• Communications of Mathematical Education
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• v.25 no.1
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• pp.63-78
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• 2011

The purpose of this study is to explore a teaching method of limits of functions with more intuitive and visual of CAS graphing calculators rather than with the rigorous ${\epsilon}-{\delta}$ method. Texas Instruments Voyage200 CAS graphing calculators are used for studying the possibility of the use of technology in calculus course. For this, various related theoretical constructs are reviewed: concept image, concept definition, cognitive conflict, the use of visualization of technology for calculus concepts, the theory of APOS, and local straightness. Based on such theoretical constructs this study suggests a teaching method of limits of functions with embodied visualization of CAS graphing calculators.

• School Mathematics
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• v.15 no.4
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• pp.921-940
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• 2013

This study is to analyze mathematically gifted middle school students' characteristics of mathematical thinking and the teacher's role in teaching and learning about the central projection and perspective drawing. And it will help to develop teaching and learning materials for the mathematically gifted. The result of this study is as followings : mathematically gifted middle school students show the various characteristics of mathematical thinking like as intuitive insight, generalization, logical thinking & mathematical abstraction and so on, and the teacher plays roles as instructional designer, facilitator, technical assistant and counselor.

• Journal of Korean Academy of Nursing
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• v.24 no.2
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• pp.206-215
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• 1994

Intuition is an abstract concept which is most often thought of as a nonrational, nonscientific mode of thought. However, since there are so many amorphous definitions of intuition that it seems important to clarify the meaning of this concept. Therefore, this study use the process of Walker & Avant’s concept analysis to define of the concept of intuition Attributes of intuition were defined as 1) Knowledge of truth that is difficult to explicate ; 2) A type of immediate knowing ; 3) Knowlwdge without reasining analysis ; 4) Knowledge that is attained based on virtue character which integrates all matter and is not attained through individual experience. Antecedents of intuition consists of 1) as ground for knowledge or truth that is not availables to trace through the analytic procedures ; & 2) the flow of Ki which unites human beings and the universe. Consequences of intuition events or incidents occuring as a result of the concept consist of verification of the truth though analytic procedures and application of knowledge in both theoretical and practical ways. To develop intuitive ability, as an educator should not only make studies in recognizine, analysing and teaching concepts related to logical, rational decision making but should also recognize and teach concepts related to intuitive components of making decisions in clinical practice and classroom learning as well.

• The Journal of the Korea institute of electronic communication sciences
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• v.19 no.1
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• pp.85-92
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• 2024

In this paper, we developed an intuitive teaching and control system that directly teaches a task by holding the tip of a robotic arm and moving it to a desired position. The developed system consists of a 6-axis force sensor that measures position and attitude forces at the tip of the robot arm, an algorithm for generating robot arm joint speed control commands based on the measured forces at the tip, and a self-made 6-axis robot arm and control system. The six-dimensional force/torque of the position posture of the robot arm operator steering the handler is detected by the force sensor attached to the handler at the leading edge and converted into velocity commands at the leading edge to control the 7-axis robot arm. The verification of the research method was carried out with a self-made 7-axis robot, and it was confirmed that the proposed force sensor-based robot end-of-arm control method operates successfully through experiments by teaching the operator to adjust the handler.

• Journal of Educational Research in Mathematics
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• v.13 no.1
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• pp.25-55
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• 2003

In the school mathematics, the negative numbers have been instructed by means of intuitive models(concrete situation models, number line model, colour counter model), inductive-extrapolation approach, and the formal approach using the inverse operation relations. These instructions on the negative numbers have caused students to have the difficulty in understanding especially why the rules of signs hold. It is due to the fact that those models are complicated, inconsistent, and incomplete. So, students usually should memorize the sign rules. In this study we studied on the didactical phenomenology of the negative numbers as a foundational study for the improvement of teaching negative numbers. First, we analysed the formal nature of the negative numbers and the cognitive obstructions which have showed up in the historic-genetic process of them. Second, we investigated what the middle school students know about the negative numbers and their operations, which they have learned according to the current national curriculum. The results showed that the degree they understand the reasons why the sign rules hold was low Third, we instructed the middle school students about the negative number and its operations using the formal approach as Freudenthal suggest ed. And we investigated whether students understand the formal approach or not. And we analysed the validity of the new teaching method of the negative numbers. The results showed that students didn't understand the formal approach well. And finally we discussed the directions for improving the instruction of the negative numbers on the ground of these didactical phenomenological analysis.

