• Research in Mathematical Education
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• v.17 no.4
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• pp.291-307
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• 2013

Piaget's revolutionary study on the cognitive development of children has focused on the development of logic. Logical operations and a variety of classifications based on the set of accepted rules involve convergent thinking. Children and adults have logical and creative thinking which deal with a reality of thinking. This study aims to examine a cognitive structure of students, which is closely related to the Piaget's cognitive development theories of students when creative thinking. Students were given an open mathematical problem and were expected to be able to take advantage of sensitivity, fluency, flexibility, originality, and elaboration which can be seen as clearly of their structure cognitive.

• Communications of Mathematical Education
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• v.20 no.1 s.25
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• pp.117-145
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• 2006

Mathematically gifted children have creative curiosity about novel tasks deriving from their natural mathematical talents, aptitudes, intellectual abilities and creativities. More effect in nurturing the creative thinking found in brilliant children, letting them approach problem solving in various ways and make strategic attempts is needed. Given this perspective, it is desirable to select open-ended and atypical problems as a task for educational program for gifted children. In this paper, various types of open-ended problems were framed and based on these, teaming activities were adapted into gifted children's class. Then in the problem solving process, the characteristic of bright children's mathematical thinking ability and examples of problem solving strategies were analyzed so that suggestions about classes for bright children utilizing open-ended tasks at elementary schools could be achieved. For this, an open-ended task made of 24 inquiries was structured, the teaching procedure was made of three steps properly transforming Renzulli's Enrichment Triad Model, and 24 periods of classes were progressed according to the teaching plan. One period of class for each subcategories of mathematical thinking ability; ability of intuitional insight, systematizing information, space formation/visualization, mathematical abstraction, mathematical reasoning, and reflective thinking were chosen and analyzed regarding teaching, teaming process and products. Problem solving examples that could be anticipated through teaching and teaming process and products analysis, and creative problem solving examples were suggested, and suggestions about teaching bright children using open-ended tasks were deduced based on the analysis of the characteristic of tasks, role of the teacher, impartiality and probability of approaching through reflecting the classes. Through the case study of a mathematics class for bright children making use of open-ended tasks proved to satisfy the curiosity of the students, and was proved to be effective for providing and forming a habit of various mathematical thinking experiences by establishing atypical mathematical problem solving strategies. This study is meaningful in that it provided mathematically gifted children's problem solving procedures about open-ended problems and it made an attempt at concrete and practical case study about classes fur gifted children while most of studies on education for gifted children in this country focus on the studies on basic theories or quantitative studies.

• The Mathematical Education
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• v.51 no.3
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• pp.265-280
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• 2012

This study aims to provide implications from mathematics education perspective by designing a process of 'validity review on the problem solving process', and then, by analyzing the results. In the result of analysis on the features of children's thinking in accordance with 4 stages of problem solving, children's thinking was equally observed in every stage rather than intensively observed in one stage, and reflective thinking related to important elements from each stage of problem solving process was observed. In the result of analysis of changes in description for problem solving process, there was a difference in the aspects of changes by children's knowledge level in mathematics, however, the activity of validity review on problem solving process in overall induced positive changes in children's description, especially the changes in problem solving process of children. Through the result of this study, we could see that the validity review on problem solving process promotes children's reflective thinking and enables meta-cognition thus has a positive influence on children's description of problem solving process.

• Research in Mathematical Education
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• v.1 no.2
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• pp.117-125
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• 1997

Many primary school children struggle with mathematics and have low self-esteem in their own abilities. They know that the subject is important but they cannot cope, get left behind in their work and begin to hate mathematics. This paper reports the efforts to encourage and help a group of seventeen low achievers in mathematics prepare for their "primary six" public examination. The children were lacking in many thinking skills, but with encouragement, guidance and practice, thirteen of them (76.5%) showed improvements in their mathematical thinking and passed this important examination. This paper discusses these children's thinking in mathematics and how improvements were made.

