• The Mathematical Education
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• v.62 no.2
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• pp.257-268
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• 2023

The purpose of the study is to analyze the characteristics of open-ended tasks in terms of cognitive demands. For this purpose, we analyzed characteristics of open-ended tasks presented in the sequence units of three high school mathematics textbooks. The results of the study have revealed that low cognitive demand levels of open-ended tasks had characteristics including procedures within previous tasks or within those tasks. On the other hand, high cognitive demand levels of open-ended tasks had characteristics of actively exploring new conditions to gain access to what is being sought, requesting a basis for judgement, linking various representations to the concepts of sequences, or requiring a variety of answers. These results are significant in that they not only specified the characteristics of open-ended tasks with high cognitive demands in terms of the intended curriculum, but also provided a direction for the development of open-ended taks with high congitive demands.

• Journal of the Korean School Mathematics Society
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• v.22 no.4
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• pp.501-520
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• 2019

This study compared and analyzed Korean, American, Singaporean, and Japanese middle school mathematics curriculum standards and the learning contents in statistics. Through a comparative analysis of the curriculums of these four countries, I found several overall features and differences between the curriculums. First, all four countries emphasized statistical education in a real-life context. Second, all four countries emphasized the use of technological tools. Third, there is a middle school grade in which only Korea does not deal with statistical domains. Fourth, the statistical areas of the United States, Singapore, and Japan focused on identifying trends or variability in data distribution. Fifth, I have found some contents that only Korea does not deal with. Based on this, the following recommendations were developed for the development of the next curriculum and new textbooks in Korea. First, the statistics curriculum should be changed from one that focuses on understanding statistical concepts to one that focuses on statistical activity that utilizes these concepts. Second, in terms of middle school statistical curriculum contents, the addition of interquartile range (IQR) and box plots as learning contents should be considered. IQR and box plots are simple and practical techniques for the comparison of multiple sets of data that can be easily learned and drawn by middle school level students and applied to real-life-related statistical data to expand statistical literacy. Through this study, it is suggested that IQR and box plots need to be included in the statistical curriculum of middle schools in Korea.

• Journal of Educational Research in Mathematics
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• v.25 no.1
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• pp.59-74
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• 2015

It is an increasing research area to explore mathematics learning from discursive perspectives. However, there have been little studies conducted on why and how discursive perspectives in mathematics learning were adopted and developed. Especially, not much discussion has been done on the later Wittgenstein's philosophical stance in terms of the relationship between language and thought as a background of discursive approach to learning mathematics. This study aims to explore the later Wittgenstein on language to get better understanding about discursive approaches to mathematics learning. For the attainment of this aim, first the later philosophy is compared with the former philosophy in depth. Then the later philosophy is discussed focusing on how his point of view on the world and the language have been changed. After providing an account of his later philosophy, it is clarified that what is discursive approaches to learning mathematics and how this philosophy brace the approaches. This research concludes with implications and limitations, as well as suggestions for future researches.

• School Mathematics
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• v.18 no.3
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• pp.589-609
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• 2016

In this study, researchers have modernly reinterpreted geometric solving of cubic equations presented by an arabic mathematician, Omar Khayyam in medieval age, and have considered the pedagogical significance of geometric solving of the cubic equations using two conic sections in terms of analytic geometry. These efforts allow to analyze educational application of mathematics instruction and provide useful pedagogical implications in school mathematics such as 'connecting algebra-geometry', 'induction-generalization' and 'connecting analogous problems via analogy' for the geometric approaches of cubic equations: $x^3+4x=32$, $x^3+ax=b$, $x^3=4x+32$ and $x^3=ax+b$. It could be possible to reciprocally convert between algebraic representations of cubic equations and geometric representations of conic sections, while geometrically approaching the cubic equations from a perspective of connecting algebra and geometry. Also, it could be treated how to generalize solution of cubic equation containing variables from geometric solution in which coefficients and constant terms are given under a perspective of induction-generalization. Finally, it could enable to provide students with some opportunities to adapt similar solving procedures or methods into the newly-given cubic equation with a perspective of connecting analogous problems via analogy.

• The Mathematical Education
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• v.48 no.4
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• pp.399-417
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• 2009

The purpose of this study was to explore the adaptability of U.S. multiple-choice items to measure Mathematical Knowledge for Teaching (MKT) in Korea. For this purpose, the authors selected the number and operations form B which was developed by Learning Mathematics for Teaching (LMT) project at the University of Michigan and then adapted items in terms of general cultural context, school cultural context, mathematical substances, and language in Korea. The survey was administrated to 77 Korean in-service teachers who had more than three years of teaching experiences. Based on the survey, the authors compared the data to that of U.S. teachers who had participated California's Mathematics Professional Development Institute. As a result, the survey measures less knowledge Korean teachers than more knowledgable Korean teachers and there are strong correlations of relative item difficulties between Korean teachers and U.S. teachers for both Content Knowledge (CK) items and Knowledge of Content and Students (KCS) items. This study implies the future direction for developing items to measure teacher knowledge as well as designing effective teacher education programs.

