• School Mathematics
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• v.3 no.1
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• pp.1-23
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• 2001

In this paper, contents related to problem solving in 7th elementary mathematics curriculum analyzed in five aspects: problem solving stages, problem solving strategies, problems, problem posing, and assessment on problem solving abilities. From the results and processes of analysis, following conclusions are obtained: First, it is difficult to say the contents related to problem solving in 7th elementary mathematics curriculum are prepared organically. Second, it is difficult to say that contents related to problem solving in 7th elementary mathematics curriculum reflect results of recent researches.

• Korean Journal of Comparative Education
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• v.20 no.3
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• pp.75-96
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• 2010

In Korea school-based management has been introduced for upgrading the quality of education from mid 1990's. Due to the change schools began to seek educational consulting services. However, educational consultancy still lies in the rudimentary stage. Recognizing the problems, it compares educational consultancy between Korea and United Kingdom. The study utilizes diverse methods such as literature review, interviews, document analysis. It covered the issues such as history and background, consultants, clients, tasks and processes, and support system for consultancy in both countries. The major findings are as follows. First, they had similar origin and motive for educational consultancy, but differences in the government's approach. Second, educational consultants in both countries have similar backgrounds and qualifications. But there are big differences in consulting firms and agencies. Third, there are also big differences in terms of clients. Fourth, there are differences in terms of consultancy tasks, but similar in consultancy process. Fifth, there are also big differences in service fees and incentives. However, there are similar problems in terms of consultancy training program and professional association of educational consultants. Based upon the findings it could draw implications such as providing more financial resources for Korean schools to purchase consultancy services.

• School Mathematics
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• v.17 no.2
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• pp.289-308
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• 2015

This study analyzed mathematical processes elaborated in the mathematics curricula of Korea, China, Japan, and the US. Ten mathematical processes were extracted: (a) learning of concepts, principles, laws, and skills; (b) problem solving; (c) reasoning; (d) communication; (e) representation; (f) connections; (g) creativity; (h) character-building; (i) self-directed learning; and (j) positive attitude toward mathematics. This study specified the meaning of such processes and their sub-domains, noticing similarities and differences among the curricula. On the basis of the results, this study includes suggestions for the development of next mathematics curriculum in Korea.

• Journal of The Korean Association For Science Education
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• v.33 no.1
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• pp.30-45
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• 2013

In this study, we developed a model for analyzing scientists' creative thinking processes, and analyzed Archimedes' thinking process in solving the golden crown problem. As results show, scientists' complex problem solving processes could be represented as a repeating circular model, and the fusion of processes of diverse thinking required for scientists' creativity could be analyzed from the case. Also in this study, we represented the role of experiments in scientists' creative discovery, and investigated the reasons for the difference between the viewpoints of textbooks and historic facts. We found the importance of abductive reasoning and advance knowledge in creative thinking. Archimedes solved the golden crown problem creatively by crossing the scientific thought of dynamics and the daily thought of baths. In this process, abductive reasoning and advance knowledge played an important role. Besides Archimedes' case, if we would reconstruct the creative discovery processes of diverse scientists' in textbooks, students could raise their creative thinking ability by experiencing these processes as educational steps.

• School Mathematics
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• v.17 no.1
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• pp.1-18
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• 2015

The mathematical processes are strongly emphasized in 2009 revised national curriculum for mathematics and are expected to be complemented and extended in 2015 revised one. This study aims to investigate how much the processes are being implemented in mathematics classroom and select some elements which need complementation. To do this, we selected the mathematical practices of CCSSM as a reference, because it plays the corresponding role in the United States to the mathematical processes in Korea. We recognized common elements and different elements between the two and analyzed. Considering those, we searched the possibility of newer mathematical process and analyzed the 4th grade mathematics textbooks in relation to questions for mathematical practices. We provided the results of analyses and several suggestions for revising mathematics curriculum and textbooks.

• School Mathematics
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• v.7 no.1
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• pp.55-75
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• 2005

Mathematical symbolizing is an important part of mathematics learning. But many students have difficulties m symbolizing mathematical ideas formally. If students had experiences inventing their own mathematical symbols and developing them to conventional ones natural way, i.e. learning mathematical symbols via expressive approaches, they could understand and use formal mathematical symbols meaningfully. These experiences are especially valuable for students who meet mathematical symbols for the first time. Hence, there are needs to investigate how early elementary school students can and should experience meaningful mathematical symbolizing. The purpose of this study was to analyze students' mathematical symbolizing processes and characteristics of theses. We carried out teaching experiments that promoted meaningful mathematical symbolizing among eight first graders. And then we analyzed students' symbolizing processes and characteristics of expressive approaches to mathematical symbols in early elementary students. As a result, we could places mathematical symbolizing processes developed in the teaching experiments under five categories. And we extracted and discussed several characteristics of early elementary students' meaningful mathematical symbolizing processes.

