• Journal of Educational Research in Mathematics
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• v.20 no.4
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• pp.493-509
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• 2010

Researchers have suggested that educators have to focus their attention on variability and reasoning about variation as means of developing students' statistical thinking in school mathematics. This paper investigated knowledge for the teaching of variability and reasoning about variation; what are sources of variability, how to cope with variability, what are types of variability, how to recognize variability, and the relationship between statistical problem solving and variability. The results involve: discussion on the sources of variability and how to cope with variability promotes students' awareness of different types of variability and students' motivation in the following steps in the statistical activity; emphasis on reasoning about variation in teaching representation of data accords with objectives of statistics education; reexamination of curriculum for statistics education is needed, which has a content-oriented arrangement.

• East Asian mathematical journal
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• v.29 no.2
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• pp.207-239
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• 2013

This research is a study on student's understanding fundamental concepts of mathematical curriculum, especially in geometry domain. The goal of researching is to analyze student's concepts about that domain and get the mathematical teaching methods. We developed various questions of descriptive assessment. Then we set up the term, procedure of research for the understanding student's knowledge of geometric figures. And we analyze the student's understanding extent through investigating questions of descriptive assessment. In this research, we concluded that most of students are having difficulty with defining the fundamental concepts of mathematics, especially in geometry. Almost all the students defined the fundamental conceptions of mathematics obscurely and sometimes even missed indispensable properties. And they can't distinguish between concept definition and concept image. Prior to this study, we couldn't identify this problem. Here are some suggestions. First, take time to reflect on your previous mathematics method. And then compile some well-selected questions of descriptive assessment that tell us more about student's understanding in geometric concepts.

• Journal of Educational Research in Mathematics
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• v.13 no.3
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• pp.329-349
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• 2003

Mathematics education is accomplished by systems such as mathematical curriculum and tools such as a textbook which reflects such systems. Human beings make such systems and tools. Therefore, a viewpoint of mathematics of those who make them is an important factor. The view point of mathematics is formed during doing and learning mathematics, but the already formed viewpoint of mathematics affects doing and teaching mathematics. Hence, it will be a factor which affects basically that those who employ themselves on mathematics education have a certain viewpoint of mathematics. This article presents dialectical materialistic viewpoint as the viewpoint of mathematics which affects fundamentally on mathematical teaching-learning practice. The dialectical materialism is carried through the process and result of mathematics development. This shows that mathematical knowledge is objective. Mathematical knowledge has developed according to three basic rules of dialectical materialism i.e. the transformation of quantity into quality, the unification of antagonistic objects, and the negation of negation. This viewpoint of mathematics should offer the viewpoint of mathematics education which is different from the view point of absolutism, relativism or formal logic. In this article I considered mathematics separating standpoint of mathematics into materialistic viewpoint and dialectical viewpoint. 1 did so for the convenience of analysis, but you will be able to look at the unified viewpoint of dialectical materialism. 1 will make mention of teaching-learning method on another occasion.

• 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.

• Journal of the Korean School Mathematics Society
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• v.9 no.2
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• pp.179-193
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• 2006

The aim of this paper is to explore and understand, using in-depth interviews, the participant's enthusiasm for and involvement in studying mathematics and the deeper nature of his/her interest in mathematics teaching. In addition a larger aim is to understand how the individual's interest in mathematics and teaching are linked to his/her larger personal fulfillment. We conducted in-depth interviews with 4 pre-service teachers' subjective experiences focusing on deep motivation, pedagogical content knowledge, inner vision. Interviews focus much more on the participant's spontaneous feeling, consciousness, and state as these arise in the interview, and on past foiling, consciousness and state as they appear to the participant subjectively retrospectively in his/her memory. The output of this research consists of 2 portraits out of 4 individual participants, highlighting and conceptually developing the specific aspects under study; different ways in which individuals' involvement with the subject area affects their motivation, inner visions and academic efforts toward becoming teachers. Larger aspects of pre-service teachers' subjective experiences were sketched by contrasting the two cases. Several suggestions were put at the end to enhance mathematics education concerning curriculum development.

