• School Mathematics
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• v.13 no.4
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• pp.651-674
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• 2011

Functional thinking is a central topic in school mathematics and the purpose of teaching functional thinking is to develop student's functional thinking ability. Functional thinking which has to be taught in elementary school must be the thinking in terms of phenomenon which has attributes of 'connection'- assignment and dependence. The qualitative methods for evaluation of development of functional thinking can be based on students' activities which are related to functional thinking. With this purpose, teachers have to provide students with paradigm of the functional situation connected to the other subjects which have attributes of 'connection' and guide them by proper questions. Therefore, the aim of this study is to find teaching method for functional thinking by situation posing connected with other subject. We suggest the following ways for functional situation posing though the process of three steps : preparation, adaption and reflection of functional situation posing. At the first stage of preparation for functional situation, teacher should investigate student's environment, mathematical knowledge and level of functional thinking. With this purpose, teachers analyze various curriculum which can be used for teaching functional thinking, extract functional situation among them and investigate the utilization of functional situation as follows : ${\cdot}$ Using meta-plan, ${\cdot}$ Using mathematical journal, ${\cdot}$ Using problem posing ${\cdot}$ Designing teacher's questions which can activate students' functional thinking. For this, teachers should be experts on functional thinking. At the second stage of adaption, teacher may suggest the following steps : free exploration ${\longrightarrow}$ guided exploration ${\longrightarrow}$ expression of formalization ${\longrightarrow}$ application and feedback. Because we demand new teaching model which can apply the contents of other subjects to the mathematic class. At the third stage of reflection, teacher should prepare analysis framework of functional situation during and after students' products as follows : meta-plan, mathematical journal, problem solving. Also teacher should prepare the analysis framework analyzing student's respondence.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.2
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• pp.287-314
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• 2010

The algorithm is a chain of mechanical procedures, capable of solving a problem. In modern mathematics educations, the teaching algorithm is performing an important role, even though contracted than in the past. The conspicuous characteristic of current elementary mathematics textbook's manner of manipulating multiplication algorithm is exceeding converge to 'standard algorithm.' But there are many algorithm other than standard algorithm in calculating multiplication, and this diversity is important with respect to didactical dimension. In this thesis, we have reconstructed the experimental learning and teaching plan of multiplication algorithm unit by making the best use of diversity of multiplication algorithm. It's core contents are as follows. Firstly, It handled various modified algorithms in addition to standard algorithm. Secondly, It did not order children to use standard algorithm exclusively, but encouraged children to select algorithm according to his interest. As stated above, we have performed teaching experiment which is ruled by new lesson design and analysed the effects of teaching experiment. Through this study, we obtained the following results and suggestions. Firstly, the experimental learning and teaching plan was effective on understanding of the place-value principle and the distributive law. The experimental group which was learned through various modified algorithm in addition to standard algorithm displayed higher degree of understanding than the control group. Secondly, as for computational ability, the experimental group did not show better achievement than the control group. It's cause is, in my guess, that we taught the children the various modified algorithm and allowed the children to select a algorithm by preference. The experimental group was more interested in diversity of algorithm and it's application itself than correct computation. Thirdly, the lattice method was not adopted in the majority of present mathematics school textbooks, but ranked high in the children's preference. I suggest that the mathematics school textbooks which will be developed henceforth should accept the lattice method.

• Journal of the Korean School Mathematics Society
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• v.12 no.2
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• pp.151-170
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• 2009

The purpose of the study is to analyze the sixth graders' understanding of concepts and operation about fraction. The test was administered and analyzed to 707 sixth graders' performance on fractions after the fraction instructions in elementary schools in Seoul, Korea. The participants are asked to answer two sets of questions for 40 minutes. First, they are asked to answer to 16 problems about the concepts of fraction with respect to part-whole, ratio, operator, measure, quotient, equivalent, and operations. Second, specially, to investigate sixth graders' ability of drawing and describing the situation of division including fraction, the descriptive problem asked students (1) to describe $3\;{\div}\;\frac{1}{2}$ into pictorial representation and (2) to write the solving process. The participants of this study didn't show deep understandings about the concepts and operation of fraction. The degree of understanding of subconstructs of fraction shows that their knowledge of ratio concept with respect to fraction was highest while their understanding of measure with respect to fraction was lowest. Considering their wrong answers, about 59% of participants showed misconception to the question of naming one fraction that appears between $\frac{1}{5}$ and $\frac{1}{6}$. Further, they didn't explain their understanding with drawing about the division of fraction ($3\;{\div}\;\frac{1}{2}$).

