• Journal of Educational Research in Mathematics
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• v.8 no.1
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• pp.59-71
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• 1998

Recently, most classrooms in Korea are fully equipped with multimedia environments such as a powerful pentium pc, a 43″large sized TV, and so on through the third renovation of classroom environments. However, there is not much software teachers can use directly in their teaching. Even with existing software such as GSP, and Mathematica, it turns out that it doesn####t fit well in a large number of students in classrooms and with all written in English. The study is to analyze the characteristics of problem-solving process and to develop a computer program which integrates the instruction of problem solving into a regular math program in areas of quadratic functions and ellipses. Problem Solving in this study included two sessions: 1) Learning of basic facts, concepts, and principles; 2) problem solving with problem contexts. In the former, the program was constructed based on the definitions of concepts so that students can explore, conjecture, and discover such mathematical ideas as basic facts, concepts, and principles. In the latter, the Polya#s 4 phases of problem-solving process contributed to designing of the program. In understanding of a problem, the program enhanced students#### understanding with multiple, dynamic representations of the problem using visualization. The strategies used in making a plan were collecting data, using pictures, inductive, and deductive reasoning, and creative reasoning to develop abstract thinking. In carrying out the plan, students can solve the problem according to their strategies they planned in the previous phase. In looking back, the program is very useful to provide students an opportunity to reflect problem-solving process, generalize their solution and create a new in-depth problem. This program was well matched with the dynamic and oscillation Polya#s problem-solving process. Moreover, students can facilitate their motivation to solve a problem with dynamic, multiple representations of the problem and become a powerful problem solve with confidence within an interactive computer environment. As a follow-up study, it is recommended to research the effect of the program in classrooms.

• School Mathematics
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• v.17 no.2
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• pp.273-287
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• 2015

The purpose of this study was to obtain a deeper understanding of didactic processing in the class that unified with engineering by analyzing on the types of the teacher's instumental orchestration and schematizing it as an activity system. In order to do so, a qualitative study of a 5th grade class for math-gifted students in Y elementary school with ethnography was conducted. Interviews with the students were held and various document data were collected during the participational observation of the class. The collected qualitative data were gone through the analytical induction while the instrumental orchestration of Drijvers, Boon, Doorman, Reed, & Gravemeijer as well as the secondgeneration activity theory of Engestrom were using as the frame of conceptional reference. According to the result of this study, there exist 4 types, such as 'technical demo' 'link screen board', 'detection-exploring small group' and 'explain the screen and technical demo'.

• Journal of The Korean Association of Information Education
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• v.7 no.1
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• pp.11-26
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• 2003

Although many mathematical teaching/learning materials are already developed in the web, diverse utilization of this materials such as calculation, searching, or reusing of expressions are limited since the expression is actually a figure. To cope with this, MathML which describing mathematical notation was developed. In the paper, we proposed the methods of developing teaching materials using MathML, making learning assistance tools which utilize MathML, and applying MathML to information exchange community for Mathematics courses in ICT environment. Using MathML to develop a teaching material makes easy to correct and reuse the mathematical notations conveniently. Furthermore, learning assistance tools made by placing MathML help teachers reorganize and utilize these materials in the classroom as well as enhancing the connection between mathematical notations and concepts. The web-board that can make a use the mathematical notations using MathML enables the teachers and students to exchange information actively. It also helps to fulfill different types of teaching using ICT such as "discussion on the web".

• Education of Primary School Mathematics
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• v.19 no.3
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• pp.177-191
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• 2016

Students can calculate the addition and subtraction problem using informal knowledge before receiving the formal instruction. Recently, the value that a computation lesson focus on the understanding and developing the various strategies is highlighted by curriculum developers as well as in reports. Ideally, a educational setting and classroom culture reflected students' learning and problem solving strategies. So, this paper analyzed the similarity and difference with respect to the numeric sentence and word problem in the addition and subtraction. The subjects for the study were 100 third-grade Korean students and 68 third-grade American students. Researcher developed the questionnaire in the addition and subtraction and used it for the survey. The following results have been drawn from this study. The computational ability of Korean students was higher than that of American students in both the numeric sentence and word problem. And it was revealed the differences of the strategies which were used problem solving process. Korean students tended to use algorithms and numbers' characters and relations, but American students tended to use the drawings and algorithms with drawings.

• Journal of Educational Research in Mathematics
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• v.21 no.1
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• pp.33-55
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• 2011

This study explores the characteristics of calculus students' and instructors' discourses on the derivative using a communicational approach to cognition. The data were collected from surveys, classroom observations, and interviews. The results show that the instructors did not explicitly address some aspects of the derivative such as the relationship between the derivative function (f'(x)) and the derivative at a point (f'(a)), and f'(x) as a function, and that students incorrectly described or used these aspects for problem solving. It is also found that both implicitness in the instructors' discourse, and students' incorrect descriptions were closely related to their use of the word, "derivative" without specifying it as "the derivative function" or "the derivative at a point." Comparison between instructors' and students' discourses suggests that explicit discussion about the derivative including exact use of terms will help students see the relationship that f'(a) is a number, a point-specific value of f'(x) that is a function, and overcome their mixed and incorrect notion "the derivative" such as the tangent line at a point.

