• School Mathematics
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• v.9 no.3
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• pp.353-373
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• 2007

The purpose of this study was to provide instructional suggestions by investigating the spatial sense and spatial reasoning ability of 6th grade students. The questionnaire consisted of 20 questions, 10 for spatial visualization and 10 for spatial orientation. The number of subjects for the survey was 145. The processes through which the students solved the problems were the basis for the assessment of their spatial reasoning. The result of the survey is as follows: First, students performed better in spatial visualization than in spatial orientation. With regard to spatial visualization, they were better in transformation than in rotation. With regard to spatial orientation, students performed better in orientation sense and structure cognitive ability than in situational sense. Second, the students that weren't excellent in spatial visualization tended to answer the familiar figures without using mental images. The students who lacked spatial orientation experienced difficulties finding figures observed from the sides. Third, students had high frequency rate on the cognition and use of transformation, the development and application of visualization methods and the use of analysis and synthesis. However they had a lower rate on a systematic approach and deductive reasoning. Further detailed investigation into how students use spatial reasoning, and apply it to actual teaching practice as a device for advancing their geometric thinking is necessary.

• Communications of Mathematical Education
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• v.35 no.4
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• pp.505-525
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• 2021

In this study, we investigated how multiplication by 2-digit numbers had been taught in elementary mathematics textbooks of Korea, Japan, Singapore, and USA. As a result of analysis, we found as follows. Korean textbooks do not teach the multiplication by 10 and the multiplication by power of 10, but Japanese, Singapore, and US textbooks explicitly teach related content. In the '×tens' teaching, Japanese and American textbooks teach formally the law of association of multiplication applied in the process of calculating the partial product of multiplication. The standard multiplication algorithm generally followed a standard method of recording partial product result according to the law of distribution, but the differences were confirmed in the multiplication model, the teaching method of the law of distribution, and the notation of the last digit '0'. Based upon these results, we suggested some proposals for improving the multiplication teaching.

• Journal of Elementary Mathematics Education in Korea
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• v.16 no.1
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• pp.39-61
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• 2012

Mathematical creativity is essential in school mathematics and mathematics curriculum and ensures the growth of mathematical ability. Therefore mathematics educators try to develop students' creativity via mathematics education for a long time. In special, 2011 revised mathematics curriculum emphasizes mathematical creativity. Yet, it may seem like a vague characterization of mathematical creativity. Furthermore, it is needed to develop the methods for developing the mathematical creativity. So, the goal of this paper is to search for teaching and learning models for developing the mathematical creativity. For this, I discuss about issues of mathematical creativity and extract the factors of mathematical creativity. The factors of mathematical creativity are divided into cognitive factors, affective factors and attitude factors that become the factors of development of mathematical creativity in the mathematical instruction. And I develop 8-teaching and learning models for development of mathematical creativity based on the characters of mathematics and the most recent theories of mathematics education. These models make it crucial for students to develop the mathematical creativity and create the new mathematics in the future.

• School Mathematics
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• v.10 no.1
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• pp.105-121
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• 2008

Even though the 7th national curriculum based on learner-centered instruction as fundamental spirit has been operated for 10 years or so, still the instruction style nation widely implemented in current classrooms is closer traditional style than it. It is a big challenge for a teacher who is used to a traditional one to try to fully make learner-centered instruction. The paper describes the teacher's cognizance change on it with the point of views of children's ability to construct knowledge, instructional materials, questioning techniques, and children's achievements.

• School Mathematics
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• v.16 no.4
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• pp.691-708
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• 2014

In general, the intuitive knowledge that can use in mathematics problem solving is one of the important knowledge to teachers as well as students. So, this study is aimed to analyze the elementary preservice teachers' intuitive knowledge in relation to intuitive and counter-intuitive problem solving. For this, I performed survey to use questionnaire consisting of problems that can solve in intuitive methods and cause the errors by counter-intuitive methods. 161 preservice teachers participated in this study. I got the conclusion as follows. preservice teachers' intuitive problem solving ability is very low. I special, many preservice teachers preferred algorithmic problem solving to intuitive problem solving. So, it's needed to try to improve preservice teachers' problem solving ability via ensuring both the quality and quantity of problem solving education during preservice training courses. Many preservice teachers showed errors with incomplete knowledges or intuitive judges in counter-intuitive problem solving process. For improving preservice teachers' intuitive problem solving ability, we have to develop the teacher education curriculum and materials for preservice teachers to go through intuitive mathematical problem solving. Add to this, we will strive to improve preservice teachers' interest about mathematics itself and value of mathematics.

