• 한국수학교육학회지시리즈D:수학교육연구
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• 제12권3호
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• pp.215-233
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• 2008

Deep comprehension of basic mathematical notions and concepts is a basic condition of a successful teaching. Some elements of algebraic thinking belong to the elementary school mathematics. The question "What stays the same and what changes?" link arithmetic problems with algebraic conception of variable. We have studied beliefs and comprehensions of future elementary school mathematics teachers on early algebra. Pre-service teachers from three academic pedagogical colleges deal with mathematical problems from the pre-algebra point of view, with the emphasis on changes and invariants. The idea is that the intensive use of non-formal algebra may help learners to construct a better understanding of fundamental ideas of arithmetic on the strong basis of algebraic thinking. In this article the study concerning arithmetic series is described. Considerable number of pre-service teachers moved from formulas to deep comprehension of the subject. Additionally, there are indications of ability to apply the conception of change and invariance in other mathematical and didactical contexts.

• 한국수학교육학회지시리즈A:수학교육
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• 제53권1호
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• pp.57-73
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• 2014

This study investigated the connections of mathematical thinking of students at the second, fourth, and sixth grades with regard to multiplication, fraction, and proportion, all of which have multiplicative structures. A paper-and-pencil test and subsequent interviews were conducted. The results showed that mathematical thinking including vertical thinking and relational thinking was commonly involved in multiplication, fraction, and proportion. On one hand, the insufficient understanding of preceding concepts had negative impact on learning subsequent concepts. On the other hand, learning the succeeding concepts helped students solve the problems related to the preceding concepts. By analyzing the connections between the preceding concepts and the succeeding concepts, this study provides instructional implications of teaching multiplication, fraction, and proportion.

• 한국수학교육학회지시리즈A:수학교육
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• 제53권2호
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• pp.163-184
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• 2014

The purpose of this study was to develop the assessment tools using graphing calculators for the assessment of the mathematical process which was emphasized in 2009 reformed mathematics curriculum. In this paper, we presented three sample calculator-based test items for the assessment of students' mathematical process abilities and scoring rubrics for the paper and pencil assessment and assessment based on observation on each item. In order to improve mathematics teachers' understanding of the assessment tools using graphing calculators and to show the procedures of assessment using technological devices, we also drew up assessment guidelines. We hope the results of the study contribute to the promotion of assessment environment encouraging the use of graphing calculators in assessments.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제22권1호
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• pp.47-82
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• 2019

Pennsylvania is one of the states that adopted the Common Core State Standards for Mathematics (CCSSM) and crafted its own standards (The PA Core State Standards). Pennsylvania teachers are required to have a clear understanding of the PA Core Standards. It is timely and appropriate to study Pennsylvania teachers' beliefs, as the standards have been adopted and implemented for several years since the revision of the PA Core Standards (2014). This study examined how eight western Pennsylvania elementary school teachers' beliefs about teaching and learning mathematics related to the SMP. To this end, I conducted an in-depth interview with each participating teacher. The in-depth interviews featured the teachers' overarching mathematical instructional goals and their productive beliefs. Furthermore, I linked these beliefs with the CCSSM Standards for Mathematical Practice (SMP).

• 한국수학교육학회지시리즈A:수학교육
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• 제44권4호
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• pp.547-563
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• 2005

There have been many papers reporting that the axiomatic approach in Abstract Algebra is a big obstacle to overcome for the students who are not trained to think in an abstract way. Therefore an instructor must seek for ways to help students grasp mathematical concepts in Abstract Algebra and select the ones suitable for students. Mathematics faculty and students generally consider Abstract Algebra in general and quotient groups in particular to be one of the most troublesome undergraduate subjects. For, an individual's knowledge of the concept of group should include an understanding of various mathematical properties and constructions including groups consisting of undefined elements and a binary operation satisfying the axioms. Even if one begins with a very concrete group, the transition from the group to one of its quotient changes the nature of the elements and forces a student to deal with elements that are undefined. In fact, we also have found through running abstract algebra courses for several years that students have considerable difficulty in understanding the concept of quotient groups. Based on the above observation, we explore and analyze the nature of students' knowledge about $Z_n$ that is the set of congruence classes modulo n. Applying the genetic decomposition method, we propose a model to lead students to achieve the correct concept of $Z_n$.

• 한국수학교육학회지시리즈A:수학교육
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• 제58권4호
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• pp.589-607
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• 2019

학생들이 수학 교과서에 대해서 어떻게 생각하는지 또한 학습에서 어떻게 활용하는지에 대하여 알려진 바가 거의 없다. 이 연구에서는 고등학생들이 수학 교과서를 어떻게 인식하고 활용하는지를 탐색하고자 하였다. 인터뷰 질문지를 개발하여서 고등학생 11명을 대상으로 인터뷰를 실시하였다. 그 결과로, 다음 세 가지 측면을 발견하였다. 첫째, 학생들은 교과서를 수업에서 활용하는 자료로 인식하며 대학 입학시험을 준비하는 데 중요한 교재로 사용하는 것으로 나타났다. 둘째, 학생들은 교과서를 학교에서 시행하는 중간 또는 기말고사 등 정기고사 시험을 대비하는 데 있어서 필수로 사용하지만, 실질적인 학습에는 매우 한정하여서 활용하는 것으로 나타났다. 셋째, 학생들은 교과서를 통해서 기르고자 하는 수학적 사고능력이 무엇인지에 대하여서는 거의 파악하지 못하는 것으로 나타났다.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제10권2호
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• pp.125-139
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• 2007

