• Communications of Mathematical Education
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• v.30 no.3
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• pp.393-418
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• 2016

Theory and fundamentals of mathematics consist mostly of proposition form. Activities by research of the proposition which leads to determine the true or false, justify the true propositions and refute with counterexample improve logical reasoning skills of students in emphases on mathematics education. Also, utilizing of counterexamples in school mathematics combines mathematical knowledge through the process of finding a counterexample, help the concept study and increase the critical thinking. These effects have been found through previous research. But many studies say that the learners have difficulty in generating counterexamples for false propositions and materials have not been developed a lot for the counterexample utilizing that can be applied in schools. So, this study analyzed the current textbook and examined the use of counterexamples and developed educational materials for counterexamples that can be applied at schools. That materials consisted of making true & false propositions and students was divided into three groups of academic achievement level. And then this study looked at the change of the students' thinking after counterexample classes. As a study result, in all three groups was showed a positive change in the cognitive domain and affective domain. Especially, in top-level group was mainly showed a positive change in the cognitive domain, in upper-middle group was mainly showed in the cognitive and the affective domain, in the sub-group was mainly found a positive change in the affective domain. Also in this study shows that the class that makes true or false propositions in education of utilizing counterexample, made students understand a given proposition, pay attention to easily overlooked condition, carefully observe symbol sign and change thinking of cognitive domain helping concept learning regardless of academic achievement levels of learners. Also, that class gave positive affect to affective domain that increase interest in the proposition and gain confidence about proposition.

• Journal of the Korean School Mathematics Society
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• v.13 no.3
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• pp.459-483
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• 2010

This study aims to develop materials related to math education for the aged and to identify the effects of application as part of active measures to the aging society with its growing elderly population which is one of the greatest changes in our society. In this purpose, the necessity and objectives for development of materials of 'Silver Math' as education for the aged are explained. Developing and disseminating materials with a role as a program for intelligent needs and physical and spiritual health of the aged presents standards for development of more systemic and meaningful educational materials at this point of time when the importance of education of the aged increases to help the old enjoy qualitatively successful lives in later years in the perspective of lifelong education. Also it aims to present standards of contents and requirements in learning that are adequate and meaningful to old learners at the actual learning sites where education takes place only in terms of making good use of spare time while at the same time suggesting plans of teaching and learning as well as conditions for learning environment. Next, the effectiveness of 'Silver Math' are explored by applying developed materials to the aged. materials of 'Silver Math' for the aged with contents that are appropriate to the definitive and cognitive level of the aged are presented. The developed materials for mathematical activities are divided into 'computation of basic numbers' for those wishing to learn calculation and concepts of numbers, 'active math' that corresponds to definitive factors of old learners, facilitates leisure time through mathematical activities, and Improves communication abilities through cooperative learning among learners, and 'math with thinking power' to solve simple calculation problems by applying to various actual situations.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.1
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• pp.105-129
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• 2016

The elements of mathematical processes include mathematical reasoning, mathematical problem-solving, and mathematical communications. Proportion reasoning is a kind of mathematical reasoning which is closely related to the ratio and percent concepts. Proportion reasoning is the essence of primary mathematics, and a basic mathematical concept required for the following more-complicated concepts. Therefore, the study aims to analyze the proportion reasoning ability of sixth graders of primary school who have already learned the ratio and percent concepts. To allow teachers to quickly recognize and help students who have difficulty solving a proportion reasoning problem, this study analyzed the characteristics and patterns of proportion reasoning of sixth graders of primary school. The purpose of this study is to provide implications for learning and teaching of future proportion reasoning of higher levels. In order to solve these study tasks, proportion reasoning problems were developed, and a total of 22 sixth graders of primary school were asked to solve these questions for a total of twice, once before and after they learned the ratio and percent concepts included in the 2009 revised mathematical curricula. Students' strategies and levels of proportional reasoning were analyzed by setting up the four different sections and classifying and analyzing the patterns of correct and wrong answers to the questions of each section. The results are followings; First, the 6th graders of primary school were able to utilize various proportion reasoning strategies depending on the conditions and patterns of mathematical assignments given to them. Second, most of the sixth graders of primary school remained at three levels of multiplicative reasoning. The most frequently adopted strategies by these sixth graders were the fraction strategy, the between-comparison strategy, and the within-comparison strategy. Third, the sixth graders of primary school often showed difficulty doing relative comparison. Fourth, the sixth graders of primary school placed the greatest concentration on the numbers given in the mathematical questions.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.2
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• pp.247-282
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• 2011

