture-based teaching/learning at the present time, this study aims to develop/present practical method of computer-using. This is devided into three methods. 1. Programming teaching/learning method This part is presented the following five types which can teach/learn the mathematical concepts and principle through concise program. (Type 1) Complete a program. (Type 2) Know the given program's content and predict the output. (Type 3) Write a program of the given flow-chart and solve the problem. (Type 4) Make an inference from an error message, find errors and correct them. (Type 5) Investigate complex mathematical fact through program and annotate a program. 2. Problem-solving teaching/learning method solving This part is illustrated how a computer can be used as a tool to help students solve realistic mathematical problems while simultaneously reinforcing their understanding of problem-solving processes. Here, four different problems are presented. For each problem, a four-stage problem-solving model of polya is given: Problem statement, Problem analysis, Computer program, and Looking back/Looking ahead. 3. CAI program teaching/learning method This part is developed/presented courseware of sine theorem section (Mathematics I for high school) in order to avail individualized learning or interactive learning with teacher. (Appendix I, II)

• School Mathematics
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• v.19 no.3
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• pp.461-480
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• 2017

The aim of this study was to analyze characteristics of teachers' knowledge about correlation with data presented in $2{\times}2$ tables. In order to achieve the aim, this study conducted didactical analysis about two-way tables through examining previous researches and developed a questionnaire with reference to the results of the analysis. The questionnaire was given to 53 middle and high school teachers and qualitative methods were used to analyze the data obtained from the written responses by the participants. This study also elaborated the framework descriptors for interpreting the teachers' responses in the light of the didactical analysis and the data was elucidated in terms of this framework. The specific features of teachers' knowledge about correlation with data presented in $2{\times}2$ tables were categorized into three types as a result. This study raised several implications for teachers' professional development for effective mathematics instruction about correlation and related concepts dealt with in probability and statistics.

• School Mathematics
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• v.17 no.2
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• pp.223-239
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• 2015

This study focused on classroom dialogue for communicating spatial information which is supposed to be implemented through learning activities using building-blocks. Even though mathematics textbooks for $2^{nd}$ graders have activities which require abilities of explaining and understanding some spatial information, we know few about how mathematical communication between teacher and students or among students and which strategies are more effective. For this reason, two building-block lessons for $2^{nd}$ graders were observed. The characteristics of teachers' instruction and students' explanation were identified and the mathematical communication between teachers and students or among students was analyzed. As a result, mains factors of impeding students' explanation and understanding were induced and the types of their communication were classified. Based on these results, several teaching strategies for effective communication in buildingblock lessons were suggested.

• Communications of Mathematical Education
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• v.37 no.2
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• pp.159-181
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• 2023

The purpose of this study is to explore secondary mathematics teachers' perceptions on Artificial Intelligence (AI). For this purpose, we conducted three focus group interviews with 18 secondary in-service mathematics teachers and analyzed their perceptions on AI for math and math for AI. The secondary in-service mathematics teachers perceive that AI allows to implement different types of mathematics instruction but has limitations in exploring students' mathematical thinking and having emotional interactions with students. They also perceive that AI makes it easy to develop assessment items for teachers but teachers' interventions are needed for grading essay-type assessment items. Lastly, the secondary in-service mathematics teachers agree the rationale of adopting the subject ＜Artificial Intelligence Mathematics＞ and its needs for students, but they perceive that they are not well prepared yet to teach the subject and do not have sufficient resources for teaching the subject and assessing students' understanding about the subject. The findings provide implications and insights for developing individualized AI learning tools for students in the secondary level, providing AI assessment tools for teachers, and offering professional development programs for teachers to increase their understanding about the subject.

• Education of Primary School Mathematics
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• v.20 no.1
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• pp.37-52
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• 2017