• Journal of information and communication convergence engineering
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• v.12 no.1
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• pp.33-38
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• 2014

This paper investigates the shaping operation problem introduced by Callahan et al., namely the k-fragility maximization problem (k-FMP), whose goal is to find a subset of personals within a terrorist group such that the regeneration capability of the residual group without the personals is minimized. To improve the impact of the shaping operation, the degree centrality of the residual graph needs to be maximized. In this paper, we propose a new greedy algorithm for k-FMP. We discover some interesting discrete properties and use this to design a more thorough greedy algorithm for k-FMP. Our simulation result shows that the proposed algorithm outperforms Callahan et al.'s algorithm in terms of maximizing degree centrality. While our algorithm incurs higher running time (factor of k), given that the applications of the problem is expected to allow sufficient amount of time for thorough computation and k is expected to be much smaller than the size of input graph in reality, our algorithm has a better merit in practice.

• School Mathematics
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• v.4 no.2
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• pp.317-331
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• 2002

The purpose of this study is to compare the eighth-grade mathematics textbooks of Korea, Japan on the one hand, and those of the United States and England on the other, and to explore the implications for mathematics education in the East and the West. As a result, the dichotomy between the East and the West were set up with the sacrifice of the details. First, the textbook development and publication policies of the East are characterized as uniformity, and those of the West are diversity. Second, for the choice of content, the East and West can be represented by essential and discretionary respectively. Third, the physical appearance of Eastern textbooks is rather plain while that of the Western textbooks is colorful, Fourth, in terms of the characteristics of the content, the dichotomies between the East and the West are linear vs. spiral, content vs. context, formal abidance vs. metacognitive shift, and simple vs. realistic. Each of the Eastern and Western approaches has its own weak points as well as its strong points. For instance, textbooks In the West may help students realize how useful mathematics can be in their lives, but if the link between a mathematical concept and the corresponding real life situation is not made clear, sometimes students may not be able to completely grasp the mathematical concept. In turn, the Eastern textbooks may succeed In conveying ideas in an economical way, but they often fail to motivate students to follow the course. Therefore it is important to take a critical view of each approach. It is through a critical understanding of the differences between different cultures that we are able to learn from each other and to put the results of such comparative studies to better use in the future.

• School Mathematics
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• v.18 no.2
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• pp.397-423
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• 2016

Mathematics learning motivation is an important variable which is not only the primary goal of learning mathematics but also mediates the effects of the mathematics learning. Nevertheless, the present learning environment is full of impeding factors which reduce learners' motivation to learn mathematics and mathematical self-regulatory efficacy. The purpose of this study is to offer various suggestions for program to enhance and forster mathematics learning motivation based on empirical findings and theories on motivation, self-regulatory learning, regulatory focus, reducing academic stress and math anxiety. The concrete and practical ideas are suggested in terms of mathematical self-regulatory efficacy, learners' characteristics, learning task. The analysis of the effects revealed a positive effect on mathematical self-regulatory learning.

• Journal of Elementary Mathematics Education in Korea
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• v.16 no.1
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• pp.63-95
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• 2012

Since performance assessment was implemented for 10 years, a survey has been carried out from 212 elementary school teachers in Seoul area in terms of their perception and status about descriptive assessment. As results, most of teachers agreed strongly that using constructed-response items is necessary for assessment, and they showed that purpose of using constructed-response items in their mathematics classrooms was to evaluate accurately student achievement in accordance with learning objectives in mathematics and they referred mainly to items which they modified from problems or items in the textbook when they generate constructed-response items. In addition, they considered level of difficulty in creating constructed-response items mostly. Moreover, they indicated that the effects of assessment through constructed-response items would be improvement of students' problem solving and reasoning skills.

• Journal of the Korean School Mathematics Society
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• v.24 no.1
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• pp.107-126
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• 2021

Lexicon is closely related to human thinking. In particular, a classroom lexicon results from objectifying the teaching-learning activity in classrooms, allowing humans to recognize and explore the activities and phenomena in classrooms explicitly. Therefore, using the lexicon and clarifying what the words mean is to enhance the understanding of teaching activities. The International Classroom Lexicon Project investigates and identifies each country's mathematics classroom lexicon, where ten countries participated. The purpose of this current study is to compare the differences in perceptions between teachers and pre-service teachers about the Korean classroom lexicon previously investigated as a part of the international collaborative project. By comparing the responses of 147 teachers and 127 pre-service teachers, the degree of familiarity with pedagogical terms and the frequency of occurrence or usage in classrooms were compared and analyzed to understand the recognition of pre-service teachers' pedagogical terms. Finally, we also discuss reflections on Korean mathematics teaching practices in Korea.