• Education of Primary School Mathematics
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• v.15 no.2
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• pp.159-170
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• 2012

Many obstacles have been found in the learning of ratio and rate. The types of epistemological obstacles concern 'terms', 'calculations' and 'symbols'. It is important to identify the epistemological obstacles that students must overcome to understand the learning of ratio and rate. In this respect, the present study attempts to figure out what types of epistemological obstacles emerge in the area of learning ratio and rate and where these obstacles are generated from and to search for the teaching implications to correct them. The research questions were to analyze this concepts as follow; A. How do elementary students show the epistemological obstacles in ratio and rate? B. What is the reason for epistemological obstacles of elementary students in the learning of ratio and rate? C. What are the teaching implications to correct epistemological obstacles of elementary students in the learning of ratio and rate? In order to analyze the epistemological obstacles of elementary students in the learning of ratio and rate, the present study was conducted in five different elementary schools in Seoul. The test was administered to 138 fifth grade students who learned ratio and rate. The test was performed three times during six weeks. In case of necessity, additional interviews were carried out for thorough examination. The final results of the study are summarized as follows. The epistemological obstacles in the learning of ratio and rate can be categorized into three types. The first type concerns 'terms'. The reason is that realistic context is not sufficient, a definition is too formal. The second type of epistemological obstacle concerns 'calculations'. This second obstacle is caused by the lack of multiplication thought in mathematical problems. As a result of this study, the following conclusions have been made. The epistemological obstacles cannot be helped. They are part of the natural learning process. It is necessary to understand the reasons and search for the teaching implications. Every teacher must try to develop the teaching method.

• Education of Primary School Mathematics
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• v.19 no.4
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• pp.329-347
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• 2016

This paper investigated the views of effective mathematics instruction on the part of school administrators, and then compared and contrasted such views with those of elementary school teachers based on the previous study. A total of 32 school administrators participated in this study and responded to three types of the questionnaire. The results of this study showed that school administrators regarded good mathematics teaching as using concrete materials and teaching students to think. School administrators put their first priority on curriculum and content among four main domains of good mathematics teaching, and did on constructing curriculum among seven sub-domains of good mathematics teaching. They agreed that good mathematics teaching includes teaching by reconstructing the curriculum according to students' various levels and teaching to emphasize the connection among mathematical concepts. However, they thought that good mathematics teaching might not include teaching for fluent calculation or teaching in well-equipped learning environment. The results of comparison of perspectives regarding good mathematics teaching between school administrators and teachers showed remarkably similar tendency. However, a noticeable difference was that school administrators agreed more than elementary school teachers with regard to the 20 elements related to effective mathematics instruction. This paper closes with implications based on the similarities and differences regarding effective mathematics instruction perceived by school administrators and teachers.

• School Mathematics
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• v.18 no.2
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• pp.257-275
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• 2016

The purpose of this study was to investigate the impact of multiple representations on students' understanding of fractions, decimals, and percent. The instructional approach integrating multiple representations was compared to traditional algorithmic instruction, a form of direct instruction. To examine and compare the impact of multiple representations instruction with traditional algorithmic instruction, pre and post tests consisting of five similar items were administered with 87 middle school students. Students' scores in these two tests and their problem solving processes were analyzed quantitatively and qualitatively. The quantitative results indicated that students taught by traditional algorithmic instruction showed higher scores on the post-test than students in the multiple representations group. Furthermore, findings suggest that instruction using multiple representations does not guarantee a positive impact on students' understanding of mathematical concepts. Qualitative results suggest that the limited use of multiple representations during a class may have hindered students from applying their use in novel problem situations. Therefore, when using multiple representations, teachers should employ more diverse examples and practice with multiple representations to help students to use them without error.

• Journal of Educational Research in Mathematics
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• v.19 no.4
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• pp.545-564
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• 2009

TPACK (Technological Pedagogical Content Knowledge) adds the technological knowledge to PCK (Shulman 1986), completing the combination of three kinds of knowledge, i.e. teacher's content knowledge (CK), pedagogical knowledge (PK), and technological knowledge (TK). In this study, I seek to design methodological ways to improve TPACK for preservice mathematics teachers by developing and analyzing team project-based classes with technology in a class of the first semester 2009 in a teacher's college in Seoul, South Korea. The goal of the team project is to design classes to teach mathematics with technology by selecting technology tools suitable for specific mathematical concepts or mathematics sections. In the early stage of the class in the college, the confidence levels among the preservice mathematics teachers were relatively low but increased in the final stage their mathematics teaching efficacy up to from 3.88 to 4.50. Also, the pre service mathematics teachers answered the team project was helpful or very helpful in developing TPACK; this result proves that lectures with technology which based on team project are excellent tools for the teacher to design classes with technology confidently. Considering the teacher's TPACK is one of the abilities to achieve the goals required in the information technology era, the preservice mathematics teachers are asked to plan and develop the lectures with technology, rather than just taught to know how to use technology tools or adapt to specific cases. Finally, we see that national-wide discussion and research are necessary to prepare customized standards and implementable plans for TPACK in South Korea.

