• Journal for History of Mathematics
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• v.20 no.2
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• pp.109-126
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• 2007

This paper is to study theorems related with congruence of triangles in Lobachevskii's and Hadamard's geometry textbooks, and to compare their proof methods. We find out that Lobachevskii's geometry textbook contains 5 theorems of triangles' congruence, but doesn't explain congruence of right triangles. In Hadamard's geometry textbook description system of the theorems of triangles' congruence is similar with our mathematics textbook. Hadamard's geometry textbook treat 3 theorems of triangles' congruence, and 2 theorems of right triangles' congruence. But in Hadamard's geometry textbook all theorems are proved.

• Communications of Mathematical Education
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• v.27 no.3
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• pp.179-203
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• 2013

The purpose of this study was to discuss the example that developed geometry model textbook based on storytelling using real-life context. To achieve this purpose, we first elaborated the meaning of the textbook based on storytelling with real-life context, and then we discussed the outline of the story and the summary of each lesson. This study defined the storytelling textbook with real-life context as the textbook consisting of activities that explored and organized mathematical concepts by using real-life situations as materials of stories. The geometry textbook we developed employed two real-life materials, a map and a set square: we used a map for the coordinate geometry and a set square for the equation of a line. To attract students' interest, we introduced confrontation between a teacher and two students and a villain. We implemented experimentation with the textbook based on storytelling in order to verify its validity. The participants were 25 students that were enrolled in a high school in Seoul. Among them, 17 participants were surveyed. Students' answers from the survey questionnaire suggested that the geometry textbook we developed based on storytelling helped them learn mathematics and that the instruments such as a map and a set square helped them understand mathematical concepts. However, their opinion implied that the story of the textbook needed to be improved so that the story reflected more realistic contexts that were familiar with students.

• 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.

• School Mathematics
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• v.9 no.2
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• pp.197-222
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• 2007

The study aims to reflect the elementary school geometry education based on the Realistic Mathematics Education in the Netherlands in the light of the results from recent researches in geometry education and the direction of geometry standards for school mathematics of the National Council of Teachers of Mathematics in order to induce implications for improving korean geometry curriculum and textbook series. In order to attain these purposes, the present paper reflects the history of elementary school geometry education in the Netherlands, sketches the elementary school geometry education based on the Realistic Mathematics Education in the Netherlands by reflecting general goals of the mathematics education, the core goals for geometry strand of the Netherlands, and geometry and spatial orientation strand of Dutch Pluspunt textbook series for the elementary school more concretely. Under these reflections on the documents, it is analyzed what is the characteristics of geometry strand in the Netherlands as follows: emphasis on realistic spatial phenomenon, intuitive and informal approach, progressive approach from intuitive activity to spatial reasoning, intertwinement of mathematics strands and other disciplines, emphasis on interaction of the students, cyclical repetition of experiencing phase, explaining phases, and connecting phase. Finally, discussing points for improving our elementary school geometry curriculum and textbook series development are described as follows: introducing spatial orientation and emphasizing spatial visualization and spatial reasoning with respect to the instruction contents, considering balancing between approach stressing on grasping space and approach stressing on logical structure of geometry, intuitive approach, and integrating mathematics strands and other disciplines with respect to the instruction method.

• Journal of the Korean School Mathematics Society
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• v.25 no.1
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• pp.61-77
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• 2022

This study looked at the deviation of each textbook, focusing on the detailed learning content related to the quadratic curve properties contained in high school geometry textbooks. Rather than criticizing the diversity of content elements covered in high school geometry textbooks and suggesting alternatives, it focused on analyzing the actual conditions of content element diversity. The curriculum specifies that the practical application of the quadratic curve should be emphasized so that student could recognize the usefulness and value. However, as a result of the analysis, it was confirmed that the purpose of the curriculum and the structure of the textbook did not match somewhat, the deviation of content elements for each textbook was quite large. In terms of acknowledging the diversity of teaching and learning, the diversity of each textbook on the methods of the introduction and the natures related to the quadratic curve can be fully recognized. But in our educational reality, which is aiming for the university entrance examination system through national evaluation such as CSAT, the results are too sensitive in society as a whole, so the diversity of expressions in mathematics textbooks is sometimes interpreted as a disadvantage of evaluation. It is time to reconsider the composition of textbooks that recognizes the diversity of content elements in textbook teaching and learning and at the same time reflects the aspect of equality in evaluation.