• The Mathematical Education
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• v.43 no.1
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• pp.51-74
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• 2004

During cooperative learning in small group, we investigate what characteristics children in elementary school show at several fields of mathematics and through communicating activity etc., what influence the cooperative learning does on children's attitude, thinking, problem solving, recognition. To know them, we observe the process of children's communication and evaluate children's attitude, thinking, problem solving, recognition with checklist at each lesson. Through this research, we conclude that the figure part is the most effective when we teach with cooperative learning type, and the cooperative learning evoke the vivid communication, and make progress in affirmative attitude, thinking etc. Also, in this thesis we suggest the points which teacher should consider when he/she use cooperative learning in small-group.

• Korean Journal of Child Studies
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• v.28 no.4
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• pp.319-331
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• 2007

This review of literature establishes a contemporary meaning of mathematical problem solving including young children's mathematical problem solving processes/assessments and teaching strategies. The contemporary meaning of mathematical problem solving involves complicated higher thinking processes. Explanations of the mathematical problem solving processes of young children include the four steps suggested by $P{\acute{o}}lya$(1957) : understand the problem, devise a plan, carry out the plan, and review/extend the plan. Assessments of children's mathematical problem solving include both the process and the product of problem solving. Teaching strategies to support children's mathematical problem solving include mathematical problems built upon children's daily activities, interests, and questions and helping children to generate new approaches to solve problems.

• Korean Journal of Child Studies
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• v.29 no.1
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• pp.15-32
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• 2008

The logical and mathematical thinking of 1- to 3-year-olds was studied by age groups at 6 month intervals; logical-mathematical thinking was examined by the two physical knowledge activities of cylinder rolling and making a slope. Results showed that in their early 1st year infants failed in both tasks. Infants in their late 2nd year showed understanding of 'rolling things' and 'non-rolling things' by comparing cylinders and cubes in the cylinder rolling activity and they showed 'spatial inference' by adjusting the position and direction of the cylinder so that the cylinder could roll properly and by adjusting the board on a block in the slope making activity. Three-year-old children rolled a cylinder and made a slope without difficulty.

• Journal of Educational Research in Mathematics
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• v.14 no.4
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• pp.421-434
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• 2004

Cognitively Guided Instruction (CGI) is one of the most successful professional development programs for elementary mathematics teachers in US. This article introduces its theoretical background, research-based framework of addition and subtraction work, and how the program has been disseminated. Carpenter and Fennema started CGI aiming to develop a professional development program that focused on research knowledge of children"s thinking. Their goal was. to bring a significant change in teaching by helping teachers understand how children think mathematically. This 3-year NSF funded project grew to be 11-year long, and a number of publications have reported consistent successful learning and teaching by CGI students and teachers compared to counterparts throughout US. CGI′s success by focusing on improving teachers′ knowledge of children′s thinking offers possible opportunities for teacher educators to re-conceptualize teacher education in Korea.

• Korean Journal of Child Studies
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• v.36 no.2
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• pp.75-94
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• 2015

The main purpose of this study was to examine the various aspects of logico-mathematical thinking and its development by observing a block building activity undertaken by infants and toddlers. The subjects comprised 73 young children from between the ages of 12- to 41-months-old. The interviewee was individually asked to build "something tall", making use of 20 blocks. The results of this study were, first, a regular increase by age is seen in congruence, the vertical use of flat blocks, and innovative ways of using triangular blocks. Second, many types of logico-mathematical thinking processes, such as classification, seriation, spatial relationship and temporal relationship, were shown during the block building activities on the part of the 12- to 41-months-olds who took part in this study.

• Korean Journal of Child Studies
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• v.25 no.4
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• pp.129-145
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• 2004

This study examined the effects of Literature-based Mathematical Activities using scaffolding (LMS) on the mathematical achievement, interest, and vocabulary of day care children. The experimental group of 15 boys and 15 girls was exposed to both literature and teacher's scaffolding while the comparison group of 14boys and 16 girls had traditional mathematics curriculum. The experiment was carried out for 8 weeks. ANCOVA and T-test were employed for a statistical analysis. The results revealed statistically significant differences in mathematical achievement, interest, and vocabulary between an experimental and control groups. We can conclude, therefore, that LMS is more effective in developing children's mathematical thinking abilities than a traditional mathematical curriculum.