• Journal of Educational Research in Mathematics
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• v.12 no.1
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• pp.125-143
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• 2002

The concept of "set" in school mathematics has undergone many changes according to the revision of curriculum and the transition of the paradigm in mathematics education. In the discipline-centered curriculum, a set was a representative concept which reflected the spirit of New Math. After the Back to Basics period, the significance of a set concept in school mathematics has been diminished. First, this paper elaborated several controversial aspects of the terms related to set, such as a collection and a set, a subset, and an empty set. In addition, the changes of the significance imposed to a set concept in school mathematics were investigated. Finally, this paper provided two alternative approaches to introduce and explain a set concept which emphasized both mathematical rigor and learner's psychology.

• Communications of Mathematical Education
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• v.14
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• pp.135-150
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• 2001

역동적 평가는 구성주의와 사회문화적 관점이 교육과정에 많은 영향을 주면서 이를 평가에 반영하기 위한 대안으로 등장한 새로운 평가의 방향이다. 전통적인 심리 측정에 대한 비판에서 시작되었으며, 통계적인 자료정리에서 벗어나 아동에 대한 변화가능성을 평가하자는 것이 주목적이다. 결과 지향적인 평가는 미래의 수행에 대한 완전한 예언을 할 수 없지만, 역동적 평가에서 각 개인의 평가는 개인의 특성에 따라 각기 다른 체제 내에서 이루어진다. 역동적 평가의 입장 가운데서도 본 연구에서는 사회문화적 체제 관점에서 실제영역과 발달가능영역에 대한 사회적 상호작용에 대해 관심을 가지고 있다. 이를 위해 개인에 작용하는 생태학적 회로망을 평가의 주요한 배경으로 선택하고 있으며, 사회문화적 관점에서 평가관의 변화를 제시하면서 이에 따른 수학교육적 시사점을 찾아본다.

• School Mathematics
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• v.18 no.3
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• pp.733-747
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• 2016

To describe mathematics learning relying on a priori assumptions about the learners has a risk of assuming the learners as well-prepared subjects. In this study we investigate the epistemological perspective of Gilles Deleuze which is expected to give overcome this risk. Then we analyze the constructivist's epistemology and prior discussions about learning mathematics in the preceding studies accordingly. As a result, a priori assumption on which students are regarded as well-prepared for learning mathematics is reconsidered and we propose a new model of thought to highlight the involuntary aspect of the occurrence of thinking facilitated by the encounter with mathematical signs. This perspective gives a new vision on involuntary aspects of mathematics learning and the learner's confusion or difficulty at the starting point of learning.

• School Mathematics
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• v.10 no.1
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• pp.123-138
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• 2008

The objective of this paper is to reveal the cause of failure of New Math in the field of the SMSG area education from the didactical point of view. At first, we analyzed Euclid's (Elements), De Morgan's (Elements of arithmetic), and Legendre's (Elements of geometry and trigonometry) in order to identify characteristics of the area conception in the SMSG. And by analyzing the controversy between Wittenberg(1963) and Moise(1963), we found that the elementariness and the mental object of the area concept are the key of the success of SMSG's approach. As a result, we conclude that SMSG's approach became separated from the mathematical contents of the similarity concept, the idea of same-area, incommensurability and so on. In this account, we disclosed that New Math gave rise to the lack of elementariness and geometrical mental object, which was the fundamental cause of failure of New Math.

• Journal of Educational Research in Mathematics
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• v.21 no.3
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• pp.221-237
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• 2011

This paper focused on three drawbacks exposed in subject matter related to solid figures in elementary school math textbook. First, general solid figure are introduced before rectangular parallelepiped and cube in fifth grade math textbook, and prism and pyramid in sixth grade math textbook are introduced. Second, the process of abstraction from concrete objects to solid figures is insufficient in sixth grade math textbook. Third, some definitions in subject matter related to solid figures are inconsistent and ambiguous. The following four suggestions can be put forward as a conclusion based on these results. First, subject matter in textbooks must be correspond with that in curriculum. Second, it is necessary to inform teachers of range of subject matter through teachers guide book and manual for curriculum definitely. Third, each grade subject matter in math textbooks must be reexamined. Fourth, regular modification of math textbooks must be possible institutionally.