• Journal of the Korean School Mathematics Society
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• v.14 no.3
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• pp.325-337
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• 2011

There have been several studies regarding strict and formal proof in the field of geometry in middle school curriculum, and the level of proof has been gradually lowered along with the changes in the curriculum. In the 2011 Revised Middle School Math Curriculum, there have been efforts to eliminate the term 'proof' and instead to replace it with the new one, 'justification'. Therefore, this study intends to present specific and practical examples of justification by analyzing the current math textbook especially in the field of geometry. As a result, it identified that strict and practical proof has been sharply increased in the second year of middle school. It also witnessed the possibility of justification from the various examples presented in the first, second, and the third year of the middle school math textbook.

• Journal of the Korean School Mathematics Society
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• v.7 no.1
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• pp.37-48
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• 2004

In this article we study on a mathematics(geometry) textbook which is written for the purpose of considering student's individual difference by famous russian author V. A. Gusev. We analyze text and exercise of the experimental textbook, form and extract some didactical ideas that help us to design individualized mathematics classroom activities with students.

• Journal of the Korean School Mathematics Society
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• v.24 no.1
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• pp.39-57
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• 2021

In this study, mathematical analysis is conducted by focusing to the 'size' of the 'point' and the 'line'. The textbook descriptions of the 'point' and the 'line' in the geometry content area of middle school mathematics 1 by the 2015 revised Korean mathematics curriculum and US geometry textbooks were compared and analyzed between. First, as a result of mathematical analysis of' 'the size of a point and a segment', it was found that the mathematical perspectives could be different according to 1) the size of a point is based on the recognition and exclusion of 'infinitesimal', and 2) the size of the segment is based on the 'measure theory' and 'set theory'. Second, as a result of analyzing textbook descriptions of the 'point' and the 'line', 1) in the geometry content area of middle school mathematics 1 by the 2015 revised Korean mathematics curriculum, after presenting a learning activity that draws a point with 'physical size' or line, it was developed in a way that describes the 'relationship' between points and lines, but 2) most of the US geometry textbooks introduce points and lines as 'undefined terms' and explicitly states that 'points have no size' and 'lines have no thickness'. Since the description of points and lines in the geometry content area of middle school mathematics 1 by the 2015 revised Korean mathematics curriculum may potentially generate mathematical intuitions that do not correspond to the perspective of Euclid geometry, this study suggest that attention is needed in the learning process about points and lines.

• Research in Mathematical Education
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• v.27 no.2
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• pp.195-210
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• 2024

Researchers and curricula continue to call for proof to serve a central role in learning of mathematics throughout kindergarten to grade 12 and beyond. Despite its prominence and recognition gained during past decades, proof is still a stumbling block for both teachers and students. Research efforts have been made to address issues related to teaching and learning of proof. An area in which such research efforts have been made is analysis of curriculum material (i.e. textbook analysis) with a focus on proof. This study is another research effort in this area of research through investigating the guidance offered in curriculum materials with the following research question: What is the nature (e.g., kinds of content knowledge, pedagogical content knowledge) of guidance is offered for teachers to implement proof tasks in grade 8 geometry textbooks? Results indicate that the guidance offered for proof tasks are concerned more with content knowledge about the content-specific instructional goals than with pedagogical content knowledge which supports teachers in preparing in-class interactions with students to teach proof.

• East Asian mathematical journal
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• v.28 no.2
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• pp.109-133
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• 2012

In this research, I selected a Singapore elementary mathematics textbook which substantially reflects Singapore curriculum, and compared it with Korean one to understand how they differ in the contents system of the curriculum focused on the contents of the geometry and measurement strand, and analyzed their common points and different points intensively with textbooks for sixth-grade students. Also, I translated a chapter of the textbook, 'Mathematics in Action'. That chapter was about circumference and the area of the circle which is related to the shapes part. Then, I taught it to the experimental group to compare their achievement and the change of reaction to studying the shape-related parts with those of the control group. The results are the followings. First, when we analyze the contents of shape-related part of the textbooks for sixth-grade students of both countries, Singaporean textbook contains more contents that are introduced for the first time, which implies that it is more desirable to teach new concepts of shapes when students are in their higher grades. Second, as for the way they develop the activity of each chapter, Korean textbook sticks to a uniform way, while the Singapore textbook uses various ways for different subjects and grades. In addition, when they organize the contents of the textbook, they emphasize the importance of student's activity and lead students with various methods by suggesting several questions and situations.