• Journal of Educational Research in Mathematics
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• v.23 no.2
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• pp.269-284
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• 2013

The aim of this paper is to explore and understand, using in-depth interviews, the participant's motivation for becoming a math teacher, ways of dealing with university math knowledge and private tutoring experiences. In addition a larger aim is to understand how the individual's interest in mathematics and turing are linked to his/her larger personal tendencies contrasting secondary and university math learning. In-depth interviews were conducted with 6 pre-service teachers' subjective experiences focusing on motivation and feelings on mathematical knowledge and private tutoring. The output of this research consists of 3 cases, highlighting and conceptually developing the specific aspects under study; different ways in which individuals' involvement with the math learning and tutoring that might be connected with the ways of becoming teachers. Larger aspects of pre-service teachers' subjective experiences were sketched by contrasting the inner aspects of the individuals. Several suggestions were presented at the end with the possible research directions for math education.

• Communications of Mathematical Education
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• v.38 no.2
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• pp.231-246
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• 2024

In this paper, we present the development and a case study on 'Mathematics & Coding Mobile Contents' tailored for secondary education. These innovative resources aim to alleviate the burden of laborious calculations, enabling students to allocate more time to engage in discussions and visualize complex mathematical concepts. By integrating these contents into the curriculum, students can effectively meet the national standards for achievement in mathematics. They are empowered to develop their mathematical thinking skills through active engagement with the material. When properly integrated into secondary mathematics education, these resources not only facilitate attainment of national curriculum standards but also foster students' confidence in their mathematical abilities. Furthermore, they serve as valuable tools for nurturing both computational and mathematical thinking among students.

• Communications of Mathematical Education
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• v.11
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• pp.47-69
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• 2001

본 논문은 고등학교 교육과정상에서 학습자들이 오류를 범하기 쉽고, 어려워 하는 극한에 대해 보다 효과적인 지도방법을 제시한다. 현실적으로 교수활동은 교실이라는 공간에서 일정한 수업시간동안에 교사와 학습자와의 관계속에서 이루어진다. 그 속에서 학습자들은 주변의 세계를 관찰함으로써, 혹은 추측과 반박을 통해 시행착오적으로 사고함으로써 혹은 모순, 어려움, 불균형을 일으키는 주위환경에 동화 ${\cdot}$ 조절을 함으로써 자신을 적응시켜 가면서 학습하게 된다. 따라서 교수학적 의도가 미비한 환경은 학습자에게 획득하기를 기대하는 학습을 할 수 없게 한다. Brousseas의 교수학적 상황론에 근거하여 교육의 현장인 교실에서의 교사와 학생간의 상호작용에 따른 교수-학습의 중요성에 초점을 둔 본 논문은 Freudenthal의 역사발생적 원리에 의한 극한의 정의와 학습자의 오류수정을 위한 교수학습 전략으로 Lakatos의 발견술을 제안하였다. 또한 극한 개념에 대해 실생활에서 학습자에게 쉽게 동화 ${\cdot}$ 조절이 일어날 수 있는 학습 방법을 제안하였다.

• School Mathematics
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• v.18 no.4
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• pp.839-856
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• 2016

In 2009 revision and 2015 revision mathematics national curriculum, 'proof' was moved to high school from middle school in consideration of the cognitive development level of students, and 'proof by contradiction' was stated in the "success criteria of learning contents" of the first year high school subject while it had been not officially introduced in $7^{th}$ and 2007 revision national curriculum. Proof by contradiction is known that it induces a cognitive conflict due to the unique nature of rather assuming the opposite of the statement for proving it. In this article, based on the logical, mathematical and historical analysis of Proof by contradiction, we looked about the introductions and the applications of the current textbooks which had been revised recently, and searched for improvement measures from the viewpoint of discovery, explanation, and consilience. We suggested introducing Proof by contradiction after describing the discovery process earlier, separately but organically describing parts necessary to assume the opposite and parts not necessary, disclosing the relationships with proof by contrapositive, and using the viewpoint of consilience.

