• School Mathematics
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• v.2 no.1
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• pp.29-51
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• 2000

In this study, we tried to suggest an example of the analysis on the use of mathematical manipulatives. Taking algebra tiles as an example of mathematical manipulatives, we analysed several effects resulted from the use of algebra tiles. The algebra tiles make it possible to do activities that are needed to introduce and explain the distributive law and factoring. The algebra tiles have a several advantages; First of all, This model is simple. Even though they cannot make algebra easy, this model can play an important role in the transition to a new algebra course. This model provides access to symbol manipulation for students who had previously been frozen out of the course because of their weak number sense. This model provides a geometric interpretation of symbol manipulation, thereby enriching students' understanding, This model supports cooperative learning, and help improve discourse in the algebra class by giving students objects to think with and talk about. On the other hand, The disadvantages of this model are as follows; the model reinforces the misconception that -x is negative, and x is positive; the area model of multiplication is not geometrically sound when minus is involved; only the simplest expressions involving minus can be represented; It is ineffective when be used the learning of already known concept. Mathematics teachers must have a correct understanding about these advantages and disadvantages of manipulatives. Therefore, they have to plan classroom work that be maximized the positive effect of manipulatives and minimized the negative effect of manipulatives.

• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.511-536
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• 2017

The present study aims to investigate ways in which pre-service secondary mathematics teachers anticipate 1) students' responses to specific mathematical tasks which are chosen or devised by the participating pre-service teachers as requiring students' higher cognitive demand and, 2) their roles as math teachers to scaffold students' mathematical thinking. To achieve the goal, we had our pre-service teachers to engage in an adapted version of Spangler & Hallman-Thrasher(2014)'s Task Dialogue writing activity whose focus was to develop pre-service elementary teachers' ability to orchestrate mathematical discussion. 14 pre-service teachers who were junior at the time enrolled in the Mathematics Teaching Method Course were subjects of the current study. In-depth analysis of both Task Dialogues which pre-service secondary mathematics teachers wrote and audiotapes of the group discussions while they wrote the dialogues suggests the following results: First, the pre-service secondary teachers anticipated how students would approach a task based on their own teaching experiences. Second, they were challenged not only to anticipate more than one correct students' responses but to generate questions for the predicted correct-responses to bring forth students' divergent thinking. Finally, although they were aware that students' knowledge should be the crucial element guiding their decision-making process in teaching, they tended to lower the cognitive demands of tasks by providing students with too much guidance which brought forth the use of procedural knowledge. The study contributes to the field as it provides insights as to what to attend in designing teacher education course whose goal is to provide a foundation for developing pre-service teachers' ability to effectively orchestrate mathematical discussion.

• Journal of Advanced Research in Ocean Engineering
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• v.1 no.1
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• pp.55-62
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• 2015

Floating structure such as tension leg platform, semi-submersible and spar are widely used in field of oil exploration and renewable energy system. All of these structures have the base cylinder support structure which have effective rule in overall dynamic of response. So the accurate and reliable modeling is needed for optimum design and understanding the physical background of these systems. The aim of this article is an analytical discussion on stochastic modeling of floating cylinder based support structure but an applicable one. Due to this a mathematical mass-damper-spring system of a floating cylinder of HAWAII WTG offshore wind as an applicable and innovative system is adopted to model a coupled degrees using random vibration in analytical way. A fully develop spectrum is adopted to solve the stochastic spectrum analytically by a proper approximation. Some acceptable assumption is adopted. The simplified but analytical and innovative hydrodynamic analysis of this study not only will help researcher to concentrate more physically on hydrodynamic analysis of floating structures but also can be useful for any quick, simplified and closed form analysis of a complicated problem in offshore engineering.

• Journal of The Korean Association of Information Education
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• v.7 no.1
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• pp.11-26
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• 2003

Although many mathematical teaching/learning materials are already developed in the web, diverse utilization of this materials such as calculation, searching, or reusing of expressions are limited since the expression is actually a figure. To cope with this, MathML which describing mathematical notation was developed. In the paper, we proposed the methods of developing teaching materials using MathML, making learning assistance tools which utilize MathML, and applying MathML to information exchange community for Mathematics courses in ICT environment. Using MathML to develop a teaching material makes easy to correct and reuse the mathematical notations conveniently. Furthermore, learning assistance tools made by placing MathML help teachers reorganize and utilize these materials in the classroom as well as enhancing the connection between mathematical notations and concepts. The web-board that can make a use the mathematical notations using MathML enables the teachers and students to exchange information actively. It also helps to fulfill different types of teaching using ICT such as "discussion on the web".

• The Mathematical Education
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• v.59 no.4
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• pp.389-403
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• 2020

This study aims to examine how information processing competency as one of the mathematical competencies has been interpreted and applied in mathematics education by analyzing tasks in middle school mathematics textbooks under the 2015 revised national curriculum. Based on the sub-elements of information processing competency organized by Park et al.(2015), we analyzed 191 tasks in 30 different middle school mathematics textbooks using descriptive statistics and ANOVA. Also, we investigated the meaning of information processing competency embedded in the tasks by distinguishing the characteristics of several different types of tasks. The results from this study showed that the number of tasks related to information processing competency in mathematics textbooks was too small and there was a huge difference across the textbooks in terms of the sub-elements. Even though there were four sub-elements of information processing competency, 'the use of manipulative and technological tools' was extremely dominant in the tasks in general. Even many of them used technology and manipulatives superficially. Furthermore, any textbook did not provide tasks dealing with all the four sub-elements. Such an unbalanced and fragmented approach to information processing competency could produce biased knowledge and insufficient experiences for information processing competency. It calls for further investigation and discussion about how to improve information processing competency in school mathematics.