• Journal of Educational Research in Mathematics
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• v.25 no.3
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• pp.323-345
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• 2015

This study examined the types of abduction appeared in the exploration activities of 'law of large numbers' in order to figure out relation between statistical reasoning and abduction. When the classroom discourse of students was analyzed by Peirce's abduction, Eco's abduction type and Toulmin's argument pattern, students used overcoded abduction the most in the discourse of abduction. However, there composed a low percent of undercoded abduction leading to various thinking, and creative abduction used to make new principles or theories. By the CAS calculators used in the process of reasoning, students were provided with empirical context to understand the concept of abstract probability, through which they actively participated in the argumentation centered on the reasoning. As a result, it was found that not only to understand the abduction, but to build statistical context with tools in the learning of statistical reasoning is important.

• School Mathematics
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• v.15 no.4
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• pp.847-866
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• 2013

The purpose of this study was to analyze students' various solution methods revealed in the lessons of finding out the area of plane figures, and to explore instructional implications on how to draw meaningful formalization out of such multiple methods. The teacher in this study tended to select a few solution methods that were easy for students to understand and to induce formalization. An analysis of students' solution methods and the process of formalization showed that students need to understand what parts of the length of the given plane figure they should know, and to identify the base, height, and diagonal line of the figure. The analysis also showed that it was effective to choose the solution methods that were used by many students and that could be easily transformed into a concise formula. Based on these results, this paper provides instructional suggestions for a teacher to orchestrate classroom discussion toward formalization based on students' multiple solution methods.

• Journal of Korea Game Society
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• v.6 no.3
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• pp.33-42
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• 2006

This study is aimed to develop adventure-game style learning program for offering different levels curriculum in mathematics and figure areas in elementary schools. The 7th mathematics curriculum introduced different levels curriculum considering learners' ability, aptitude, requirement, interest so that it could improve learners' growth potential and educational efficiency. But in reality, it is quite difficult to increase educational efficiency by conducting individual learning classes according to students' ability due to the big differences among students' levels in addition to high population in each classroom. The purpose of this study is to offer different levels curriculum based on van Hiele theory and develop adventure-game style learning program to increase interests of the learners. This program can improve students' academic achievement by offering differentiated curriculums to learners who need advanced or supplementary learning materials. And it also enhances leaners' spatial-perceptual ability by offering various operating activities in figures learning.

• Journal of the Korean School Mathematics Society
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• v.16 no.2
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• pp.319-335
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• 2013

Chinese mathematical curriculum is divided 4 areas(number and algebra, space and figure, statistics and probability, practice and synthetic application). The purpose of this paper is to analyze the contents of the practice and synthetic application in yanbian elementary textbook. For this, 12-textbook which was published in yeonbeon a publishing company is analyze by topic, mathematical process, area of content and mathematical activity. mathematical process The following results have been drawn from this study. First, contextual backgrounds of practice are restricted in classroom. The contents of synthetic application are limited in connection of mathematical areas. Mathematical problem solving is a main in mathematical process, whereas reasoning activity is a few. Mathematical experience activity is a main in mathematical process, whereas synthetic activity is a few. We can use the suggestions of this paper for development of textbook and the contents of mathematical process.

• School Mathematics
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• v.10 no.2
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• pp.139-154
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• 2008

The primary purpose of this study was to investigate how sixth grade elementary school students react to the types of letters use, what levels of understanding letters students are in and what difficulties are in understanding letters, and to raise issues about instructional methods of algebra. A descriptive study through pencil-and- paper tests was conducted. The test instruments consisted of 18 questions with 6 types of letters use. According to the results of testing, students' types of letter use and the levels of understanding letters were classified. The conclusions from the results of this study were as follows: First, the higher the types of letters use, the more sixth grade elementary school students had low scores on the types. Therefore, teaching methodologies of letters and expressions in the classroom need to encourage for students to improve their ability of using and understanding letter. Second, approximately 40% of students were categorized in level 3. Accordingly it is necessary to have a program of teaching and learning to improve their understanding levels of letters. Third, approximately 15% of students were categorized in level 0. In order to develop understanding of letters, it is important that students use letter evaluated and letter used as an object. Fourth, students had the difficulties in understanding letters. It is informative for teachers to understand these students' difficulties and thinking processes. Finally, we must treat the different uses of letters and introduce them successively according to the student's understanding levels of letters.