• Korean Journal of Comparative Education
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• v.28 no.3
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• pp.333-354
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• 2018

The study aimed to compare and analyze Nuri curriculum and contents for mathematics in Korea and the Common Core State Standards(CCSS) and New Jersey Preschool Standards for mathematics in the United States. With the results as basis, this study intended to provide suggestions and directions for improving Nuri curriculum of mathematics for young children. For the goal of this study, educational goals, categories of contents, and specific contents were reviewed. First, results of this study indicated that Nuri curriculum for mathematics provides comprehensive educational goals that promote problem-solving ability in everyday contexts with composing mathematical knowledge. On the contrary, CCSS and Preschool Standards provide specific educational goals that focus on children's mathematical skills and concepts. Second, the contents of both countries' curriculum concentrate on 'counting and cardinality', 'measurement', and 'spatial and geometric sense.' There are 5 categories of CCSS, 4 categories of Preschool Standards based on CCSS and one category of Nuri curriculum for mathematics. Third, there are the differences between the two countries' curriculum in continuity from kindergarten to first grade and description method for curriculum.

• Asia-pacific Journal of Multimedia Services Convergent with Art, Humanities, and Sociology
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• v.9 no.5
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• pp.147-157
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• 2019

In this study, mathematics education program was developed for the foreign students who entered the science and engineering college of Korea in order to improve their basic competency and to prevent dropouts. It is applied to 5 Chinese students, 4 male students and 1 female student. Three students are majoring in engineering college and two students are majoring in natural science college. Before applying the mathematics education program to foreign students, most students did not draw a graph of the 'irrational function' and the 'exponential function' and did not understand the concept of the 'limit' at all. However, after applying the mathematics program, all foreign students were able to draw graphs of the various function and the limit values were calculated accurately. Through the results of this study, the researcher proposes some of the following. When developing mathematics education programs for foreign students, it is very important to develop teaching materials suitable for their level. Textbook developers need to select and organize contents that are essential for learning in university mathematics and to present mathematical concepts and examples considering the Korean language level of foreign students. Moreover, it will be necessary to try to present mathematical terms commonly used in Korea in their native language or English.

• 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.

• Journal of Science Education
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• v.44 no.3
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• pp.331-344
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• 2020

This study aims to find meaningful implications for the development of Korean elementary school math education courses and textbooks by comparing and analyzing the number and arithmetic areas of Korean and Canadian math textbooks in fifth and sixth grades. To this end, the textbook composition system of Korean and Canadian elementary schools was compared and analyzed, and the number and timing of introduction of math textbooks and math textbooks by grade, and the number in fifth and sixth grade and the learning contents of math textbooks were compared and analyzed. The following conclusions were obtained from this study: First, it is necessary to organize a textbook that can solve the problem in an integrated way by introducing the learned mathematical concepts and computations naturally in the context of problems closely related to real life, regardless of the type of private calculation or mathematics area. Second, it is necessary to organize questions using materials such as real photography and mathematics, science, technology, engineering, art, etc. and to organize textbooks that make people feel the necessity and usefulness of mathematics. Third, sufficient learning of the principles of mathematics through the use of various actual teaching aids and mathematical models, and the construction of textbooks focusing on problem-solving strategies using engineering tools are needed. Fourth, in-depth discussions are needed on the timing of learning guidance for fractions and minority learning or how to organize and develop learning content.

• Communications of Mathematical Education
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• v.35 no.4
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• pp.527-546
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• 2021

The purpose of this study is to reveal what mathematics teachers focus on and how they assess students' thinking during lessons enacted. For this purpose, we googled and searched internet sites to collect formative assessment materials for the year 2014 to 2019. The formative assessment tasks data were analyzed according to the levels cognitive demand levels and tasks suggested in textbooks in terms of degrees to which how they are related. The data analysis suggested as follows: a) most of the formative assessment tasks were at the low-level, in particular, PNC level tasks that require applying particular procedures without connections to concepts and meaning underlying the procedures, b) the assessment tasks appeared to be very similar to the tasks suggested in the secondary mathematics textbooks, and c) it seemed that 3 types of formative assessment, observation notes, self-assessment, and peer-assessment were dominantly utilized during mathematics lessons and these different types of formative assessment were employed apparently to find out whether students participated actively in class and in group activity, not how they go through understanding or thinking processes.

• Education of Primary School Mathematics
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• v.25 no.1
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• pp.81-100
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• 2022

The purpose of this study is to develop a framework for analyzing the solution spaces of open-ended task and to explore their usefulness and applicability based on the analysis of solution spaces constructed by students. Based on literature reviews and previous studies, researchers developed a framework for analyzing solution spaces (OMR-framework) organized into subspaces of outcome spaces, method spaces, representation spaces which could be used in structurally analyzing students' solutions of open-ended tasks. In our research, we developed open-ended tasks which had various outcomes and methods that could be solved by using the concepts of factors and multiples and assigned the tasks to 181 elementary school fifth and sixth graders. As a result of analyzing the student's solution spaces by applying the OMR-framework, it was possible to systematically analyze the characteristics of students' understanding of the concept of factors and multiples and their approach to reversible and constructive thinking. In addition to formal mathematical representations, various informal representations constructed by students were also analyzed. It was revealed that each space(outcome, method, and representation) had a unique set of characteristics, but were closely interconnected to each other in the process. In conclusion, it can be said that method of analyzing solution spaces of open-ended tasks of this study are useful for systemizing and analyzing the solution spaces and are applicable to the analysis of the solutions of open-ended tasks.