• Journal of Educational Research in Mathematics
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• v.11 no.1
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• pp.179-191
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• 2001

The Study investigated the contexts and probable difficulties of the teaching of the number of cases and the introduction of probability concept. In our mathematical curriculum, the contexts of the teaching of probability can be classified into five cases. We suggested some intuitive diagrams to be likely to decrease the cognitive complications caused by the equal possibilities of the unit event in the cases, respectively.

• The Mathematical Education
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• v.40 no.2
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• pp.345-350
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• 2001

This study suggested a teaching method to improve intuitive understanding of the statistical basic concepts about the central limit theorem with experiment. It is very hard to understand about the concept of the central limit theorem in the school mathematics class. The result of this study experiment for the class of statistics education shows that the students and mathematics teachers were interesting at this experiment. They corrected their misunderstanding about the central limit theorem by discussion for the result of experiment with team members. I think that this study can help teachers to teach the students using the experiment method.

• School Mathematics
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• v.4 no.2
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• pp.205-222
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• 2002

In school mathematics, the negative numbers have been instructed using the intuitive models such as the number line model, the counting model, and inductive-extrapolation on the additionand multiplication and using inverse operation on the subtraction and division. Theseinstructions on the negative numbers did not present their formal nature and caused the difficulty for students to understand their operations because of the incomplete function of the intuitive models. In this study, we tried to improve such problems of the instructions of the negative numbers on the basis of the didactical phenomenological analysis. First of all, we analysed the nature of the negative numbers and the cognitive obstructions through the examination about the historic process of them. Second, we examined hew the nature of the negative numbers were analysed and described in mathematics. Third, we explored the improving directions for them on the ground of the didactical phenomenological analysis. In school mathematics, the rules of operations using the intuitive models of the negative numbers have been Instructed rather than approaching toward the nature of them. The negative numbers have been developed from the necessity to find the general solution of equations. The study tries to approach the operations instructions of the negative numbers formative]y to overcome the problems of those that are using the intuitive models and to reflect the formative Furthermore of the negative numbers. Furthermore, we examine the way of the instruction of the negative numbers in real context so that the algebraic feature and the real context should be Interactive.

• Journal of the Korean School Mathematics Society
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• v.11 no.1
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• pp.97-115
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• 2008

In high school mathematics class, to subtract a number b from a, we add the additive inverse of b to a and to divide a number a by a non-zero number b, we multiply a by the multiplicative inverse of b, which is the formal approach for operations of real numbers. This article aims to give a connection between the intuitive models in middle school mathematics class and the formal approach in high school for teaching operations of negative integers. First, we highlight the teaching methods(Hwang et al, 2008), by which subtraction of integers is denoted by addition of integers. From this methods and activities applying the counting model, we give new teaching methods for the rule that the product of negative integers is positive. The teaching methods with horizontal mathematization(Treffers, 1986; Freudenthal, 1991) of operations of integers, which is based on consistently applying the intuitive model(number line model, counting model), will remove the gap, which is exist in both teachers and students of middle and high school mathematics class. The above discussion is based on students' cognition that the number system in middle and high school and abstracted number system in abstract algebra course is formed by a conceptual structure.

• Journal of Institute of Control, Robotics and Systems
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• v.22 no.8
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• pp.656-664
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• 2016

While anthropomorphic robots are gaining interest, dual-arm robots are widely used in the industrial environment. Many methods exist in order to implement bimanual tasks by dual-arm robot. However, kinesthetic teaching is used in this paper. This paper suggests three different kinesthetic teaching methods that can implement most of the human task by the robot. The three kinesthetic teaching methods are joint level, task level, and contact level teaching. The task introduced in this paper is box packing, which is a popular and complex task in industrial environment. The task is programmed into the dual-arm robot by utilizing the suggested kinesthetic teaching method, and this paper claims that most tasks can be implemented by using the suggesting kinesthetic teaching methods.

• Research in Mathematical Education
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• v.6 no.2
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• pp.117-122
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• 2002

From the beginning of the 20th century, calculus is gradually offered to high school students in many countries. However, in Chinese high school, the instruction on calculus is nearly an untouched field. Many people don't believe that high school students can study calculus well. They think calculus knowledge in students' brains is likely to become the “half-cooked food”, and this can produce a bad effect on the study of formal calculus at university. The authors consider that the emphasis of calculus in high school should be the intuitive understanding of fundamental calculus concepts, and it is also the basis of the understanding of formal concepts. Traditional mathematics course with chalk can't meet the needs of calculus teaching. The use of technologies can enhance the calculus teaching, especially the informal and visual calculus teaching, help students understand the underlying concepts. The authors describe how the use of technologies can improve the calculus teaching and learning, and point out that the use of technologies can clear up people's doubts.

• Journal of Educational Research in Mathematics
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• v.16 no.2
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• pp.95-113
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• 2006

The study tries to differentiate the levels of mathematical reasoning from inductive reasoning to formal reasoning for teaching gradually. Because the formal point of view without the relation to objects has limitations in the creation of a new knowledge, our mathematics education needs consider the such characteristics. We propose an intuitive level of proof related in concrete operations and perceptual experiences as an intermediating step between inductive and formal reasoning. The key activity of the intuitive level is having insight on the generality of reasoning. The details of the process should pursuit the direction for going away from objects and near to formal reasoning. We need teach the mathematical reasoning gradually according to the appropriate level of reasoning more differentiated.

• Journal of Educational Research in Mathematics
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• v.23 no.4
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• pp.567-584
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• 2013

In school mathematics, the concept of continuous functions has been intuitively taught. Many researches reported that many students identified the continuity of function with the connectedness of the graphs. Several researchers proposed some ideas which are enhancing the formal aspects of the definition as alternative. We analysed the historical developments of the concept of continuous functions and drew pedagogical implications for the intuitive teaching of continuous functions from the result of analysis.

• Journal of the Korean Society for Precision Engineering
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• v.30 no.1
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• pp.96-104
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• 2013

Study of human-robot Interaction gets more and more attention to expand the robot application for tasks difficult by robot alone. Developed countries are preparing for a new market by introducing the concept of 'Co-Robot' model of human-robot Interaction. Our research of direct teaching is a way to instruct robot's trajectory by human's handling of its end device. This method is more intuitive than other existing methods. The benefit of this approach includes easy and fast teaching even by non-professional workers. And it can enhance utilization of robots in small and medium-sized enterprises for small quantity batch production. In this study, we developed the algorithms for creating accurate trajectory from repeated inaccurate direct teaching and GUI for the direct teaching. We also propose the basic framework for direct teaching.

• Journal of the Korean School Mathematics Society
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• v.21 no.2
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• pp.113-139
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• 2018

There is no doubt about the importance of teacher knowledge for good teaching. Many researches attempted to conceptualize elements and features of teacher knowledge for teaching in a quantitative way. Unlike existing researches, this article suggests an interpretation of preservice teacher knowledge in the field of geometry using the Shulman - Fischbein framework in a qualitative way. Seven female preservice teachers voluntarily participated in this research and they performed a series of written tasks that asked their subject matter knowledge (SMK) and pedagogical content knowledge (PCK). Their responses were analyzed according to mathematical algorithmic -, formal -, and intuitive - SMK and PCK. The interpretation revealed that preservice teachers had overally strong SMK, their deeply rooted SMK did not change, their SMK affected their PCK, they had appropriate PCK with regard to knowledge of student, and they tended to less focus on mathematical intuitive - PCK when they considered instructional strategies. The understanding of preservice teachers' knowledge throughout the analysis using Shulman-Fischbein framework will be able to help design teacher preparation programs.