• Journal for History of Mathematics
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• v.22 no.1
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• pp.1-24
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• 2009

In this paper we have inferred the influence of Zeno on the construction of the potential infinite of Aristotle based on arguments of Zeno's paradoxes. When we examine the potential infinite of Aristotle as the basis of the ancient Greek mathematics, we can see that they did not permit the concept of the actual infinite necessary for calculus. The reason Why they recognized the potential infinite, denying the actual infinite as seen in Aristotle's physics could be found in their attempt to escape the illogicality shown in Zeno's arguments. Accordingly, this paper could provided one of reasons why the ancient Greeks had used uneasy exhaustion's method instead of developing the quadrature involving the limit concept.

• School Mathematics
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• v.14 no.4
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• pp.565-577
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• 2012

In this study, we investigated the process of constructing the geometrical solutions to quadratic equation, through proportions between lengths of similar triangles in a dynamic environment. To do this, we provided one task to 4 ninth grades students and observed the process of the students' activities and strategies. As a result of this pilot lesson study, our research shows the advantage and possibility of geometrical method in learning and teaching quadratic equation.

• Journal for History of Mathematics
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• v.21 no.4
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• pp.105-126
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• 2008

This article summarizes the historical changes of the secondary school geometry to give insights into the new direction of geometry education for the 21th century. Geometry has been considered as an essential subject in high school since mid-nineteen century in accordance with the social changes. Since the development of computer softwares such as CAD effects on the role of geometry in work and professional societies, the knowledge and skills the contemporary world require to school geometry have being changed. More focus on applications and modeling aspects, expansion of reasoning and problem solving, emphasis on design-related elements are features of the school geometry for the new century.

• Education of Primary School Mathematics
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• v.21 no.2
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• pp.237-260
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• 2018

This study investigated the models of four countries' elementary mathematics textbooks in Ratio and Rate and identified how multiplicative perspectives on proportional relationships and the structure of proportion situations are reflected in the textbooks. For this, textbooks of 5th and 6th grade textbooks in Korea Japan, Singapore and U.S. are compared and analyzed. As a result, we can find multiplicative perspectives on proportional relationships and the structure of proportion situations on pictorial models, ratio tables, double number lines and double tape diagrams. Also, the development of Japanese textbooks from multiple batches perspectives to variable parts perspectives and the examples of the use with two models together implied the connection and union of two multiplicative perspectives. Based on these results, careful verification and discussion for the next textbook is needed to develop students' proportional reasoning and teach some effective reasoning strategies. And this study will provide the implication for what kinds of and how visual models are presented in the next textbook.

• Communications of Mathematical Education
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• v.34 no.2
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• pp.161-177
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• 2020

This study constructed an experiment group and a comparative group, composed of high school students preparing for "Na" type math exam and provided one-to-many tutoring cooperative learning. This study tested the differences between group and between pre- and post-treatment scores by group using non-parametric statistics techniques. Moreover, this study conducted an open-type survey twice and had individual interviews to examine the affective domains of students. The difference in scores between the experimental group and the comparative group was not significant. However, the difference between pre- and post-treatment math scores was only significant in the experiment group among the three groups. Additionally, the student-teacher could reflect on him or her and improve self-efficacy while teaching other ordinary students. The ordinary students were more interested and motivated in the lessons and became more confident. In terms of mathematics competency, we could see that communication, problem-solving, reasoning, and attitude & practice were improved.

• The Mathematical Education
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• v.58 no.3
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• pp.367-381
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• 2019

This investigation engaged elementary and middle school pre-service teachers in a task of modeling and explaining the magnitude of $0.14m^2$ and examined their responses. The study analyzed both successful and unsuccessful responses in order to reflect on the patterns of misconceptions relative to pre-service teachers' prior knowledge. The findings suggest a need to promote opportunities for pre-service teachers to make connections between different domains through meaningful tasks, to reason abstractly and quantitatively, to use proper language, and to refine conceptual understanding. While mathematics teacher educators (MTEs) could use such mathematical tasks to identify the mathematical content needs of pre-service teachers, MTEs generally use instructional time to connect content and pedagogy. More importantly, an early and consistent exposure to a combined experience of mathematics and pedagogy that connects and deepens key concepts in the program's curriculum is critical in defining the important content knowledge for K-8 mathematics teachers.