• The Mathematical Education
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• v.55 no.2
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• pp.193-208
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• 2016

This study analyzes the likelihood principle and elicits an educational implication. As a result of analysis, this study shows that Frequentist and Bayesian interpret the principle differently by assigning different role to that principle from each other. While frequentist regards the principle as 'the principle forming a basis for statistical inference using the likelihood ratio' through considering the likelihood as a direct tool for statistical inference, Bayesian looks upon the principle as 'the principle providing a basis for statistical inference using the posterior probability' by looking at the likelihood as a means for updating. Despite this distinction between two methods of statistical inference, two statistics schools get clues to compromise in a regard of using frequency prior probability. According to this result, this study suggests the statistics education that is a help to building of students' critical eye by their comparing inferences based on likelihood and posterior probability in the learning and teaching of updating process from frequency prior probability to posterior probability.

• School Mathematics
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• v.11 no.3
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• pp.415-429
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• 2009

In this study, in order to use history of mathematics in mathematical learning effectively, we investigate application of history of mathematics shown textbooks in simultaneous equations. History of Mathematics can be used in order to enhance comprehension and increase interest in an introduction to the simultaneous equations. It also can be used to help motivate middle school students to solve the simultaneous equations with much interest during the development phase, and develope open thinking and reflective thinking in the enrichment learning.

• The Mathematical Education
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• v.63 no.2
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• pp.209-231
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• 2024

The education sector is undergoing significant changes due to the Fourth Industrial Revolution and the advancement of artificial intelligence. Particularly, the importance of education based on artificial intelligence is being emphasized. Accordingly, the purpose of this study is to develop a statistics education program using deep learning prediction in high school mathematics and to examine the impact of such statistically problem-solvingcentered statistics education programs on high school students' statistical literacy and computational thinking. To achieve this goal, a statistics education program using deep learning prediction applicable to high school mathematics was developed. The analysis revealed that students' understanding of context improved through experiencing how data was generated and collected. Additionally, they enhanced their comprehension of data variability while exploring and analyzing various datasets. Moreover, they demonstrated the ability to critically analyze data during the process of validating its reliability. In order to analyze the impact of the statistics education program on high school students' computational thinking, a paired sample t-test was conducted, confirming a statistically significant difference in computational thinking between before and after classes (t=-11.657, p<0.001).

• Journal of Educational Research in Mathematics
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• v.13 no.3
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• pp.247-265
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• 2003

The purpose of this study is to analyze the essence of ratio concept from educational viewpoint. For this purpose, it was tried to examine contents and organizations of the recent teaching of ratio concept in elementary school text of Korea from ‘Syllabus Period’ to ‘the 7th Curriculum Period’ In these text most ratio problems were numerically and algorithmically approached. So the Wiskobas programme was introduced, in which the focal point was not on mathematics as a closed system but on the activity, on the process of mathematization and the subject ‘ratio’ was assigned an important place. There are some educational implications of this study which needs to be mentioned. First, the programme for developing proportional reasoning should be introduced early Many students have a substantial amount of prior knowledge of proportional reasoning. Second, conventional symbol and algorithmic method should be introduced after students have had the opportunity to go through many experiences in intuitive and conceptual way. Third, context problems and real-life situations should be required both to constitute and to apply ratio concept. While working on contort problems the students can develop proportional reasoning and understanding. Fourth, In order to assist student's learning process of ratio concept, visual models have to recommend to use.

• Journal of Educational Research in Mathematics
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• v.21 no.4
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• pp.399-422
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• 2011

There has been an agreement on the necessity for each citizen is to be educated, so called, to develop quantitative literacy or statistical literacy, dealing with real world data. For this reason, it is highly demanded to improve traditional statistics education. In particular, critical thought and statistical communication competency cultivation is becoming more crucial in statistics classes. In line with this reform movement in statistics education, we developed tasks facilitating statistical debate among students through inducing cognitive conflict. The tasks employed for this study resulted in playing crucial role to activate statistical debate. Including aforementioned feature about the tasks for this study, we obtained several positive results such as promoting critical thought and conceptual extension by designed teaching experiment focusing on statistical debate.