• East Asian mathematical journal
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• v.24 no.5
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• pp.527-545
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• 2008

One of the education purpose of the section "Figures" in the eighth grade is to develop students' deductive reasoning ability, which is basic and essential for living in a democratic society. However, most or middle school students feel much more difficulty or even frustration in the study of formal arguments for geometric situations than any other mathematical fields. It is owing to the big gap between inductive reasoning in elementary school education and deductive reasoning, which is not intuitive, in middle school education. Also, it is very burden for students to describe geometric statements exactly by using various appropriate symbols. Moreover, Usage of the same symbols for angle and angle measurement or segments and segments measurement makes students more confused. Since geometric relations is mainly determined by the measurements of geometric objects, students should be able to interpret the geometric properties to the algebraic properties, and vice verse. In this paper, we first compare and contrast inductive and deductive reasoning approaches to justify geometric facts and relations in school curricula. Convincing arguments are based on experiment and experience, then are developed from inductive reasoning to deductive proofs. We introduce teaching methods to help students's understanding for deductive reasoning in the textbook by using stepwise visualization materials. It is desirable that an effective proof instruction should be able to provide teaching methods and visual materials suitable for students' intellectual level and their own intuition.

• Journal of Educational Research in Mathematics
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• v.8 no.2
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• pp.527-540
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• 1998

In the teacher's guide of mathematics textbook for the 1st grade of the middle school, the clear and logical reason why the multiplication of negative number to negative number makes positive number, and $a^{-m}$ with a>0 and m>0, is defined by ${\frac{1}{a^m}}$ is not given. When we define the multiplication or the power by successive addition or successive multiplication of the same number, respectively, we encounter this ambiguity, in the case that the number of successive operations is negative, In this paper, we name this number, negative counting number, and we make the following more logical and intuitive definition, which is "negatively many successive operations is defined by positively many successive inverse operations." According to this new definition, we define the multiplication by the successive addition or the successive subtraction of the same number, when the multiplier is positive or negative respectively, and the power by the successive multiplication or the power is positive or negative, respectively. In addition, using this new definition and following the E.R.S Instruction strategy which revised and complemented the Bruner's E.I.S Instruction strategy, we develope new teaching model available in the 1st grade class of middle school where the concept of integers, three operations of integers are introduced.ntroduced.

• Korean Journal of Computational Design and Engineering
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• v.15 no.3
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• pp.234-242
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• 2010

3D CAD technology has been extended to a medical area including dental clinic beyond industrial design. The 2D images obtained by CT(Computerized Tomography) and MRI(Magnetic Resonance Imaging) are not intuitive, and thus the volume rendering technique, which transforms 2D data into 3D anatomic information, has been in practical use. This paper has focused on a method and its implementation for forming 3D geometric surface model from laminated CT images of the pubis. The implemented system could support a dental clinic to observe and examine the status of a patient's pubis before implant surgery. The supplement of 3D implant model would help dental surgeons settle operation plans more safely and confidently. It also would be utilized with teaching materials for a practice and training.

• The Mathematical Education
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• v.49 no.1
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• pp.53-65
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• 2010

The congruent conditions of triangles' plays an important role to connect intuitive geometry with deductive geometry in school mathematics. It is induced by 'three determining conditions of triangles' which is justified by classical geometric construction. In this paper, we analyze the essential meaning and geometric position of 'congruent conditions of triangles in Euclidean Geometry and investigate introducing processes for them in the Elements of Euclid, Hilbert congruent axioms, Russian textbook and Korean textbook, respectively. Also, we give justifications of construction methods for triangle having three segments with fixed lengths and angle equivalent to given angle suggested in Korean textbooks, are discussed, which can be directly applicable to teaching geometric construction meaningfully.

• Journal of the Korean Data and Information Science Society
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• v.18 no.4
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• pp.859-868
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• 2007

The present paper deals with the ordering problem for how to teach mathematical concepts successfully. Main object is the concept of continuous functions which is fundamental in analysis and topology. At first, the theoretical organization of this concept is investigated through several texts in related field, calculus, analysis and topology. And next, the historical order for this concept from the viewpoint of problem-solving is considered. Based on these two materials, we suggest a lecturing organization order in order to establish a balanced unification of three concepts - intuitive, logical and formal concepts.