• Journal of Educational Research in Mathematics
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• v.22 no.3
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• pp.331-352
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• 2012

The purpose of the study is to verify what cognitive variables have significant effect on proportional problem solving. For this aim, the study classified proportional problem into well-structured, moderately-structured, ill-structured problem by the level of structuredness, then classified the cognitive variables as well into factual algorithm knowledge, conceptual knowledge, knowledge of problem type, quantity change recognition and meta-cognition(meta-regulation and meta-knowledge). Then, it verified what cognitive variables have significant effects on 6th graders' proportional problem solving abilities through multiple regression analysis technique. As a result of the analysis, different cognitive variables effect on solving proportional problem classified by the level of structuredness. Through the results, the study suggest how to teach and assess proportional reasoning and problem solving in elementary mathematics class.

• The Mathematical Education
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• v.49 no.2
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• pp.223-246
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• 2010

Goos(2004) introduced educational researchers' demand for change on the way that mathematics is taught in schools and the series of curriculum documents produced by the National council of Teachers of Mathematics. The documents have placed emphasis on the processes of problem solving, reasoning, and communication. In Korea, the national curriculum documents have also placed increased emphasis on mathematical activities such as reasoning and communication(1997, 2007).The purpose of this study is to analyze the impact of inquiry-oriented instruction with guided reinvention on students' mathematical activities containing communication and reasoning for science high school students. In this paper, we introduce an inquiry-oriented instruction containing Polya's plausible reasoning, Freudenthal's guided reinvention, Forman's sociocultural approach of learning, and Vygotsky's zone of proximal development. We analyze the impact of mathematical findings from inquiry-oriented instruction on students' mathematical activities containing communication and reasoning.

• Review of KIISC
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• v.28 no.2
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• pp.61-77
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• 2018

차분 프라이버시는 통계 데이터베이스 상에서 수행되는 질의 결과에 의한 개인정보 추론을 방지하기 위한 수학적 모델로써 2006년 Dwork에 의해 처음 소개된 이후로 통계 데이터에 대한 프라이버 보호의 표준으로 자리잡고 있다. 차분 프라이버시는 데이터의 삽입/삭제 또는 변형에 의한 질의 결과의 변화량을 일정 수준 이하로 유지함으로써 정보 노출을 제한하는 개념이다. 이를 구현하기 위해 메커니즘 상의 연구(라플라스 메커니즘, 익스퍼넨셜 메커니즘)와 다양한 데이터 분석 환경(히스토그램, 회귀 분석, 의사 결정 트리, 연관 관계 추론, 클러스터링, 딥러닝 등)에 차분 프라이버시를 적용하는 연구들이 수행되어 왔다. 본 논문에서는 처음 Dwork에 의해 제안되었을 때의 차분 프라이버시 개념에 대한 이해부터 오늘날 애플 및 구글에서 차분 프라이버시가 적용되고 있는 수준에 대한 연구들의 진행 상황과 앞으로의 연구 주제에 대해 소개한다.

• Journal of Gifted/Talented Education
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• v.17 no.1
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• pp.1-26
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• 2007

The purpose of this study was to develop a math test for identification of the mathematically gifted on the basis of their math creative problem solving ability and to evaluate the goodness of the test. Especially, testing reliability and validity of scoring method on the basis of fluency only for evaluation of math creative problem solving ability was one of the main purposes. Ten closed math problems and 5 open math problems were developed requiring math thinking abilities such as intuitive insight, organization of information, inductive and deductive reasoning, generalization and application, and reflective thinking. The 10 closed math test items of Type I and the 5 open math test items of Type II were administered to 1,032 Grade 7 students who were recommended by their teachers as candidates for gifted education programs. Students' responses were scored by math teachers. Their responses were analyzed by BIGSTEPS and 1 parameter model of item analyses technique. The item analyses revealed that the problems were good in reliability, validity, item difficulty and item discriminating power even when creativity was scored based on the single criteria of fluency. This also confirmed that the open problems which are less-defined, less-structured and non-entrenched were good in measuring math creative problem solving ability of the candidates for math gifted education programs. In addition, it was found that the math creative problem solving tests discriminated applicants for the two different gifted educational institutions.