• Journal of The Korean Association For Science Education
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• v.34 no.3
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• pp.295-301
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• 2014

The purpose of this study is to investigate the difficulties of teachers and students on the unit about 'measuring weight.' In this research, we have acquired data about teachers through survey, interview, and self-reflection journals, at the same time we have collected information on the students through survey, assessment test, and interview. We have extracted the difficulties from analysis with constant comparison method. In addition, we have analysed the curriculum of science and mathematics to know the leaning sequence. The analysis had been checked up by experts in science education. The result of the study is as follows: The difficulties of teachers are from the lack of teachers' descriptive knowledge, disorder of conceptual hierarchy in the curriculum, poor experimental instruments, and low psychomotor skill of students. The difficulties of students are from common misconceptions, opaque concepts, lack of manipulation skill, insufficiency of mathematical ability, difficulty of application of principles to the real situation, and lack of problem-solving ability. In addition, teachers have recognized that students face more difficulties in experiment class, while students think that they face more difficulties in conceptual understanding class.

• Journal of Gifted/Talented Education
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• v.20 no.1
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• pp.61-77
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• 2010

The purpose of this study was to analyze the items that were used in entrance examination for science gifted education center for middle school students by using content analysis and classical item analysis. In content analysis, objective type items exhibited mathematics and physics were dominant. Science giftedness & creativity items were dominant. And essay type items consisted of physics items, have evaluated creative problem solving ability. Item difficulty and discrimination index, on the whole, were appropriate. Comparing with objective type, essay type has higher discrimination index. In correlation analysis between total score and score of each type of items, total score has the highest correlation with essay type items and science giftedness & creativity. It was recommended that mathematics, physics and chemistry items with focusing giftedness & creativity could give some implications for future selection methods of science gifted education center.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.19 no.12
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• pp.872-877
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• 2018

STEAM is an acronym for Science, Technology, Engineering, Arts, and Mathematics. It is considered important to equip students with a creative thinking ability and the core competences required in future society, helping them devise new ideas emerging from branches of study. This study is about the convergence of instructional design in private finance for the life sciences, which aims to foster talent through problem-based learning (PBL). Skills like collaboration, creativity, critical thinking, and problem solving are part of any STEAM PBL, and are needed for students to be effective. STEAM projects give students a chance to problem-solve in unique ways, because they are forced to use a variety of methods to solve problems that pop up during these types of activities. The results of this study are as follows. First is the structured process of convergence lessons. Second is the convergence lesson process. Third is the development of problems in the introduction of private finance and the life sciences for a convergence lesson at Dornod University. Learning motivation shows the following results: understanding of learning content (66.6%), effectiveness (63.3%), self-directed learning (59.9%), motivation (63.2%), and confidence (63.3%). To make an effective model, studies applying this instructional design are to be implemented.

• School Mathematics
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• v.19 no.3
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• pp.423-441
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• 2017

New Zealand had reformed their national curriculum with competence and are applying the revised curriculum. As the 2015 revised national curriculum is clothed with competency-based curriculum, New Zealand may have important implications for the study of the Korean revised curriculum. In this study, we examine characteristics of the education system and the national curriculum in New Zealand. In addition, we analyze the standards into the New Zealand national curriculum in terms of 'curriculum connectivity' that is one of important curriculum criteria for improving the quality of education. For this, we look an overview of the relation between the New Zealand curriculum and NCEA, which is the core of the student-centered education system in New Zealand, and analyze the correspondence between the New Zealand curriculum and the Korean curriculum. And we establish analysis framework of curriculum connectivity based on these comparison analysis contents, and analyze Korean mathematics standards with corresponding levels from among the New Zealand mathematics curriculum. According to the results of this study, the New Zealand curriculum includes the most of standards which Korean high school students who want to enter university of natural sciences of engineering need to require. In addition, the New Zealand curriculum highlights statistical research activities for developing problem-solving ability in real life. From perspective of curriculum connectivity, 'in-depth contents' adding on to repeating mathematical concepts or contents are included in the New Zealand curriculum.