The purpose of this thesis is to analyze the current status of a program for an elementary math class for gifted students in Daegu and to propose a remedy. The main results of this thesis are as follows. First, goals of the gifted class and the basic operation direction were satisfactory, however plans for parent training programs and self evaluation of the classes were not presented. Therefore, it needs when and how to do for specific plan of gifted class evaluation and parent training programs. Second, The annual instruction plan has been restricted to the subject matter education and field trips and has not included specific teaching methods in accordance with the contents of learning program. The management of gifted classes, therefore, requires not only the subject matter education and field trips but also output presentations, leadership programs, voluntary activities, events and camps which promote the integral development of gifted students. Third, there is no duplication of content to another grade, and various activities did not cover the whole scope of math topics(eg. number and operation, geometry, measurement, pattern) equally. In accordance with elementary mathematics characteristics, teachers should equally distribute time in whole range of mathematics while they teach students in the class because it is critical to discover gifted students throughout the whole curriculum of elementary mathematics. Fourth, as there are insufficient support and operational lack of material development, several types of programs are not utilized and balanced. It is necessary for teachers to try to find the type of teaching methods in accordance with the circumstances and content, so that students can experience several types of programs. If through this study, we can improve the development, management and quality of gifted math programs, it would further the development of gifted education.

• The Mathematical Education
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• v.54 no.2
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• pp.119-141
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• 2015

As the population of senior citizens has been increasing very rapidly, the importance of their education is gradually emphasized. To maintain their mental and physical health, the solution on the biological, physical, and educational approach might be helpful and effective. Especially in the aspect of the educational approach, the mathematics education can be regarded as an important subject for keeping the seniors in a good mental health. The reason is that the ultimate goal of mathematics education is to pursue an enhancement of mathematical thinking ability. By the reason, this study aimed to develop mathematical materials for enhancing seniors' thinking ability, and the seniors usually belong to fifties and sixties. To this purpose, this study selected the six essential mathematical thinking elements and four mathematical domains of 'number and operation', 'shape and measurement', 'possibility', and 'patterns'. Based on these elements, the mathematical materials including the nine types of activities using games and commercial manipulatives were developed. On the subject of 52 female seniors, the instruction was conducted using a part of the materials during 100 minutes. Also, 13 survey items were developed beforehand, and the survey was implemented after the class, and eventually 48 seniors responded in the survey. As a result, it is meaningful to develop the materials not only for enhancing mathematical thinking ability but for understanding and utilizing the content of materials. Furthermore, it is requested that those materials be differentiated according to the degree or the difference of age, academic ability, and sex.

• Journal of Elementary Mathematics Education in Korea
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• v.16 no.1
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• pp.125-143
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• 2012

This study is designed to see the characteristics of elementary students' arithmetic error patterns and error rates by going up grades and to draw some implications for effective instruction. For this, 580 elementary students of grade 3-6 are tested with the same subtraction, multiplication and division problems. Their errors are analyzed by the frame of arithmetic error types this study sets. As a result of analysis, it turns out that the children's performance in arithmetic get well as their grades go up and the first learning year of any kind of arithmetic procedures has the largest improvement in arithmetic performance. It is concluded that some arithmetic errors need teachers' caution, but we fortunately find that children's errors are not so seriously systematic and sticky that they can be easily corrected by proper intervention. Finally, several instructional strategies for arithmetic procedures are suggested.

• Communications of Mathematical Education
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• v.37 no.4
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• pp.635-652
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• 2023

This study conducts a comprehensive analysis of the curricular progression of the concepts and learning sequences of 'lines', specifically, 'line segments', 'straight lines', and 'rays', at the elementary school level. By examining mathematics curricula and textbooks, spanning from 2nd to 7th and 2007, 2009, 2015, and up to 2022 revised version, the study investigates the timing and methods of introducing these essential geometric concepts. It also explores the sequential delivery of instruction and the key focal points of pedagogy. Through the analysis of shifts in the timing and definitions, it becomes evident that these concepts of lines have predominantly been integrated as integral components of two-dimensional plane figures. This includes their role in defining the sides of polygons and the angles formed by lines. This perspective underscores the importance of providing ample opportunities for students to explore these basic geometric entities. Furthermore, the definitions of line segments, straight lines, and rays, their interrelations with points, and the relationships established between different types of lines significantly influence the development of these core concepts. Lastly, the study emphasizes the significance of introducing fundamental mathematical concepts, such as the notion of straight lines as the shortest distance in line segments and the concept of lines extending infinitely (infiniteness) in straight lines and rays. These ideas serve as foundational elements of mathematical thinking, emphasizing the necessity for students to grasp concretely these concepts through visualization and experiences in their daily surroundings. This progression aligns with a shift towards the comprehension of Euclidean geometry. This research suggests a comprehensive reassessment of how line concepts are introduced and taught, with a particular focus on connecting real-life exploratory experiences to the foundational principles of geometry, thereby enhancing the quality of mathematics education.