• Journal of Educational Research in Mathematics
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• v.17 no.4
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• pp.453-475
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• 2007

School algebra starts with introducing algebraic expressions which have been one of the cognitive obstacles to the students in the transfer from arithmetic to algebra. In the recent studies on the teaching school algebra, algebraic thinking is getting much more attention together with algebraic expressions. In this paper, we examined the processes of the transfer from arithmetic to algebra and ways for teaching early algebra through algebraic thinking factors. Issues about algebraic thinking have continued since 1980's. But the theoretic foundations for algebraic thinking have not been founded in the previous studies. In this paper, we analyzed the algebraic thinking in school algebra from historico-genetic, epistemological, and symbolic-linguistic points of view, and identified algebraic thinking factors, i.e. the principle of permanence of formal laws, the concept of variable, quantitative reasoning, algebraic interpretation - constructing algebraic expressions, trans formational reasoning - changing algebraic expressions, operational senses - operating algebraic expressions, substitution, etc. We also identified these algebraic thinking factors through analyzing mathematics textbooks of elementary and middle school, and showed the middle school students' low achievement relating to these factors through the algebraic thinking ability test. Based upon these analyses, we argued that the readiness for algebra learning should be made through the processes including algebraic thinking factors in the elementary school and that the transfer from arithmetic to algebra should be accomplished naturally through the pre-algebra course. And we searched for alternative ways to improve algebra curriculums, emphasizing algebraic thinking factors. In summary, we identified the problems of school algebra relating to the transfer from arithmetic to algebra with the problem of teaching algebraic thinking and analyzed the algebraic thinking factors of school algebra, and searched for alternative ways for improving the transfer from arithmetic to algebra and the teaching of early algebra.

• Journal of Educational Research in Mathematics
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• v.14 no.1
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• pp.19-37
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• 2004

In school mathematics, polygon and polyhedron are defined by vague terms such as "surrounded" or "formed" Moreover, the inclusion of boundary and interior in the definition of polygon and polyhedron is varied according to the context. Polygon and polyhedron are considered as "context-dependent concept" in school mathematics. Elementary school mathematics introduces a surface only in the context of solid, yet secondary school mathematics explains a surface as the trace of the line movement. From the perspective of fallabilism, it is possible and desirable to lead students to revise and improve their conceptions on polygon, polyhedron, and surface. It is more appropriate to name a face, an edge, and a vertex rather than to express a face of polyhedron, an edge of polyhedron, and a vertex of polyhedron in textbooks. The term "surface as a polygon" in secondary mathematics textbooks shows a conflict between intuitive approach in elementary school and logical approach in secondary school.

• Education of Primary School Mathematics
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• v.16 no.1
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• pp.21-33
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• 2013

In this study, We analyzed the mathematical thinking of sixth grade students showed mathematics lessons through the application of Lakatos' methodology and search for the role of their teachers in this lessons. We supposed to find the solution to the way of teaching-learning regarding the Lakatos' methodology for the elementary school level. According to the stages of presenting a problem situation, suggesting an initial conjecture, examining the conjecture, and improving the conjecture, we had lessons 8 times that are applied to Lakato's methodology. We gathered and analyzed data from lessons and interviews recording videotapes, documents for this study. The participants showed a lot of mathematical thinking. They understood the problem situation with the skill of fundamental thinking and suggested the initial conjecture by the skill of developmental thinking and they found a counter-example to be able to rebut the initial conjecture by critical thinking. Correcting the conjecture not to have counter-example, they drew developmental thinking and made their thinking generalize.

• Journal of Elementary Mathematics Education in Korea
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• v.22 no.2
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• pp.161-181
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• 2018

This study involved an investigation of prospective elementary teachers' preconceptions and experiences of diagrams and their ability to draw diagrams in solving math word problems. A questionnaire and two math word problems were administered to prospective elementary teachers who began to taking an introductory mathematics education course. The results from the analysis of their responses to the questionnaire items indicate that prospective elementary teachers appreciate the value of diagrams as tools for problem solving and communication. In addition, prospective elementary teachers have the will not only to teach their future students how to use diagrams but also to encourage them to draw diagrams in solving math word problems. However, the results also indicates that prospective elementary teachers neither use diagrams spontaneously in their math problem solving activities nor have confidence in drawing useful diagrams. Prospective elementary teachers also manifested low scores on the questionnaire items asking whether they were taught how to draw useful diagrams or encouraged by their teachers to use diagrams in their previous learning experiences. The results from the analysis of the diagrams that prospective elementary teachers drew in solving math word problems showed that most of them had difficulty drawing diagrams that represent their reasoning and solving process.