• Journal of Educational Research in Mathematics
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• v.23 no.2
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• pp.253-267
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• 2013

The newly revised mathematics curriculum of 2007 speaks of ultimate goal to develop ability to think and communicate mathematically, in order to develop ability to rationally deal with problems arising from the life around, which puts emphasize on mathematical communication. In this study, analysis on mathematical communication and analogical thinking process of group of students with similar level of academic achievement and that with different level, and thus analyzed if such communication has affected analogical thinking process in any way. This study contains following subjects: 1. Forms of mathematical communication took placed at the two groups based on achievement level were analyzed. 2. Analogical thinking process was observed through trapezoid's area obtaining activity and analyzed if communication within groups has affected such process anyhow. A framework to analyze analogical thinking process was developed with reference of problem solving procedure based on analogy, suggested by Rattermann(1997). 15 from 24 students of year 5 form of N elementary school at Gunpo Uiwang, Syeonggi-do, were selected and 3 groups (group A, B and C) of students sharing the same achievement level and 2 groups (group D and E) of different level were made. The students were led to obtain areas of parallelogram and trapezoid for twice, and communication process and analogical thinking process was observed, recorded and analyzed. The results of this study are as follow: 1. The more significant mathematical communication was observed at groups sharing medium and low level of achievement than other groups. 2. Despite of individual and group differences, there is overall improvement in students' analogical thinking: activities of obtaining areas of parallelogram and trapezoid showed that discussion within subgroups could induce analogical thinking thus expand students' analogical thinking stage.

• Journal of Elementary Mathematics Education in Korea
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• v.13 no.1
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• pp.1-15
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• 2009

This research is to provide a useful reference for the future revision of textbook by comparative analysis with the textbook in the 4th grade of elementary school in Japan. The results from this research is same as follows: First, Korean curriculum is emphasizing the reasonable problem-solving ability developed on the base of the mathematical knowledge and skill. Meantime, Japanese puts much value on the is focusing on discretion and the capability in life so that they emphasize each person's learning and raising the power of self-learning and thinking. The ratio on mathematics in both company are high, but Japanese ensures much more hours than Korean. Second, the chapter of Korean textbook is composed of 8 units and the title of the chapter is shown as key word, then the next objects are describes as 'Shall we do$\sim$' type. Hence, the chapter composition of Japanese textbook is different among the chapter and the title of the chapter is described as 'Let's do$\sim$'. Moreover, Korean textbook is arranged focusing on present study, however Japanese is composed with each independent segments in the present study subject to the study contents. Third, Japanese makes students understand the decimal as the extension of the decimal system with measuring unit($\ell$, km, kg) then, learn the operation by algorithm. In Korea, students learn fraction earlier than decimal, but, in Japan students learn decimal earlier than fraction. For the diagram, in Korea, making angle with vertex and side comes after the concept of angle, vertex and side is explained. Hence, in Japan, they show side and vertex to present angle.

• Journal of the Korean earth science society
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• v.40 no.5
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• pp.518-537
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• 2019

This study examined the implications of a place-based earth science program integrated with Mathematics. 11 pre-service earth science teachers and 22 middle school students participated in the service education activities of earth science for 30 hours focusing on the measurement of the earth's size through earth science experiments as part of the middle school curriculum. In order to minimize errors that may occur during the earth's size measurement experiments using Eratosthenes's shadows length method of the ancient Greek era, the actual data were collected after triangulation ratios were conducted in the locations of two middle schools: one in remote metropolitan and the other in rural area. The two schools' students shared the final estimate result. Through this process, they learned the mathematical method to express the actual data effectively. Participants, experienced the importance and difficulty of the repetitive and accurate data acquisition process, and also discussed the causes of errors included in the final results. It implies that a Place-Based Earth Science Program activity can contribute to students' increased-understanding of the characteristics of earth science inquiry and to developing their problem solving skills, thinking ability, and communication skills as well, which are commonly emphasized in science and mathematics in the 2015 reunion curriculum. It is expected that a place-based science program can provide a foundation for developing an integrated curriculum of mathematics and science.