• Journal of the Korean School Mathematics Society
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• v.17 no.2
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• pp.251-274
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• 2014

The purpose of this study is to analyze characteristics of PCK before class, investigate how these characteristics are enacted in classrooms when beginning and experienced teachers teach mathematical functions, and provide pedagogical implications. Two beginning teachers and two experienced teachers participated in the study. In order to analyze characteristics of PCK before class, interviews and survey research were conducted. An investigation of classroom discourse was used to examine how the PCK characteristics appear in classrooms. Results show that experiences teachers enacted their PCK about learner, curriculum, teaching methods, and teaching environment in classrooms, whereas beginning teachers could not show their PCK. These results suggest practical implications for the developments of teacher education curriculum and teacher training program.

• Journal of Elementary Mathematics Education in Korea
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• v.21 no.1
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• pp.1-22
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• 2017

The properties of arithmetic are considered as essential to understand the principles of calculation and develop effective strategies for calculation in the elementary school level, thanks to agreement on early algebra. Therefore elementary students' misunderstanding of the properties of arithmetic might cause learning difficulties as well as misconcepts in their following learning processes. This study aims to provide elementary teachers a part of pedagogical content knowledge about the properties of arithmetic and to induce some didactical implications for teaching the properties of arithmetic in the elementary school level. To do this, elementary school mathematics textbooks since the period of the first curriculum were analyzed. These results from analysis show which properties of arithmetic have been taught, when they were taught, and how they were taught. Based on them, some didactical implications were suggested for desirable teaching of the properties of arithmetic.

• The Mathematical Education
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• v.50 no.3
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• pp.355-365
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• 2011

The purpose of this study is to provide mathematical knowledge for supporting the didactical knowledge on circular measure and radian in the high school curriculum. We show that circular measure related to arcs can be mathematically justified as an angular measure and radian is a well defined concept to be able to reconcile the values of trigonometric functions and ones of circular functions, which are real variable functions. Radian has two-fold intrinsic attributes of angular measure and arc measure on the unit circle, in particular, the latter property plays a very important role in simplifying the trigonometric derivatives. To improve students's low academic achievement in trigonometry section, the useful advantage and the background over the introduction of radian should be preferentially taught and recognized to students. We suggest some teaching plans to practice in the class of elementary and middle school for enhancing teachers' and students' understanding of radian.

• Journal for History of Mathematics
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• v.22 no.3
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• pp.113-130
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• 2009

It can be said that the teaching and learning of mathematical problem solving has been greatly influenced by G. Polya. His heuristics shows down the explicit process of mathematical problem solving in detail. In contrast, Polanyi highlights the implicit dimension of the process. Polanyi's theory can play complementary role with Polya's theory. This study outlined the epistemology of Polanyi and his theory of problem solving. Regarding the knowledge and knowing as a work of the whole mind, Polanyi emphasizes devotion and absorption to the problem at work together with the intelligence and feeling. And the role of teachers are essential in a sense that students can learn implicit knowledge from them. However, our high school students do not seem to take enough time and effort to the problem solving. Nor do they request school teachers' help. According to Polanyi, this attitude can cause a serious problem in teaching and learning of mathematical problem solving.

• Communications of Mathematical Education
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• v.32 no.4
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• pp.537-554
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• 2018

The era of the Fourth Industrial Revolution calls for creativity - convergence talent. In addition to having mathematical knowledge, they can create new technologies by linking them to other fields. This social trend is also reflected in the 2015 revised curriculum, and plans to further expand the STEAM education emphasized since 2011. Many teachers who had previous experience with STEAM training were satisfied with the STEAM teaching effectiveness. However, the reality is that the lack of expertise in other subjects is causing a burden on the ongoing implementation of convergence education. One way to alleviate these teachers' burden is to find the STEAM elements and then apply. Since the convergence education is required continuously, it is necessary to analyze the textbook according to the 2015 curriculum. In this study, we examined how the elements of the STEAM were apply in 7th grade textbooks. Based on the classification framework proposed by Yakman (2008), a new classification framework was devised and applied to the analysis.