• Title/Summary/Keyword: example spaces

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An Analysis of Example Spaces Constructed by Students in Learning the Area of a Trapezoid based on Dienes' Theory of Learning Mathematics (Dienes의 수학학습이론에 따른 사다리꼴의 넓이 학습에서 학생들이 구성한 예 공간 분석)

  • Oh, Min Young;Kim, Nam Gyun
    • Education of Primary School Mathematics
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    • v.24 no.4
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    • pp.247-264
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    • 2021
  • The area of a trapezoid is an important concept to develop mathematical thinking and competency, but many students tend to understand the formula for the area of a trapezoid instrumentally. A clue to solving these problems could be found in Dienes' theory of learning mathematics and Watson and Mason' concept of example spaces. The purpose of this study is to obtain implications for the teaching and learning of the area of the trapezoid. This study analyzed the example spaces constructed by students in learning the area of a trapezoid based on Dienes' theory of learning mathematics. As a result of the analysis, the example spaces for each stage of math learning constructed by the students were a trapezoidal variation example spaces in the play stage, a common representation example spaces in the comparison-representation stage, and a trapezoidal area formula example spaces in the symbolization-formalization stage. The type, generation, extent, and relevance of examples constituting example spaces were analyzed, and the structure of the example spaces was presented as a map. This study also analyzed general examples, special examples, conventional examples of example spaces, and discussed how to utilize examples and example spaces in teaching and learning the area of a trapezoid. Through this study, it was found that it is appropriate to apply Dienes' theory of learning mathematics to learning the are of a trapezoid, and this study can be a model for learning the area of the trapezoid.

An Analysis on the Example Spaces of the Concepts of Triangles in the Korean Elementary Mathematics Textbooks (초등 수학교과서의 삼각형의 개념에 대한 예 공간의 분석)

  • Park, Man-Goo
    • Journal of the Korean School Mathematics Society
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    • v.13 no.1
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    • pp.143-161
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    • 2010
  • The purpose of this paper was to analyze the example spaces related with the concepts of triangles in the 2nd grade Korean elementary mathematics textbooks, investigate the meaning of example spaces, and suggest the implications to teaching and learning geometrical concepts in the elementary schools. Mathematics textbooks are usually major materials in teaching and learning mathematics in Korea, and the content of the textbooks affects the quality of teaching and learning in the classroom. The results of the study showed that the Korean elementary textbooks provided examples with limited example spaces concerning the concepts of triangles. The researcher suggested that we should provide rich examples spaces, encourage learner-generated example spaces, and strengthen the connections of examples between in textbooks and in the classroom.

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A Study on the Expression by Anamorphose Phenomenon (아나모르포즈(anamorphose)지각현상에 의한 공간 표현 연구)

  • Lee, Jeong-Yoon;Kim, Kai-Chun
    • Korean Institute of Interior Design Journal
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    • v.23 no.4
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    • pp.63-71
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    • 2014
  • Anamorphosis is highly favored in modern days as the atmosphere of pursuing unusual manners is growing while transformation and distortion of images are freely available. This research is to understand the affect of these distorted images on space designs and the close connection between anamorphosis and visual perceptions, and to identify the new perceptual phenomenon created through it, and the methods of expressing those. Four expressional methods were defined through the process of studying Anamorphosis based on its definition by Niceron, examining artworks such as paintings and photographs, and case-studying example spaces of visual perception experiments. Expressing anamorphosis through visual perceptions are broadly categorized to directional, dimensional, flatness, and optical. The analysis of 10 case projects suggests that the experimental spaces offer joys of finding and interpreting metaphorical forms and meanings caused by the four characteristic categories above. Also, they artificially show the boundaries between reality and virtual spaces in 2-dimensional or 3-dimensional spaces, and form hyper-boundaries, new experience, and an internal mechanism that is vague and chaotic. Therefore, this research concludes that anamorphosis which is a distorted perspective, is not only a simple measure to overcome perspectival errors, but is an existence suitable to the current era, that will extend its potential and value in spatial design.