In the elementary school mathematics textbooks of the 7th national curriculum, just simple construction education is provided by having students draw a circle and triangle with compasses and drawing vertical and parallel lines with a set square. The purpose of this study was to examine the mathematical thinking of sixth-grade elementary school students in the construction process in a bid to give some suggestions on elementary construction guidance. As a result of teaching the sixth graders in gifted and nongifted classes about the equal division of line segments and evaluating their mathematical thinking, the following conclusion was reached, and there are some suggestions about that education: First, the sixth graders in the gifted classes were excellent enough to do mathematical thinking such as analogical thinking, deductive thinking, developmental thinking, generalizing thinking and symbolizing thinking when they learned to divide line segments equally and were given proper advice from their teacher. Second, the students who solved the problems without any advice or hint from the teacher didn't necessarily do lots of mathematical thinking. Third, tough construction such as the equal division of line segments was elusive for the students in the nongifted class, but it's possible for them to learn how to draw a perpendicular at midpoint, quadrangle or rhombus and extend a line by using compasses, which are more enriched construction that what's required by the current curriculum. Fourth, the students in the gifted and nongifted classes schematized the problems and symbolized the components and problem-solving process of the problems when they received process of the proble. Since they the urally got to use signs to explain their construction process, construction education could provide a good opportunity for sixth-grade students to make use of signs.

• Journal of Elementary Mathematics Education in Korea
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• v.21 no.2
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• pp.309-341
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• 2017

This study aims to investigate an approach to teach percentages in elementary mathematics class by analyzing calculating strategies with percentage the students use to solve the percentage tasks and their percentages of correct answers, as well as types of errors with percentages the students make. For this research 182 sixth graders were examined. The instrument test consists of various task types in reference to the previous study; the percentages tasks are divided into algebraic-geometric, part whole-comparison-change and find part-find whole-find percentage tasks. According to the analysis of this study, percentages of correct answers of students with percentage tasks were lower than we expected, approximately 50%. Comparing the percentages of correct answers according to the task types, the part-whole tasks are higher than the comparison and change tasks, the geometric tasks are approximately equal to the algebraic tasks, and the find percentage tasks are higher than the find whole and find part tasks. As to the strategies that students employed, the percentage of using the formal strategy is not much higher than that of using the informal strategy, even after learning the formal strategy. As an insightful approach for teaching percentages, based on the study results, it is suggested to reinforce the meaning of percentage, include various types of the comparison and change tasks, emphasize the informal strategy explicitly using models prior to the formal strategy, and understand the relations among part, whole and percentage throughly in various percentage situations before calculating.

• Communications of Mathematical Education
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• v.25 no.2
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• pp.473-495
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• 2011

Across the secondary school, students deal with the algebraic conditions like as identity, inverse, commutative law, associative law and distributive law. The algebraic structures, group, ring and field, are determined by these algebraic conditions. But the conditioning of these algebraic structures are not mentioned at all, as well as the meaning of the algebraic structures. Thus, students is likely to be considered the algebraic conditions as productions from the number sets. In this study, we systematize didactically the meanings of algebraic conditions and algebraic structures, considering connections between the number systems and the solutions of the equation. Didactically systematizing is to construct the model for student's natural mental activity, that is, to construct the stream of experience through which students are considered mathematical concepts as productions from necessities and high probability. For this purpose, we develop the program for the gifted, which its objective is to teach the meanings of the number system and to grasp the algebraic structure conceptually that is guaranteed to solve equations. And we verify the effectiveness of this developed program using didactical experiment. Moreover, the program can be used in ordinary students by replacement the term 'algebraic structure' with the term such as identity, inverse, commutative law, associative law and distributive law, to teach their meaning.

