• Title/Summary/Keyword: Geometric figures

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A Study on the Effectiveness of Dynamic Geometry Software in Solving High School Analytic Geometry Problems. (탐구형 소프트웨어를 활용한 고등학교 해석 기하 교육에 관한 사례 연구)

  • 황우형;차순규
    • The Mathematical Education
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    • v.41 no.3
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    • pp.341-360
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    • 2002
  • The purpose of the study was to investigate the effectiveness of dynamic software in solving high school analytic geometry problems compared with traditional algebraic approach. Three high school students who have revealed high performance in mathematics were involved in this study. It was considered that they mastered the basic concepts of equations of plane figure and curves of secondary degree. The research questions for the study were the followings: 1) In what degree students understand relationship between geometric approach and algebraic approach in solving geometry problems? 2) What are the difficulties students encounter in the process of using the dynamic software? 3) In what degree the constructions of geometric figures help students to understand the mathematical concepts? 4) What are the effects of dynamic software in constructing analytic geometry concepts? 5) In what degree students have developed the images of algebraic concepts? According to the results of the study, it was revealed that mathematical connections between geometric approach and algebraic approach was complementary. And the students revealed more rely on the algebraic expression over geometric figures in the process of solving geometry problems. The conceptual images of algebraic expression were not developed fully, and they blamed it upon the current college entrance examination system.

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An Analysis of Students' Communication in Lessons for the Geometric Similarity Using AlgeoMath (알지오매스를 활용한 도형의 닮음 수업에서 학생들의 의사소통 분석)

  • Kim, Yeonha;Shin, Bomi
    • Journal of the Korean School Mathematics Society
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    • v.26 no.2
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    • pp.111-135
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    • 2023
  • This study conducted a student-centered inquiry lesson on the similarity of figures using AlgeoMath, with student learning aspects analyzed from a communication perspective. This approach aimed to inform pedagogical implications related to teaching geometric similarity. Through utilizing AlgeoMath, students were able to visually confirm that their chosen figures were similar, experiencing key mathematical concepts such as the ratio of similarity to the area of similar figures, and congruency and similarity conditions of triangles. In the lessons applying this concept, we categorized the features of similarity learning displayed by students, as seen in the communication aspects of their exploratory activities, into 'Understanding similarity ratios', 'Grasping conditions of similarity in triangles', and 'Comparing concepts of congruency and similarity'. Through exploratory activities based on AlgeoMath, students discussed the meaning and mathematical relationships of key concepts related to similarity, such as the ratio of similarity to the area of figures, and the meaning and conditions of congruence and similarity in triangles. By improving misconceptions about the similarity of figures, they were able to develop deeper mathematical understanding. This study revealed that in teaching and learning the geometric similarity using AlgeoMath, obtaining meaningful pedagogical outcome was not solely due to the features of the AlgeoMath environment, but also largely depended on the teacher's guidance and intervention that stimulated students' thinking.

A Study on the Proof Education in the Middle School Geometry - Focused on the Theory of van Hiele and Freudenthal - (중학교 기하의 증명 지도에 관한 소고 - van Hiele와 Freudenthal의 이론을 중심으로 -)

  • 나귀수
    • Journal of Educational Research in Mathematics
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    • v.8 no.1
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    • pp.291-298
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    • 1998
  • This study deals with the problem of proof education in the middle school geometry bby examining van Hiele#s geometric thought level theory and Freudenthal#s mathematization teaching theory. The implications that have been revealed by examining the theory of van Hie이 and Freudenthal are as follows. First of all, the proof education at present that follows the order of #definition-theorem-proof#should be reconsidered. This order of proof-teaching may have the danger that fix the proof education poorly and formally by imposing the ready-made mathematics as the mere record of proof on students rather than suggesting the proof as the real thought activity. Hence we should encourage students in reinventing #proving#as the means of organization and mathematization. Second, proof-learning can not start by introducing the term of proof only. We should recognize proof-learning as a gradual process which forms with understanding the meaning of proof on the basic of the various activities, such as observation of geometric figures, analysis of the properties of geometric figures and construction of the relationship among those properties. Moreover students should be given this natural ground of proof.

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The Effects of Using the Geometric Manipulative for the Development of Spatial Sense (기하 교구의 활용이 공간 지각 능력에 미치는 영향)

  • Park, Man-Goo;ChoiKoh, Sang-Sook;Jung, In-Chul;Kim, Eun-Young
    • Journal of the Korean School Mathematics Society
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    • v.13 no.2
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    • pp.303-322
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    • 2010
  • The purpose of this study was to analyze the effects of using the geometric manipulative for the development of spatial sense and thus to find out a better mathematics teaching and learning method that could help develop students' spatial senses. The two fifth grade classes were randomly chosen as an experimental group (31 students) and a control group (32 students), respectively. This study implemented nonequivalent control group pretest-posttest design of quasi-experimental design. The test instrument used in this study was a spatial sense test. The pretest and posttest were implemented with the same instrument. In addition, their classes were observed and videotaped, and the data and their study activities were analyzed. In conclusion, first, the geometric manipulative-aided activities contributes to developing students' spatial senses and their two sub-factors involves perceptual consistency and perception of spatial relationship. Second, the activities of grasping the components of solid figures, sketches and development figures by using the geometric manipulative contribute to boost students' perceptual consistencies and their perceptions of spatial relationship.

