• Communications of Mathematical Education
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• v.33 no.3
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• pp.295-317
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• 2019

Angle concept is widely used in all mathematics curriculums and is a basic concept in geometric domain. Since angle have a multifaceted and affect subsequent learning, it is necessary for students to understand various angle concepts. In this study, Singapore, U.K., Australia, and U.S. are selected as comparable countries to examine the angle-related contents and learning process that appear in the curriculum as a whole, and then look at the perspectives and the size aspects of angle in detail and give implications to the Korean curriculum based on them. According to the analysis, the four countries except Korea, supplement angle, complement angle, angles on a straight line, angles at a point, and finding angle were explicitly covered in the curriculum. And most countries gradually covered angle-related contents over several years, compared to Korea which intensively studied in a particular school year. In common, definition of angle was described as static, measurement of angle was described as dynamic. But in Korean curriculum, dynamic views on angles are described later and less compared to other countries, and range of angle size was narrower than in other countries'. From this comparison, this study suggest to discuss how to place and develop various contents of characteristics of angle in curriculum, address the angle using both static and dynamic perspectives, and introduce the angle size as the amount of rotation to learn the reflex angle, $180^{\circ}$, $360^{\circ}$ angle.

• Communications of Mathematical Education
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• v.34 no.2
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• pp.119-134
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• 2020

Korea, where the national curriculum is run, can change school education by specifying basic competence in the common curriculum of elementary and middle schools for students to pursue school learning and real life. The numeracy as a basic competence should not be limited to mathematics, so it needs to be specified in the national curriculum covering several subjects and guided through various subject curriculums. To this end, the study proposed concepts, components, and levels of numeracy and proposed ways to reflect them in the national curriculum and other subjects' curricula. To ensure its validity, the UK, Canada and Australia curriculum are analyzed, and the results of the survey are proposed for various education experts. This study proposed two ways to briefly state the numeracy in the national curriculum and to imply the contents related to the numeracy in each subject curriculum, and to present the concepts, components and levels of numeracy in the national curriculum in detail and to describe numeracy code in each subject curriculum. These suggestions obtained high consent from experts.

• Journal of Educational Research in Mathematics
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• v.26 no.3
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• pp.403-420
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• 2016

Some of the critical changes in the revised 2015 Korean Mathematics curriculum were that direct proportion and inverse proportion were moved from elementary school to middle school and that supplementary content related to correlation was included. These decisions were based on comparative studies of international curriculum. Therefore in this study, we selected countries for comparison; United States, England, France, Finland, Australia, Japan, Singapore, China and Taiwan. We looked into the timing and scope for direct/inverse proportion and correlation in curricula of these countries. Along with this, we established four criteria; vertical sequence, horizontal sequence, external connection, and internal connection for an analysis framework. Then we compared and analysed the direct/inverse proportion and correlation in each curriculum. As a result, in most of these curricula, the direct/inverse proportions are introduced at middle school or are introduced at elementary school and then developed further at middle school. Most of curriculums on direct/inverse proportion and correlation match the four criteria. Correlation is introduced in high school mathematics in all counties except Finland and it is dealt in diverse context introducing related concepts, for example, correlation coefficient, regression straight line, and least square. We suggested that it is necessary to refer these international trends for the next revision of curriculum.

• Communications of Mathematical Education
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• v.34 no.3
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• pp.393-419
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• 2020

Trigonometry allows us to recognize the usefulness of mathematics through connection with real life and other disciplines, and lays the foundation for the concept of higher mathematics through connection with trigonometric functions. Since international comparisons on the trigonometry area of textbooks can give implications to trigonometry teaching and learning in Korea, this study attempted to compare trigonometry in textbooks in Korea, Australia and Finland. In this study, through the horizontal and vertical analysis presented by Charalambous et al.(2010), the objectives of the curriculum, content system, achievement standards, learning timing of trigonometry content, learning paths, and context of problems were analyzed. The order of learning in which the three countries expanded size of angle was similar, and there was a difference in the introduction of trigonometric functions and the continuity of grades dealing with trigonometry. In the learning path of textbooks on the definition method of trigonometric ratios, the unit circle method was developed from the triangle method to the trigonometric function. However, in Korea, after the explanation using the quadrant in middle school, the general angle and trigonometric functions were studied without expanding the angle. As a result of analyzing the context of the problem, the proportion of problems without context was the highest in all three countries, and the rate of camouflage context problem was twice as high in Korea as in Australia or Finland. Through this, the author suggest to include the unit circle method in the learning path in Korea, to present a problem that can emphasize the real-life context, to utilize technological tools, and to reconsider the ways and areas of the curriculum that deal with trigonometry.

• School Mathematics
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• v.17 no.3
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• pp.515-530
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• 2015

The concepts of sample and sampling are central to make a statistically correct decision, so we need to be emphasized their importance in the statistics education. Nevertheless, there were not enough studies which discuss how to teach the concepts of sample and sampling. In this study, teaching sample and sampling is addressed by foreign curricula and cases of instruction in order to obtain suggestions for teaching sample and sampling. In particular, the curricular of Australia, New Zealand, England and the United States are analyzed, considering the sample representativeness and the sampling variability; the two elements in the concept of sample. Also foreign textbooks and cases of instruction when it comes to teach sample are analyzed. The results say that with respect to teach sample can be divided into four suggestions: first, sample was taught in the process of statistical inquiry such as data collection, analysis, and results. Second, sample was introduced earlier than Korea curriculum. Third, when it comes to teach sample, sample variability, as well as sample representativeness was considered. Fourth, technological tools were used to enhance understanding sample.

