• The Mathematical Education
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• v.34 no.1
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• pp.17-63
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• 1995

The exploration of Mathematics-learningmodel on the basis of Cognitive development The purpose of this paper is to sequenctialize Mathematics-learning contents, and to explore teaching-learning model for mathematics, with on the basis of the theory of cognitive development and the period of condservation formation for children. The Specific topics are as follows: (1) Systemizing those theories of cognitive development which are related to Mathematics - learning for children. (2) Organizing a sequence of Mathematics - learning, on the basis of experimental research for the period of conservation formation for children. (3) Comparing the effects of 4 types of teaching - learning model, on the basis of inference activity and operational learning principle. $\circled1$ Induction-operation(IO) $\circled2$ Induction-explanation(IE) $\circled3$ Deduction-operation(DO) $\circled4$ Deduction-explanation(DE) The results of the subjects are as follows: (1) Cognitive development theory and Mathe-matics education. $\circled1$ Congnitive development can be achieved by constant space and Mathematics know-ledge is obtained by the interaction of experience and reason. $\circled2$ The stages of congnitive development for children form a hierarchical system, its function has a continuity and acts orderly. Therefore we need to apply cognitive development for children to teach mathematics systematically and orderly. (2) Sequence of mathematical concepts. $\circled1$ The learning effect of mathematical concepts occurs when this coincides with the period of conservation formation for children. $\circled2$ Mathematics Curriculum of Elementary Schools in Korea matches with the experimental research about the period of Piaget's conservation formation. (3) Exploration of a teaching-learning model for mathematics. $\circled1$ Mathematics learning is to be centered on learning by experience such as observation, operation, experiment and actual measurement. $\circled2$ Mathematical learning has better results in from inductional inference rather than deductional inference, and from operational inference rather than explanatory inference.

• Journal of the Korean School Mathematics Society
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• v.16 no.4
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• pp.841-862
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• 2013

This study analyzed issues in the mathematics curriculum concerning the cognitive development of the vector and inner product concepts in the light of Tall's and Watson's research(Tall, 2004a; Tall, 2004b; Watson et al., 2003; Watson, 2002). Some suggestions in teaching the vector and inner product concepts were elaborated in the terms of these analyses. First, the position vector needs to be represented by an arrow on the coordinate system in order to introduce the component form of a vector represented by a directed line segment. Second, proofs of the vector operation law should be carried out by symbolic manipulations based on the algebraic concept of a vector in the symbolic world. Third, it is appropriate that the inner product is defined as $\vec{a}{\cdot}\vec{b}=a_1b_1+a_2b_2$ (when, $\vec{a}=(a_1,a_2)$, $\vec{b}=(b_1,b_2)$) when it comes to considering the meaning of the inner product relevant to vector space in the formal world. Cognitive growth of concepts of the vector and inner product can be properly induced through revising explanation methods about the concepts in the curriculum in the basis of the above suggestions.

• Journal of Educational Research in Mathematics
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• v.8 no.2
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• pp.651-662
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• 1998

Mathematics is means for making sense of one's experiential world and products of human activities. A usefulness of mathematics is derived from this features of mathematics. Keeping the meaning of situations during the mathematizing of situations. However, theories about the development of mathematical concepts have turned mainly to an understanding of invariants. The purpose of this study is to show the possibility of computer in representing situation and phenomena. First, we consider situated cognition theory for looking for the relation between various representation and situation in problem. The mathematical concepts or model involves situations, invariants, representations. Thus, we should involve the meaning of situations and translations among various representations in the process of mathematization. Second, we show how the process of computational mathematization can serve as window on relating situations and representations, among various representations. When using computer software such as ALGEBRA ANIMATION in mathematics classrooms, we identified two benifits First, computer software can reduce the cognitive burden for understanding the translation among various mathematical representations. Further, computer softwares is able to connect mathematical representations and concepts to directly situations or phenomena. We propose the case study for the effect of computer software on practical mathematics classrooms.