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초등수학 기하문제해결에서의 시각화 과정 분석

  • Yun, Yea-Joo;Kim, Sung-Joon
    • East Asian mathematical journal
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    • v.26 no.4
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    • pp.553-579
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    • 2010
  • Geometric education emphasize reasoning ability and spatial sense through development of logical thinking and intuitions in space. Researches about space understanding go along with investigations of space perception ability which is composed of space relationship, space visualization, space direction etc. Especially space visualization is one of the factors which try conclusion with geometric problem solving. But studies about space visualization are limited to middle school geometric education, studies in elementary level haven't been done until now. Namely, discussions about elementary students' space visualization process and ability in plane or space figures is deficient in relation to geometric problem solving. This paper examines these aspects, especially in relation to plane and space problem solving in elementary levels. Firstly we propose the analysis frame to investigate a visualization process for plane problem solving and a visualization ability for space problem solving. Nextly we select 13 elementary students, and observe closely how a visualization process is progress and how a visualization ability is played role in geometric problem solving. Together with these analyses, we propose concrete examples of visualization ability which make a road to geometric problem solving. Through these analysis, this paper aims at deriving various discussions about visualization in geometric problem solving of the elementary mathematics.

A Simple Geometric Approach to Evaluating a Bivariate Normal Orthant Probability

  • Lee, Kee-Won;Kim, Yoon-Tae;Kim, U-Jung
    • Communications for Statistical Applications and Methods
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    • v.6 no.2
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    • pp.595-600
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    • 1999
  • We present a simple geometric approach which uses polar transformation and elementary trigonometry to evaluating an orthant probability in a bivariate normal distribution. Figures are provided to illustrate the situation for varying correlation coefficient. We derive the distribution of the sample correlation coefficient from a bivariate normal distribution when the sample size is 2 as an application.

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A experimental model of combining exploratory learning and geometry problem solving with GSP (기하문제해결에서의 GSP를 활용한 탐구학습 신장)

  • Jun, Young-Cook;Joo, Mi
    • Journal of Educational Research in Mathematics
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    • v.8 no.2
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    • pp.605-620
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    • 1998
  • This paper suggested a geometry learning model which relates an exploratory learning model with GSP applications, Such a model adopts GSP's capability of visualizing dynamic geometric figures and exploratory learning method's advantages of discovering properties and relations of geometric problem proving and concepts associated with geometric inferencing of students. The research was conducted for 3 middle school students by applying the proposed model for 6times at computer laboratory. The overall procedure was videotaped so that the collected data was later analyzed by qualitative methodology. The analysis indicated that the students with less than van Hiele 4 level took advantages of adoption our proposed model to gain concrete understandings of geometric principles and concepts with GSP. One of the lessons learned from this study suggested that the roles of students and a teacher who want to employ the proposed model need to change their roles respectively.

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시각화를 이용한 증명교육

  • Kang, Mee-Kwang;Kim, Myung-Jee
    • 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.

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Development of 3D Modeling System to Display the Cutting Shape of H-Beam Used in Ships and Ocean Plants (선박 및 해양 플랜트용 H-빔 절단을 위한 3차원 형상 모델링 구현 시스템 개발)

  • Park, Ju-Yong;Jo, Hyo-Jae;Lee, Ji-Hoon;Park, Ji-Yong
    • Journal of Ocean Engineering and Technology
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    • v.25 no.3
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    • pp.47-52
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    • 2011
  • 3D geometric modeling has a lot of advantages in the field of design and manufacturing. Many manufacturing processes and production lines are using 3D geometric modeling technique. These help reduce the cost and time for manufacturing. The purpose of this study is the realization of a 3D cutting shape for an H-Beam used in ships and ocean plants. The complex 3D cutting shapes could be represented by using the boolean operation of basic figures. Graphic functions with parameters were used to simply define the basic figures. The developed system can show the complex cutting shape of an H-beam simply and quickly. This system can be utilized for the automatic cutting system for an H-beam.

The influence of Mandala coloring activity for early childhood mathematics capacity (만다라 색칠활동이 유아의 수학적 능력에 미치는 영향)

  • Kye, Young Hee
    • Communications of Mathematical Education
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    • v.29 no.4
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    • pp.687-698
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    • 2015
  • This research is based on Jungian psychology. The founder psychoanalysist Jung introduced the notion of unconsciousness. This researcher made Mandala figures as an intermediary between consciousness and unconsciousness, and then took Mandala figures a research starting point. Until now, Mandala has been used therapy tool for emotional stability. But, this researcher tried Mandala coloring to develope cognitive and emotional abilities for early childhood. This paper is a result of experiment to recognize geometric and spacial conceptions for early childhood.