• Journal of the Korean School Mathematics Society
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• v.6 no.1
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• pp.1-17
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• 2003

In this paper, we study the methods of improving an ability of a creative solving mathematical problem belonging to an educational system which every province office of education has adopted for the mathematically talented students. Especially, we give an attention on a preferential reaction in teaching styles according to student's LQ., the relationship between student's LQ. and an ability of creative solving mathematical problems, and seeking for an appropriative teaching methods of the improvement ability of a creative solving problem. As results, we have the followings; 1. The group having excellent students who have a higher intelligential ability prefers inquiry learning which is composed of several sub-groups to a teacher-centered instruction. 2. The correlation coefficient between student's LQ. and an ability creative solving of mathematical is not high. 3. Although the contents and the model of thematic inquiry learning don't have a great influence on the divergent thinking (ex. fluency, flexibility, originality), they affect greatly the convergent thinking - a creative mathematical - problem solving ability. Accordingly, our results show that we should use a variety of mathematical teaching materials apart from our regular textbooks used in schools to improve a creative mathematical problem solving ability in the process of thematic inquiry learning. Also we can see that an inquiry learning which stimulates student's participation and discussion can be a desirable model in the thematic mathematical classroom activities.

• Journal of the Korean School Mathematics Society
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• v.8 no.1
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• pp.55-75
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• 2005

As part of development research of a gender-neutral mathematics program, this paper provides a discussion of the fearures of the developed mathematics program. Based on the theory of feminist pedagogy and critical theories about women' ways of knowing, this mathematics program for girls pursues the mathematical empowerment of girls. Specifically, this mathematics program facilitates girls' awareness of their mathematical potentials, encourage them to position women at a center of mathematics in order for th equity in mathematics education. For the purpose, this program emphasizes constructive learning through girls' active participation. Thus, the instructions will value girls' own cognitive resources such as their experiential knowledge and ways of mathematical justification and provide an environment to support the growth of girls' own mathematical potential. This developmental research will be furthered to the systematic program evaluation to extend this program to support the equity for the marginalized poppulations as well as girls in mathematics education.

• Journal of Educational Research in Mathematics
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• v.11 no.1
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• pp.11-35
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• 2001

Many teachers report familiarity with and adherence to reform ideas, but their actual teaching practices do not reflect a deep understanding of reform. Given the challenges in implementing reform, this study intended to explore the breakdown that may occur between teachers' adoption of reform objectives and their successful incorporation of reform ideals. To this end, this study compared and contrasted the classroom social norms and sociomathematical norms of two United States second-grade teachers who aspired to implement reform. This study is an exploratory, qualitative, comparative case study. This study uses the grounded theory methodology based on the constant comparative analysis for which the primary data sources were classroom video recordings and transcripts. The two classrooms established similar social norms including an open and permissive learning environment, stressing group cooperation, employing enjoyable activity formats for students, and orchestrating individual or small group session followed by whole group discussion. Despite these similar social participation structures, the two classes were remarkably different in terms of sociomathematical norms. In one class, the students were involved in mathematical processes by which being accurate or automatic was evaluated as a more important contribution to the classroom community than being insightful or creative. In the other class, the students were continually engaged in significant mathematical processes by which they could develop an appreciation of characteristically mathematical ways of thinking, communi-eating, arguing, proving, and valuing. It was apparent from this study that sociomathematical norms are an important construct reflecting the quality of students' mathematical engagement and anticipating their conceptual learning opportunities. A re-theorization of sociomathematical norms was offered so as to highlight the importance of this construct in the analysis of reform-oriented classrooms.

• School Mathematics
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• v.12 no.4
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• pp.547-561
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• 2010

Even though statistics is considered as one of the areas of mathematical science in the school curriculum, it has been well documented that statistics has distinct features compared to mathematics. However, there is little empirical educational research showing distinct features of statistics, especially research into the understanding of statistical concepts which are different from other areas in school mathematics. In addition, there is little discussion of a relationship between the ability of mathematical thinking and the ability of understanding statistical concepts. This study extracted some important concepts which consist of the fundamental statistical reasoning and investigated how mathematically high achieving students understood these concepts. As a result, there were both kinds of concepts that mathematically high achieving students developed well or not. There is a weak correlation between mathematical ability and the level of understanding statistical concepts.

• Bulletin of the Korean Mathematical Society
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• v.21 no.2
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• pp.99-106
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• 1984

J. Yeh has recently introduced the concept of conditional Wiener integrals which are meant specifically the conditional expectation E$^{w}$ (Z vertical bar X) of a real or complex valued Wiener integrable functional Z conditioned by the Wiener measurable functional X on the Wiener measure space (A precise definition of the conditional Wiener integral and a brief discussion of the Wiener measure space are given in Section 2). In [3] and [4] he derived some inversion formulae for conditional Wiener integrals and evaluated some conditional Wiener integrals E$^{w}$ (Z vertical bar X) conditioned by X(x)=x(t) for a fixed t>0 and x in Wiener space. Thus E$^{w}$ (Z vertical bar X) is a real or complex valued function on R$^{1}$. In this paper we shall be concerned with the random vector X given by X(x) = (x(s$_{1}$),..,x(s$_{n}$ )) for every x in Wiener space where 0=s$_{0}$ $_{1}$<..$_{n}$ =t. In Section 3 we will evaluate some conditional Wiener integrals E$^{w}$ (Z vertical bar X) which are real or complex valued functions on the n-dimensional Euclidean space R$^{n}$ . Thus we extend Yeh's results [4] for the random variable X given by X(x)=x(t) to the random vector X given by X(x)=(x(s$_{1}$).., x(s$_{n}$ )).