• Title/Summary/Keyword: Geometry proof

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Effectiveness of mathematics education through the process-oriented evaluation - Focusing on Geometry and vector subjects - (과정 중심 평가를 통한 수학교과 인성 함양 효과 - 기하와 벡터 과목을 중심으로 -)

  • Kim, Hyunjoo
    • Journal of the Korean School Mathematics Society
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    • v.22 no.4
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    • pp.369-393
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    • 2019
  • The purpose of this study is to find the commonality between process-focused assessment and existing performance evaluation and to find out whether the process-focused assessment is effective for the development of the character of school mathematics. By analyzing the previous research, this study defined the meaning of process-focused assessment as an evaluation that can improve students' growth and quality of class through immediate feedback by introducing various performance tasks and evaluation methods. The character of school mathematics refers to personality factors that are easily expressed and cultivated during math classes. Therefore, this study presented examples of the feasibility of process-focused assessment focusing on geometry and vector subjects and examined the effectiveness of mathematics and character development through process-based evaluation. Four course-based assessments (math experiments, logic, proof, and communication) aimed at cultivating the character of school mathematics were conducted from March to June 2019 for the third year of high school. The index was measured. Analysis of the results using the corresponding variable t-test showed that the process-based evaluation in this study had a significant effect on the character of school mathematics development.

Rapid Repair of Severely Damaged RC Columns with Different Damage Conditions: An Experimental Study

  • He, Ruili;Sneed, Lesley H.;Belarbi, Abdeldjelil
    • International Journal of Concrete Structures and Materials
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    • v.7 no.1
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    • pp.35-50
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    • 2013
  • Rapid and effective repair methods are desired to enable quick reopening of damaged bridges after an earthquake occurs, especially for those bridges that are critical for emergency response and other essential functions. This paper presents results of tests conducted as a proof-of-concept in the effectiveness of a proposed method using externally bonded carbon fiber reinforced polymer (CFRP) composites to rapidly repair severely damaged RC columns with different damage conditions. The experimental work included five large-scale severely damaged square RC columns with the same geometry and material properties but with different damage conditions due to different loading combinations of bending, shear, and torsion in the previous tests. Over a three-day period, each column was repaired and retested under the same loading combination as the corresponding original column. Quickset repair mortar was used to replace the removed loose concrete. Without any treatment to damaged reinforcing bars, longitudinal and transverse CFRP sheets were externally bonded to the prepared surface to restore the column strength. Measured data were analyzed to investigate the performance of the repaired columns compared to the corresponding original column responses. It was concluded that the technique can be successful for severely damaged columns with damage to the concrete and transverse reinforcement. For severely damaged columns with damaged longitudinal reinforcement, the technique was found to be successful if the damaged longitudinal reinforcement is able to provide tensile resistance, or if the damage is located at a section where longitudinal CFRP strength can be developed.

Characteristics of Stacked Probe-Fed Sqare-Ring Microstrip Antenna (적층구조, 프로브 급전방식, 정사각형 링형태 마이크로스트립 안테나 특성에 관한 연구)

  • 이정연;이중근;김성철
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.12 no.1
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    • pp.143-152
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    • 2001
  • A method for miniaturization of microstrip patch antenna without degrading its radiation characteristics is investigated in this paper. It involves perforating the patch to form a microstrip square-ring antenna, and it's BW enhancement is investigated numerically and experimentally. A ring geometry introduces additional parameters to the antenna, and those are used to control impedances, resonance frequencies, and bandwidths. For a single square ring antenna, an increase of the size of perforation increases its input impedance, decreases the resonance frequency, and bandwidths. But it affects little on directivity of the antenna. To match the antenna to a transmission line and also enhance its bandwidth, the ring is stacked by a square patch or another square ring. Also numerically simulated results by the IE3D, and experimental data are compared for proof.