• Journal of Gifted/Talented Education
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• v.19 no.2
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• pp.353-380
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• 2009

The significant reason for studying computer science lies in the efficient resolution of various problems which can arise in actual life. Consequently, algorithm education is very important in the computer science and plays a great part in helping to enhance the creative ability to solve problems and to improve the programming ability. However, the current algorithm education at an computer science educational institute for the gifted has inadequate systematic quality and is only treated as a part of programming education. From this perspective, this paper carried out following studies in order to design the algorithm education for elementary computer science prodigies. First, the core educational contents was selected by extracting the common elements from existing books related to algorithm education, common study contents on algorithm lesson websites and the study area of ACM's computer algorithm. Second, using the development criteria and selected educational contents, the educational theme for the If weeks load was set. Additionally, the algorithm educational contents were designed for the elementary computer science prodigy based on such theme. Third, the activity site for the use of prodigy educational institute was developed with the background in the educational contents for the elementary computer science prodigy. Fourth, the Delphi analysis technique was used to verify the appropriateness of contents and activity site developed in this paper. It was carried out in 2 separate processes where the first process verified the design of educational contents, and the second process verified the appropriateness of developed activity site.

• Journal of Educational Research in Mathematics
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• v.23 no.2
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• pp.153-171
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• 2013

The purpose of this study is to investigate characteristics of students' problem solving processes based on their mathematical thinking styles and thus to provide implications for teachers regarding how to employ multiple representations. In order to analyze these characteristics, 202 university freshmen were recruited for a paper-and-pencil survey. The participants were divided into four groups on a mathematical-thinking-style basis. There were two students in each group with a total of eight students being interviewed. Results show that mathematical thinking styles are related to defining a mathematical concept, problem solving in relation to representation, and translating between mathematical representations. These results imply methods of utilizing multiple representations in learning and teaching mathematics by embodying Dienes' perceptual variability principle.

• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.391-410
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• 2017

This study aims to analyze mathematically gifted students' characteristics of generalization and justification for a given mathematical task and induce didactical implications for individual teaching methods by students' learning styles. To do this, we identified the learning styles of three mathematically gifted 6th graders and observed their processes in solving a given problem. Paper-pencil environment as well as dynamic geometrical environment using Geogebra were provided for three students respectively. We collected and analyzed qualitatively the research data such as the students' activity sheets, the students' records in Geogebra, our observation reports about the processes of generalization and justification, and the records of interview. The results of analysis show that the types of the students' generalization are various while the level of their justifications is identical. Futhermore, their preference of learning environment is also distinguished. Based on the results of analysis, we induced some implications for individual teaching for mathematically gifted students by learning styles.

• Journal of Educational Research in Mathematics
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• v.11 no.1
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• pp.11-35
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• 2001

Many teachers report familiarity with and adherence to reform ideas, but their actual teaching practices do not reflect a deep understanding of reform. Given the challenges in implementing reform, this study intended to explore the breakdown that may occur between teachers' adoption of reform objectives and their successful incorporation of reform ideals. To this end, this study compared and contrasted the classroom social norms and sociomathematical norms of two United States second-grade teachers who aspired to implement reform. This study is an exploratory, qualitative, comparative case study. This study uses the grounded theory methodology based on the constant comparative analysis for which the primary data sources were classroom video recordings and transcripts. The two classrooms established similar social norms including an open and permissive learning environment, stressing group cooperation, employing enjoyable activity formats for students, and orchestrating individual or small group session followed by whole group discussion. Despite these similar social participation structures, the two classes were remarkably different in terms of sociomathematical norms. In one class, the students were involved in mathematical processes by which being accurate or automatic was evaluated as a more important contribution to the classroom community than being insightful or creative. In the other class, the students were continually engaged in significant mathematical processes by which they could develop an appreciation of characteristically mathematical ways of thinking, communi-eating, arguing, proving, and valuing. It was apparent from this study that sociomathematical norms are an important construct reflecting the quality of students' mathematical engagement and anticipating their conceptual learning opportunities. A re-theorization of sociomathematical norms was offered so as to highlight the importance of this construct in the analysis of reform-oriented classrooms.