• Journal of Educational Research in Mathematics
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• v.14 no.4
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• pp.387-401
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• 2004

The recent international comparative studies such as PISA(Program for International Student Assessment) and TIMSS-R(Third International Mathematics and Science Study-Repeat) provide results of relative mathematics achievement of participating countries. The purpose of this paper is to compare the mathematics results of PISA and TIMSS-R. To make PISA and TIMSS-R results comparable, they were standardized. The close investigation of these standardized results reveals that the two Asian countries(Korea and Japan) and several English speaking countries have the commonality in mathematics achievement. Thus this study looks for patterns and similarities within a group of Asian countries(Korea and Japan) and Western countries(the U.S and Australia) by in-depth analysis of PISA mathematics achievement based on item response theory. As a result, it was noted that Western countries tend to perform well on open constructed items and are likely to perform better when an item involves less formal mathematics. On the other hand, Asian countries perform well when an item involves numeric or algebraic computation related to curriculum-based content, but they are relative poor at an item calls for verbal explanations or interpretations of graphs.

• Communications of Mathematical Education
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• v.37 no.3
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• pp.349-368
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• 2023

The revised 2022 educational curriculum highlighted the significance of mathematical literacy as a foundational competency that can be cultivated through the learning of various subjects, along with language proficiency and digital literacy. However, due to the lack of a precise definition for mathematical literacy, there exists a challenge in systematically implementing it across all subjects in the educational curriculum. The aim of this study is to clarify the definition of mathematical literacy in the curriculum through a literature review and to analyze the application patterns of mathematical literacy in other subjects so that mathematical literacy can be systematically applied as a basic literacy in Korea's curriculum. To achieve this, the study first clarifies and categorizes the meaning of mathematical literacy through a comparative analysis of terms such as numeracy and mathematical competence via a literature review. Subsequently, the study compares the categories of mathematical literacy identified in both domestic and international educational curricula and analyzes the application of mathematical literacy in the education curriculum of New South Wales (NSW), Australia, where mathematical literacy is reflected in the achievement standards across various subjects. It is expected that understanding each property by subdividing the meaning of mathematical literacy and examining the application modality to the curriculum will help construct a curriculum that reflects mathematical literacy in subjects other than mathematics.

• Communications of Mathematical Education
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• v.24 no.1
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• pp.235-257
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• 2010

Contemporary belief is that the creative talented can create new knowledge and lead national development, so lots of countries in the world have interest in Gifted Education. As we well know, U.S.A., England, Russia, Germany, Australia, Israel, and Singapore enforce related laws in Gifted Education to offer Gifted Classes, and our government has also created an Improvement Act in January, 2000 and Enforcement Ordinance for Gifted Improvement Act was also announced in April, 2002. Through this initiation Gifted Education can be possible. Enforcement Ordinance was revised in October, 2008. The main purpose of this revision was to expand the opportunity of Gifted Education to students with special education needs. One of these programs is, the opportunity of Gifted Education to be offered to lots of the Gifted by establishing Special Classes at each school. Also, it is important that the quality of Gifted Education should be combined with the expansion of opportunity for the Gifted. Social opinion is that it will be reckless only to expand the opportunity for the Gifted Education, therefore, assessment on the Teaching and Learning Program for the Gifted is indispensible. In this study, 3 middle schools were selected for the Teaching and Learning Programs in mathematics. Each 1st Grade was reviewed and analyzed through comparative tables between Regular and Gifted Education Programs. Also reviewed was the content of what should be taught, and programs were evaluated on assessment standards which were revised and modified from the present teaching and learning programs in mathematics. Below, research issues were set up to assess the formation of content areas and appropriateness for Teaching and Learning Programs for the Gifted in mathematics. A. Is the formation of special class content areas complying with the 7th national curriculum? 1. Which content areas of regular curriculum is applied in this program? 2. Among Enrichment and Selection in Curriculum for the Gifted, which one is applied in this programs? 3. Are the content areas organized and performed properly? B. Are the Programs for the Gifted appropriate? 1. Are the Educational goals of the Programs aligned with that of Gifted Education in mathematics? 2. Does the content of each program reflect characteristics of mathematical Gifted students and express their mathematical talents? 3. Are Teaching and Learning models and methods diverse enough to express their talents? 4. Can the assessment on each program reflect the Learning goals and content, and enhance Gifted students' thinking ability? The conclusions are as follows: First, the best contents to be taught to the mathematical Gifted were found to be the Numeration, Arithmetic, Geometry, Measurement, Probability, Statistics, Letter and Expression. Also, Enrichment area and Selection area within the curriculum for the Gifted were offered in many ways so that their Giftedness could be fully enhanced. Second, the educational goals of Teaching and Learning Programs for the mathematical Gifted students were in accordance with the directions of mathematical education and philosophy. Also, it reflected that their research ability was successful in reaching the educational goals of improving creativity, thinking ability, problem-solving ability, all of which are required in the set curriculum. In order to accomplish the goals, visualization, symbolization, phasing and exploring strategies were used effectively. Many different of lecturing types, cooperative learning, discovery learning were applied to accomplish the Teaching and Learning model goals. For Teaching and Learning activities, various strategies and models were used to express the students' talents. These activities included experiments, exploration, application, estimation, guess, discussion (conjecture and refutation) reconsideration and so on. There were no mention to the students about evaluation and paper exams. While the program activities were being performed, educational goals and assessment methods were reflected, that is, products, performance assessment, and portfolio were mainly used rather than just paper assessment.