• Journal for History of Mathematics
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• v.27 no.4
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• pp.271-283
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• 2014

This study takes a look at Polya's analysis on Archimedes' "The Method" from a math-historical perspective. We, based on the elaboration of Polya's analysis, investigate the analytic geometric characteristics of Archimedes' "The Method" and discuss the way of using the characteristics in education of school calculus. So this study brings up the educational need of approach of teaching the definite integral by clearly disclosing the transition from length, area, volume etc into the length as an area function under a curve. And this study suggests the approach of teaching both merit and deficiency of the indivisibles method, and the educational necessity of making students realizing that the strength of analytic geometry lies in overcoming deficiency of the indivisibles method by dealing with the relation of variation and rate of change by means of algebraic expression and graph.

• Journal for History of Mathematics
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• v.28 no.3
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• pp.151-164
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• 2015

The purpose of this paper is to develop a teaching and learning material integrated two subjects Pythagorean theorem and Fibonacci numbers. Traditionally the former subject belongs to geometry area and the latter is in algebra area. In this work we integrate these two issues and make a discovery method to generate infinitely many Pythagorean numbers by means of Fibonacci numbers. We have used this article as a teaching and learning material for a science high school and found that it is very appropriate for those students in advanced geometry and number theory courses.

• School Mathematics
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• v.1 no.1
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• pp.109-122
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• 1999

In this paper we give a description of students' obstacles in their learning of geometry, especially resulted from their confusing a physical drawing with a figure, a geometrical object which a physical drawing represents. In computer-based teaching-learning environment, we could relieve such obstacles through providing students for experiences in which they must focus on elements of a figure and relations of them. But there may be potential in computer-based environment if we offer students only visual experience for validity of geometrical gacts: students' lack of understanding for need of proof and experience of cognitive obstacles which is very important for students to reflect their thinking and activities. Thus an didactical treatment must follows, which we also give an example.

• Research in Mathematical Education
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• v.25 no.3
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• pp.227-244
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• 2022

The concrete-representational-abstract integrated (CRA-I) sequence is an explicit approach for teaching students who struggle in mathematics. This approach is beneficial because it assists students in the development of conceptual understanding. This article describes how the approach is used in general as well as its use with a specific geometry concept, area of a rectangle. The author will describe why one might choose CRA-I and the steps needed for implementation. Finally, the CRA-I steps will be shown with a lesson series related to teaching the concept of area. The article will describe lesson activities, methods, materials, and procedures.

• Research in Mathematical Education
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• v.27 no.1
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• pp.1-24
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• 2024

In this paper, the author analyzed characteristics of deep mathematics learning in problem solving and problem-posing classroom teaching. Based on a simple wrong plane geometry problem, the author describes the classroom experience how one expert Chinese mathematics teacher guides students to modify geometry problems from solution to investigation, and guides the students to learn how to pose mathematics problems in inquiry-based deep learning classroom. This also demonstrates how expert mathematics teacher can effectively guide students to teach deep learning in regular classroom.

• School Mathematics
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• v.14 no.3
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• pp.331-355
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• 2012

All the method used in teaching the ellipse was to have students draw the points which have the same sum of distances from the two points so that they can confirm the shapes of the ellipse before showing them the definition of ellipse. In this process, students would not get an opportunity to think or make the definition of ellipse for themselves. This deductive way can hinder students from having clear understanding of why such definition was made. This paper introduces a method of defining the ellipse based on the similarity between a circle and an ellipse, leading into the equation. This method is possible by introducing Analytic Geometry taught in current school mathematics and Transformation Geometry. By doing so, this paper will discuss a fundamental understanding about the ellipse and the feature of the ellipse expandable by intuition. Furthermore this paper will also show various advantages which can be given by defining the ellipse in Transformation Geometry.

• Journal of Educational Research in Mathematics
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• v.19 no.2
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• pp.185-206
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• 2009

In the study, I conducted the teaching experiment designed to instruct proof to four 7th grade students by utilizing the analysis method. As the results of this study I could identified that it is effective to teach and learn to find proof methods using the analysis. The results of the study showed that four 7th grade students succeeded in finding the proof methods by utilizing the analysis and representing the proof after 15 hours of the teaching experiment. In addition to the difficulties that students faced in learning proof utilizing the analysis were related to the search for the light conditions for triangles to be congruent, symbolic representation of the proof methods, reinterpretation of drawings given in the proof problems.

• Research in Mathematical Education
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• v.17 no.2
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• pp.99-118
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• 2013

The present study focuses on the contribution of a teaching unit to the development of spatial ability of third graders in general and from a gender point of view in particular. The research population consisted of seventy-four pupils: thirty-seven pupils in the experimental group who attended the teaching unit and thirty-seven pupils in the control group. The spatial ability of all the pupils was examined by means of common tests which checked cognitive capabilities of spatial ability. The research findings illustrate an improvement in the spatial ability of the experimental group pupils following the participation in the teaching unit. Moreover, regarding the gender aspect, the findings show that there was no significant differentiation between the spatial ability of third grade boys and the spatial ability of girls of the same age group.

• 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 for History of Mathematics
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• v.20 no.2
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• pp.73-88
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• 2007

In this paper, we study the symmetry of figures in elementary geometry. First, we investigate the historical and mathematical background of symmetry of figures and we explore the suitable teaching and learning methods for symmetry in elementary geometry. Also we study the major problem of geometry education that occurring in elementary school.