• Communications of Mathematical Education
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• v.36 no.4
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• pp.589-610
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• 2022

This study aimed to derive pedagogical implications by comparing and analyzing how the concept of pi is taught in 10 different elementary mathematics textbooks, which are scheduled to be applied from 2023. We developed a textbook analysis framework by previous studies on the concept of pi and the teaching of pi, and analyzed in terms of three instructional elements (i.e. inferring conceptsof pi, understanding properties of pi, and applying relationships). We derived the need to emphasize various contexts for estimation of pi, presentation of problem situations that provide motivation to actually measure diameters and circumferences, providing an opportunity to explore the properties of measurement, and an experience the flexibility of selecting an approximate value of pi. Based on the above conclusions and pedagogical implications through the research results., we suggested ways to teach the concept of pi in elementary mathematics and improvement points for developing textbooks focusing on the context of introduction of pi and the use of technological tools.

• Journal of the Korean Institute of Intelligent Systems
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• v.26 no.3
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• pp.226-232
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• 2016

The research for the improvement in math and science scores is active by the brain exercises, stress reliefs, and emotion sensitized illuminations. This principle is based on the following facts that the most effective brain turns are supported with the circumstances not only when the brain wave should keep stability and comfort in science criticism, but also when minimized stress and comfortable illumination should be adjusted in solving math problem. In this paper, in order to effectively learn mathematics and science, the most optimized simulating tests in learning conditions are conducted by using a stress relief. However, depending on the users' tastes, the effectiveness on favorite music or colors therapy have no convergency but many differentiations. Therefore, in this paper, in order to solve this problem, the proposed optimal illumination and music therapy treatment using fuzzy inference method.

• The Journal of Korean Association of Computer Education
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• v.14 no.4
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• pp.43-51
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• 2011

Recently, by the development of information technology, we can get various information from anywhere in real time. However, personal information is exposed to threats which may incur unwanted information leakage. Cryptography serves as a primary study to prevent this leakage. However, some theories of cryptography are based on complex mathematical theories which make many people confused. Therefore, in this paper, we develope a software which is helpful to understand RSA algorithm, which is widely used algorithm in digital signature to protect personal information.

• Journal of the Korean School Mathematics Society
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• v.14 no.4
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• pp.443-458
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• 2011

There has been a lively discussion on improving Korean students' academic achievement and the imbalance in their recognition of the value of mathematics. In this context, there is a need for a program that enables the majority students who regards mathematics as a subject for the entrance examination to recognize the practicality and historicity of mathematics. Educational books on mathematics in everyday life or the history of mathematics are also expected to serve as an effective tool. In addition, Web 2.0 Map is another means of representing mathematics in everyday life and the history of mathematics in connection with the practical context. The active storytelling process in which mathematics in the practical context in mathematical educational books is represented in Web 2.0 Map is expected to help to understand in depth the practicality and historicity of mathematics. Nevertheless, mathematical educational books and Web 2.0 Map may lead to a considerable variety of outcomes and speeds if carrying out tasks depending on the student's competence and may have practical difficulties in being operated in class. These concerns, however, can be resolved through the creative activity programs adopted in conformance with the 2009 revised curriculum. Therefore, this study intends to develop a program for creating mathematical story maps through mathematical educational books and the Mashup of Web 2.0 Map in accordance with the process of developing activity programs. This study also intends to determine its effectiveness in enabling students to recognize the practical and historical values of mathematics.