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A Mathematics Tutoring Model That Supports Interactive Learning of Problem Solving Based on Domain Principles (공식원리에 기반한 대화식 문제해결 학습을 지원하는 수학교수 모형)

  • Kook, Hyung-Joon
    • The KIPS Transactions:PartB
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    • v.8B no.5
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    • pp.429-440
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    • 2001
  • To achieve a computer tutor framework with high learning effects as well as practicality, the goal of this research has been set to developing an intelligent tutor for problem-solving in mathematics domain. The maine feature of the CyberTutor, a computer tutor developed in this research, is the facilitation of a learning environment interacting in accordance with the learners differing inferential capabilities and needs. The pedagogical information, the driving force of such an interactive learning, comprises of tutoring strategies used commonly in various domains such as phvsics and mathematics, in which the main contents of learning is the comprehension and the application of principles. These tutoring strategies are those of testing learners hypotheses test, providing hints, and generating explanations. We illustrate the feasibility and the behavior of our propose framework with a sample problem-solving learning in geometry. The proposed tutorial framework is an advancement from previous works in several aspects. Firstly, it is more practical since it supports handing of a wide range of problem types, including not only proof types but also finding-unkown tpes. Secondly, it is aimed at facilitating a personal tutor environment by adapting to learners of varying capabilities. Finally, learning effects are maximized by its tutorial dialogues which are derived from real-time problem-solving inference instead of from built-in procedures.

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A comparative study of domestic and international research trends of mathematics education through topic modeling (토픽모델링을 활용한 국내외 수학교육 연구 동향 비교 연구)

  • Shin, Dongjo
    • The Mathematical Education
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    • v.59 no.1
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    • pp.63-80
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    • 2020
  • This study analyzed 3,114 articles published in KCI journals and 1,636 articles published in SSCI journals from 2000 to 2019 in order to compare domestic and international research trends of mathematics education using a topic modeling method. Results indicated that there were 16 similar research topics in domestic and international mathematics education journals: algebra/algebraic thinking, fraction, function/representation, statistics, geometry, problem-solving, model/modeling, proof, achievement effect/difference, affective factor, preservice teacher, teaching practice, textbook/curriculum, task analysis, assessment, and theory. Also, there were 7 distinct research topics in domestic and international mathematics education journals. Topics such as affective/cognitive domain and research trends, mathematics concept, class activity, number/operation, creativity/STEAM, proportional reasoning, and college/technology were identified from the domestic journals, whereas discourse/interaction, professional development, identity/equity, child thinking, semiotics/embodied cognition, intervention effect, and design/technology were the topics identified from the international journals. The topic related to preservice teacher was the most frequently addressed topic in both domestic and international research. The topic related to in-service teachers' professional development was the second most popular topic in international research, whereas it was not identified in domestic research. Domestic research in mathematics education tended to pay attention to the topics concerned with the mathematical competency, but it focused more on problem-solving and creativity/STEAM than other mathematical competencies. Rather, international research highlighted the topic related to equity and social justice.

On bi(必, necessity) and xianzhi(先知, a priori knowledge) of Mojing (『묵경』에 있어서 '선지(先知)'와 '필(必)' 개념의 문제)

  • Chong, Chaehyun
    • (The)Study of the Eastern Classic
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    • no.35
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    • pp.275-295
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    • 2009
  • The aim of this paper is to reject Graham's interpretation of bi (必) and xianzhi (先知) of Later Mohists' Mojing ("墨經") as logical necessity and a priori knowledge respectively. Graham's interpretations of them are based on his beliefs that Mojing distinguishes lun (論), the art of description from bian (辯), the art of inference in the Mohist disciplines and that the latter art should be seen as such a rigorous proof as Euclidean geometry even though it is not a Western formal logic. His beliefs also start from his distinguishing 'knowledge of names' from 'knowledge of conjunction of names and objects' according to the objects of knowledge. In my reading, the art of description and the art of inference, however, can't be sharply distinguished each other in Mojing and bi and xianzhi should be taken as suggesting both a normative necessity and an empirical necessity. A normative necessity is derived from 'normative theory of definition' which comes form the theory of rectification of names in China. The normative theory of definition, unlike the descriptive theory of definition, defines terms normatively rather than descriptively. For example, although such a definition of father, 'father is beneficient', has the form of being descriptive, but it actually is prescriptive and therefore means 'father should be beneficient'. Through this normative theory of definition, empirical knowledge, as long as it is a knowledge, is seen as necessary and so can't be wrong. To conclude, for Mohists an empirical knowledge is always a basis of an inferential knowledge or a priori knowledge, so Mohists' a priori knowledge is not really a fundamental knowledge and its necessity therefore is nothing but both a normative necessity and an empirical necessity.