본 연구는 교구활용을 강화한 수업이 학업 성취와 수학적 성향 및 태도에 어떠한 영향을 미치는지 살펴봄으로써 교구활용을 활성화할 수 있는 방안을 모색하는 데 있다. 본 연구에서 실험반과 비교반에 적용한 변수는 교구활용 빈도를 제외하고 기타 수업 환경은 동일에게 적용하였다. 연구 결과 학업 성취도를 t-검정한 결과 사전검사 점수는 두 집단 사이에 유의한 차이가 없는 것으로 나타났으나, 사후검사에서는 실험반이 비교반보다 10점 정도(t=0.519, p<0.01) 평균적으로 높은 것으로 나타났다. 또 실험 집단 내에서 교구활용이 학습 수준별 학업 성취에 미치는 효과는 사전점수를 공변인으로 하는 공변량분산분석(ANCOVA)을 실시한 결과 5% 유의수준에서 수준별 차이를 보였으며 (F=4.885, p<0.05), 중 상위 수준의 학생보다 하위 수준의 학생들에게 더 긍정적인 효과를 미치는 것으로 나타났다.

• 대한수학교육학회지:수학교육학연구
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• 제11권2호
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• pp.239-256
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• 2001

The notion of metaphor has been increasingly popular in research of mathematics education. In particular, metaphor becomes a useful unit for analysis to provide a profound insight into mathematical reasoning and problem solving. In this context, this paper takes metaphor as an analytic unit to examine the relationship between objectivity and subjectivity in mathematical reasoning. Specifically, the discourse analysis focuses on the code switching between literal language and metaphor in mathematical discourse. It is shown that the linguistic code switching is parallel with the switching between two different kinds of mathematical knowledge, that is, factual knowledge and mathematical imagination, which constitute objectivity and subjectivity in mathematical reasoning. Furthermore, the pattern of the linguistic code switching reveals the dialectical relationship between the two poles of mathematical reasoning. Based on the understanding of the dialectical relationship, this paper provides some educational implications. First, the code-switching highlights diverse aspects of mathematics learning. Learning mathematics is concerned with developing not only technicality but also mathematical creativity. Second, the dialectical relationship between objectivity and subjectivity suggests that teaching and teaming mathematics is socioculturally constructed. Indeed, it is shown that not all metaphors are mathematically appropriated. They should be consistent with the cultural model of a mathematical concept under discussion. In general, this sociocultural perspective on mathematical metaphor highlights the sociocultural organization of teaching and loaming mathematics and provides a theoretical viewpoint to understand epistemological diversities in mathematics classroom.

• 한국초등수학교육학회지
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• 제14권3호
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• pp.885-905
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• 2010

수학과 평가에서 주로 제기되는 문제점은 평가 내용이 단편적인 지식을 암기하는 쪽으로 치우쳐 있다는 점과 평가 문항이 객관식 문제 중심의 지필 검사에 한정되어 있다는 것이다. 교육현장에서는 이러한 문제점올 해결하기 위한 방안으로 서술형 평가를 통해 학생들의 문제해결과정을 검토하고, 이 과정에서 비롯되는 오류 유형을 분석하려는 연구가 진행되어왔다. 곧, 서술형 평가를 통해 학생들이 알고 있는 수학적 지식을 수학적 용어로 자유롭게 표현하는 과정에서 그 과정이 옳은지, 개념 이해가 정확한지를 검토하고, 만약 잘못 이해하고 있다면 무엇 때문에 이러한 오류를 범하고 있는지를 분석함으로써, 수학문제해결과정에서 비롯되는 오류에 대한 피드백을 제공할 수 있기 때문이다. 본 연구는 초등학교 4학년 학생을 연구대상으로 하며, 수와 연산 영역에서 서술형 평가 문항을 개발하여 진행된 것이다. 연구 과정은 먼저 서술형 평가에서 나타나는 오류를 문항 이해의 오류, 개념 원리의 오류, 자료 사용의 오류, 풀이 과정의 오류, 기록 단계의 오류, 풀이 과정의 생략 등 6가지 유형으로 구분하여 문항별 답안에서 나타나는 유형별 오류를 분석하였다. 이와 함께 학업성취도에 따라 오류 유형이 다르게 나타날 수 있다는 점에 착안하여, 상 중 하 성취도에 따른 오류 유형을 분석하였다. 서술형 평가를 통해 학생들의 문제해결과정을 검토하고 이 과정에서 나타나는 오류를 분석함으로써, 평가를 통한 피드백이 효과적인 수학학습지도로 연결될 수 있기를 기대한다.

• 대한수학교육학회지:수학교육학연구
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• 제10권1호
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• pp.85-102
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• 2000

The concept of variables is central to mathematics teaching and learning in junior and senior high school. Understanding the concept provides the basis for the transition from arithmetic to algebra and necessary for the meaningful use of all advanced mathematics. Despite the importance of the concept, however, much has been written in the last decade concerning students' difficulties with the concept. This Thesis is based on research to investigate the hypothesis that LOGO programming will contribute to 6th grader' learning of variables. The aim of the research were to; .investigate practice on pupils' understanding of variables before the activity with a computer; .identify functions of LOGO programming in pupils' using and understanding of variable symbols, variable domain and the relationship between two variable dependent expressions during the activity using a computer; .investigate the influence of pupils' mathematical belief on understanding and using variables. The research consisted predominantly of a case study of 6 pupils' discourse and activities concerning variable during their abnormal lessons and interviews with researcher. The data collected for this study included video recordings of the pupils'work with their spoken language.