• Journal of the Korean School Mathematics Society
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• v.15 no.3
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• pp.535-563
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• 2012

This study was conducted to confirm the necessity of analogical thinking and to empirically verify the effectiveness of analogical reasoning through the visual representation by analyzing the factors of problem solving depending on analogical conditions. Four conditions (a visual representation mapping condition, a conceptual mapping condition, a retrieval hint condition and no hint condition) were set up for the above purpose and 80 twelfth-grade students from C high-School in Cheong-Ju, Chung-Buk participated in the present study as subjects. They solved the same mathematical problem about sequence of complex numbers in their differed process requirements for analogical transfer. The problem solving rates for each condition were analyzed by Chi-square analysis using SPSS 12.0 program. The results of this study indicate that retrieval of base knowledge is restricted when participants do not use analogy intentionally in problem solving and the mapping of the base and target concepts through the visual representation would be closely related to successful analogical transfer. As the results of this study offer, analogical thinking is necessary while solving mathematical problems and it supports empirically the conclusion that recognition of the relational similarity between base and target concepts by the aid of visual representation is closely associated with successful problem solving.

• School Mathematics
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• v.10 no.4
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• pp.515-535
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• 2008

As part of developmental research of a student-teaching practicum program, this research analyzed a mathematics preservice teacher's questioning. The practicum program is based on the model of reflective practice in a collaborative inquiry community for learning-to-teach. This paper describes how a preservice teacher's questioning pattern had changed on the program participation and explain how the change in discourse can be considered as an indicator for the pre service teacher's professional development. Suggestions for the future program development are discussed.

• Journal for History of Mathematics
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• v.24 no.4
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• pp.119-141
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• 2011

This paper analysed the mathematical paradoxes which would be based in the probability and statistics. Teachers need to endeavor various data in order to lead student's interest. This paper says mathematical paradoxes in mathematics education makes student have interest and concern when they study mathematics. So, teachers will recognize the need and efficiency of class for using mathematical Paradoxes, students will be promoted to study mathematics by having interest and concern. These study can show the value of paradoxes in the concept of probability and statistics, and illuminate the concept being taught in classroom. Consequently, mathematical paradoxes in mathematics education can be used efficient studying tool.

• Communications of Mathematical Education
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• v.28 no.4
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• pp.513-528
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• 2014

This study is intended to examine 36 in-service secondary school mathematics teachers' conceptions of proof in the context of mathematics and mathematics education. The results suggest that almost teachers recognize the role as justification well but have the insufficient conceptions about another various roles of proof in mathematics. The results further suggest that many of teachers have vague concept-images in relation with the requirement of proof and recognize the insufficiency about the actual teaching of proof. Based on the results, implications for revision of mathematics curriculum and mathematics teacher education are discussed.

• Journal of Educational Research in Mathematics
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• v.19 no.2
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• pp.233-256
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• 2009

The notions of conditional probability and independence are fundamental to all aspects of probabilistic reasoning. Several previous studies identified some misconceptions in students' thinking in conditional probability. However, they have not analyzed enough the nature of conditional probability. The purpose of this study was to analyze conditional probability and students' knowledge on conditional probability. First, we analyzed the conditional probability from mathematical, historico-genetic, psychological, epistemological points of view, and identified the essential aspects of the conditional probability. Second, we investigated the high school students' and undergraduate students' thinking m conditional probability and independence. The results showed that the students have some misconceptions and difficulties to solve some tasks with regard to conditional probability. Based on these analysis, the characteristics of reasoning about conditional probability are investigated and some suggestions are elicited.

• Communications of Mathematical Education
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• v.30 no.3
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• pp.263-280
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• 2016

This study aims to examine the impact of RUBRIC writing on students' mathematical modeling. By analyzing 23 tenth grade students' responses to seven problems related to mathematical modeling, we found that the students who used RUBRIC writing could not only get more correct answers but also could use more various representations and mathematical models than the students who did not use it. The students with RUBRIC writing also could translate between reality and mathematics more appropriately, and better explain the process to solve the problem than the counterpart. It implies that RUBRIC writing can help improve students' mathematical modeling and problem solving as an alternative instruction and assessment.