• Communications of Mathematical Education
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• v.29 no.3
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• pp.391-421
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• 2015

The scientific technology developed rapidly and the internet became more popular, also, the world became interactive with one another and the word 'Global' became popular and built a new paradigm. As the development of the society, the ideal criteria for the competent student changed. Consequently, the attention for the globalized education increased. From the points of view of mathematical education, it became a important task to be prepared for international competitiveness for korean talented students. For theses reasons, this article analyzes the characteristics of IBDP and its textbook, which is an international official curriculum and one of the actualizing method for internalization Korean high school curriculum and text book, specifically, focusing on algebra part. Especially, Korean curriculum textbooks and the Mathematical Higher Level textbooks of IBDP was compared and analyzed. As a result, the depth and range of the content, standard level of the question, methods being used to explain the concept, type of questions as well as teaching - learning method were analyzed and in each chapter of the algebra we give meaningful result and proposed discussion.

• The Mathematical Education
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• v.56 no.3
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• pp.301-318
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• 2017

This paper explores students' question generation process and their study in small group discussion. The research is based on Anthropological Theory of the Didactic developed by Chevallard. He argues that the savior (knowledge) we are dealing with at school is based on a paradigm that we prevail over whether we 'learn' or 'study' socially. In other words, we haven't provided students with autonomous research and learning opportunities under 'the dominant paradigm of visiting works'. As an alternative, he suggests that we should move on to a new didactic paradigm for 'questioning the world a question', and proposes the Study and Research Courses (SRC) as its pedagogical structure. This study explores the SRC structure of small group activities in solving ill-structured problems. In order to explore the SRC structure generated in the small group discussion, one middle school teacher and 7 middle school students participated in this study. The students were divided into two groups with 4 students and 3 students. The teacher conducted the lesson with ill-structured problems provided by researchers. We collected students' presentation materials and classroom video records, and then analyzed based on SRC structure. As a result, we have identified that students were able to focus on the valuable information they needed to explore. We found that the nature of the questions generated by students focused on details more than the whole of the problem. In the SRC course, we also found pattern of a small group discussion. In other words, they generated questions relatively personally, but sought answer cooperatively. This study identified the possibility of SRC as a tool to provide a holistic learning mode of small group discussions in small class, which bring about future mathematics classrooms. This study is meaningful to investigate how students develop their own mathematical inquiry process through self-directed learning, learner-specific curriculum are emphasized and the paradigm shift is required.

• School Mathematics
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• v.15 no.1
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• pp.179-199
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• 2013

In this study we grasp what contents in the mathematics curriculum the students of multicultural and North Korean migrant families are vulnerable to and we would like to provide the bases to devise the appropriate teaching and learning methods for them. In order to this work we used the results of 2011 National Assessment Educational Achievement. We categorized students from multicultural and North Korean migrant families into children from international marriage family (born in country or immigrated), foreign family, and North Korean migrant family and compared each category with the whole students. First, for each school class we analyzed characteristics of academic achievement by ratio of achievement level, means of calibrated score, and percentages of correct answers in NAEA, mean percentages of correct answers by content domains, and percentages of correct answers by items. In addition to these we analysed items qualitatively and investigated study conditions in which the students of multicultural and North Korean migrant families have difficult times. In every subgroup the more ratio of advanced level decreases and ratio of below basic level increases the more school classes go up. Also these phenomena appear differently by each group and by content domain. For this reason by group, the supporting on learning will be needed.

• Communications of Mathematical Education
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• v.25 no.3
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• pp.497-524
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• 2011

This study was to understand students' learning about the function of math combined with molecular motions of science using the block scheduling. It was based on the revised Class Structure Model of Lee et al.(2010) where MBL as a tool was used to increase students' participation and understanding in the integrated concepts. The researcher provided the 6th grade students who lived in Sung Nam-Si, Kyung Gi-Do with 8 unit lessons, consisting of 5 stages of CSM. As a result of the study, the integrated education of Mathematics and Science showed synergic effect in studying both subjects and brought a positive result in gradual mathematization. It may be hard to combine all the contents of mathematics and science together. However, learning the relation between volume and pressure, and between volume and temperature of gas used as an example of function shown in our daily life was appropriate through Fogarty's integrated education model because it supported the objective of both subjects. Also, it was a good idea to develop CSM because it was composed of the contents from both subjects held in the same period of a year. Through the five stages, students were able to establish and generalize the definitions and the concepts of function.