• 한국지구과학회:학술대회논문집
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• 2005.02a
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• pp.239-248
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• 2005

이 논문은 과학영재교육원의 학생 선발과정을 중심으로 과학영재아 판별과정을 분석해보고, 과학영재교육원의 학생 선발과정에서 발생할 수 있는 오류를 점검하여, 이를 보완할 수 있는 개선안을 마련하고자 하는데 목적을 두고 있다. 분석결과 과학, 수학과 관련된 창의적 문제의 지필평가 성적이 선발의 가장 중요한 기준이었다. 지필평가 단계에서 지망분야에 관계없이 과학, 수학 및 창의력검사를 모두 치러야 하는 교육원에 초점을 맞추어 그 점수 활용에 있어서 발생할 수 있는 오류를 점검하였다. A 교육원의 경우 학생 선발은 다단계 평가를 원칙으로 하고 있었으며, 1단계 지필평가에서 과학, 수학, 창의력검사라는 세 과목 시험의 합산점수로서 선발하고 있었다. 이 교육원의 ○○년도 중등과정 응시자 276명을 대상으로 합격자와 불합격자의 지필평가 점수를 분석하여 과학, 수학, 창의력검사의 시행에 오류가 없었는지 점검하였다. 또 이들의 합산에 의한 선발이 의미 있는 결과를 보이는지 분석하였다. 그 결과 과학, 수학, 창의력검사의 상관도분석에서 과학은 수학 및 창의력검사와 유의미한 상관이 있었으나, 수학과 창의력검사는 독립적으로 분석되었다. 또 이들의 합산에 지원분야별 배점으로 계산한 선발은 본래의 취지, 즉 과학, 수학, 창의력에서 모두 우수한 학생을 선발하고자 하는 의도대로 진행되었으나, 판별분석 결과 합격과 불합격자 판별에서 88.1%의 정확도를 보여 다소 오류가 있었음을 발견하였다. 이는 해당년도에 출제된 문제의 난이도 및 시험 과목별 평균점수 차를 고려하지 않아 발생하는 문제로 파악되어져 원점수 대신 표준점수로 변환하여 오류를 보완할 것을 제안한다. 자체와 직접 관련되는 영역으로는 좌반구의 측두엽과 전두엽 부분이 관찰되었다. 특히 한국어 어말어미 산출시 나타나는 형태점화 양상과 관련된 대뇌영역으로 발견된 브로카 영역에서의 활성화는 어미 변환과 관련된 영역이라기보다는 산출시 관련되는 articulation, motor coordinate관련 영역으로 추정되고, 측두엽의 활성화는 형태소, 의미 관련 지식의 data base로 추정된다. 또한 우반구 전두엽 부분에서 관찰된 활성화는 억제관련 영역으로 짐작된다.러한 동물실험이 그 기초를 제공해 줄 수 있을 것이다. 또한 행동성향 및 기억의 종류에 따른 약물효과의 차이는 기억과 관련된 질병인 알츠하이머 환자에 있어 개개인에게 맞는 적절한 특징적인 치료약물이 존재할 것이라는 가능성을 제공해줄 뿐만 아니라 학습과 기억력 증진 효과를 기대해 볼 수 있을 것이라고 생각된다. 및 지역산업발전의 기획${\sim}$조정기구로서, 선진국의 지역발전기구(Regional Development Agency : RDA)인 지역전략산업기획단이 2002년도부터 산업자원부와 9개 시도에 의해 설립되어 지역네트워크의 활성화와 클러스터의 형성 촉진을 하게 되었고 2004년도에는 13개시도로 확대${\sim}$운영되고 있고, 지역특화사업(H/W)과 지역산업기술개발과제(S/W)와 함께 패케지 형태로 지원되며, 주요역할은 크게 지역산업의 정책기획 분야와 평가관리, 지역혁신역량 조사 및 DB구축 등으로 구분된다. 그중에서도 권역별, 지역별, 지역산업진흥사업 육성과 중장기 산업발전계획을 수립하기 위하여 지역혁신역량을 바탕으로 한 지역 Technol

• Journal of Educational Research in Mathematics
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• v.13 no.2
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• pp.107-122
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• 2003

The present study aims at theoretically reviewing studies en the need of alignments among assessment, curriculum and instruction in order to implement the goals of mathematics education. This paper discusses about issues and models fer alignment between instruction and curriculum, and then mainly focuses on alignment of assessment with instruction and curriculum at two levels, classroom and large-scale assessment. It was pointed out that both many published standardized tests for large-scale assessment and classroom assessments failed to meet curricular goals and contents, and instructional methods. The findings imply that reform in mathematics education should not be driven by assessment, but be embedded in instructional practices.