• The Mathematical Education
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• v.60 no.1
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• pp.1-19
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• 2021

This study investigates students' conceptions of fractions from a measurement approach while providing a technological environment designed to support students' understanding of the relationships between quantities and adjustable units. 13 third-graders participated in this study and they were involved in a series of measurement tasks through task-based interviews. The tasks were devised to investigate the relationship between units and quantity through manipulations. Screencasting videos were collected including verbal explanations and manipulations. Drawing upon the theory of semiotic mediation, students' constructed concepts during interviews were coded as mathematical words and visual mediators to identify conceptual profiles using a fine-grained analysis. Two students changed their strategies to solve the tasks were selected as a representative case of the two profiles: from guessing to recursive partitioning; from using random units to making a relation to the given unit. Dragging mathematical objects plays a critical role to mediate and formulate fraction understandings such as unitizing and partitioning. In addition, static and dynamic representations influence the development of unit concepts in measurement situations. The findings will contribute to the field's understanding of how students come to understand the concept of fraction as measure and the role of technology, which result in a theory-driven, empirically-tested set of tasks that can be used to introduce fractions as an alternative way.

• Journal of the Korean School Mathematics Society
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• v.13 no.3
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• pp.381-395
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• 2010

The purpose of this paper is to examine the competence and the methods of problem solving in four operations word problems based on the informal knowledges by five-year-old children. The numbers which are contained in problems consist of the numbers bigger than 5 and smaller than 10. The subjects were 21 five-year-old children who didn't learn four operations. The interview with observation was used in this research. Researcher gave the various materials to children and permitted to use them for problem solving. And researcher read the word problems to children and children solved the problems. The results are as follows: five-year-old children have the competence of problem solving in four operations word problems. They used mental computation or counting all materials strategy in addition problem. The methods of problem solving were similar to that of addition in subtraction, multiplication and division, but the rate of success was different. Children performed poor1y in division word problems. According to this research, we know that kindergarten educators should be interested in children's informal knowledges of four operations including shapes, patterns, statistics and probability. For this, it is needed to developed the curriculum and programs for informal mathematical experiences.

• School Mathematics
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• v.18 no.1
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• pp.159-173
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• 2016

In real educational field, there are cases that concrete problematic situations are introduced after abstract concepts are taught on the contrary to process that abstract from concrete contexts. In other words, there are cases that abstract knowledge has to be concreted. Freudenthal expresses this situation to antidogmatical inversion and indicates negative opinion. However, it is open to doubt that every class situation can proceed to abstract that begins from concrete situations or concrete materials. This study has done a comparative analysis in difference of mathematical thinking between a process that builds abstract context after being abstracted from concrete materials and that concretes abstract concepts to concrete situations and attempts to examine educational implication. For this, this study analyzed the mathematical thinking in the abstract process of concrete materials by manipulating AiC analysis tools. Based on the AiC analysis tools, this study analyzed mathematical thinking in the concrete process of abstract concept by using the way this researcher came up with. This study results that these two processes have opposite learning flow each other and significant mathematical thinking can be induced from concrete process of abstract knowledge as well as abstraction of concrete materials.

• Communications of Mathematical Education
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• v.33 no.3
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• pp.295-317
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• 2019

Angle concept is widely used in all mathematics curriculums and is a basic concept in geometric domain. Since angle have a multifaceted and affect subsequent learning, it is necessary for students to understand various angle concepts. In this study, Singapore, U.K., Australia, and U.S. are selected as comparable countries to examine the angle-related contents and learning process that appear in the curriculum as a whole, and then look at the perspectives and the size aspects of angle in detail and give implications to the Korean curriculum based on them. According to the analysis, the four countries except Korea, supplement angle, complement angle, angles on a straight line, angles at a point, and finding angle were explicitly covered in the curriculum. And most countries gradually covered angle-related contents over several years, compared to Korea which intensively studied in a particular school year. In common, definition of angle was described as static, measurement of angle was described as dynamic. But in Korean curriculum, dynamic views on angles are described later and less compared to other countries, and range of angle size was narrower than in other countries'. From this comparison, this study suggest to discuss how to place and develop various contents of characteristics of angle in curriculum, address the angle using both static and dynamic perspectives, and introduce the angle size as the amount of rotation to learn the reflex angle, $180^{\circ}$, $360^{\circ}$ angle.

• Journal of Elementary Mathematics Education in Korea
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• v.23 no.1
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• pp.59-74
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• 2019

According to previous studies, it shows that the metacognitive ability that makes the positive element of the problem solver positively affects the problem-solving process of mathematics. In order to accurately grasp causality, this study investigates the specific characteristics of the meta-affect factor in the process of problem-solving. To do this, we analyzed the types and frequency of data collected from collaborative problem-solving situations composed of 4th~6th grade mathematically gifted children in small group of two. As a result, it can be seen that the type of meta-affect in the problem-solving process of mathematically gifted children is related to the correctness rate of the problem. First, regardless of the success or failure of the problem-solving, the meta-affect appeared relatively frequently in the meta-affect types in which the cognitive factors related to the context of problem-solving appeared first, and acted as the meta-functional type of the evaluation and attitude. Especially, in the case of successful problem-solving of mathematically gifted children, meta-affect showed a very active function as meta-functional type of evaluation.