• Education of Primary School Mathematics
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• v.26 no.4
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• pp.317-332
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• 2023

Mathematical modeling activities hold the potential for diverse applications, involving the transformation of real-life situations into mathematical models to facilitate problem-solving. In order to assess the cognitive, affective, and social dimensions of students' engagement in mathematical modeling activities, this study conducted sessions with ten groups of fifth-grade elementary school students. The ensuing processes and outcomes were thoroughly analyzed. As a result, each group effectively applied mathematical concepts and principles in creating mathematical models and gathering essential information to address real-world tasks. This led to notable shifts in interest, enhanced mathematical proficiency, and altered attitudes towards mathematics, all while promoting increased collaboration and communication among group members. Based on these analytical findings, the study offers valuable pedagogical insights and practical guidance for effectively implementing mathematical modeling activities.

• The Mathematical Education
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• v.62 no.2
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• pp.257-268
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• 2023

The purpose of the study is to analyze the characteristics of open-ended tasks in terms of cognitive demands. For this purpose, we analyzed characteristics of open-ended tasks presented in the sequence units of three high school mathematics textbooks. The results of the study have revealed that low cognitive demand levels of open-ended tasks had characteristics including procedures within previous tasks or within those tasks. On the other hand, high cognitive demand levels of open-ended tasks had characteristics of actively exploring new conditions to gain access to what is being sought, requesting a basis for judgement, linking various representations to the concepts of sequences, or requiring a variety of answers. These results are significant in that they not only specified the characteristics of open-ended tasks with high cognitive demands in terms of the intended curriculum, but also provided a direction for the development of open-ended taks with high congitive demands.

• Education of Primary School Mathematics
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• v.3 no.2
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• pp.89-101
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• 1999

The reform movements of current mathematics education have based on several major ideas, in order to provide a new vision of the teaching and loaming of mathematics. Of the ideas, the motto of communication of mathematics appears to be a significant factor to change teaching practices in mathematics classroom. Through Vygotsky's sociocultural theory, the psychological background is presented for both supporting the motto and extracting important suggestions of the reform of mathematics education. The development of higher mental functions is explained by internalization, semiotic mediation, and the zone of proximal development. Above all, emphasis is put on the concepts of scaffolding and inter subjectivity related to the zone of proximal development. Seven implications are proposed by Vygotsky's sociocultural theory for the new forms of the teaching and learning of mathematics.

• Korean Journal of Cognitive Science
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• v.27 no.2
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• pp.159-219
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• 2016

Mathematical ability is important for academic achievement and technological renovations in the STEM disciplines. This study concentrated on the relationship between neural basis of mathematical cognition and its mechanisms. These cognitive functions include domain specific abilities such as numerical skills and visuospatial abilities, as well as domain general abilities which include language, long term memory, and working memory capacity. Individuals can perform higher cognitive functions such as abstract thinking and reasoning based on these basic cognitive functions. The next topic covered in this study is about individual differences in mathematical abilities. Neural efficiency theory was incorporated in this study to view mathematical talent. According to the theory, a person with mathematical talent uses his or her brain more efficiently than the effortful endeavour of the average human being. Mathematically gifted students show different brain activities when compared to average students. Interhemispheric and intrahemispheric connectivities are enhanced in those students, particularly in the right brain along fronto-parietal longitudinal fasciculus. The third topic deals with growth and development in mathematical capacity. As individuals mature, practice mathematical skills, and gain knowledge, such changes are reflected in cortical activation, which include changes in the activation level, redistribution, and reorganization in the supporting cortex. Among these, reorganization can be related to neural plasticity. Neural plasticity was observed in professional mathematicians and children with mathematical learning disabilities. Last topic is about mathematical creativity viewed from Neural Darwinism. When the brain is faced with a novel problem, it needs to collect all of the necessary concepts(knowledge) from long term memory, make multitudes of connections, and test which ones have the highest probability in helping solve the unusual problem. Having followed the above brain modifying steps, once the brain finally finds the correct response to the novel problem, the final response comes as a form of inspiration. For a novice, the first step of acquisition of knowledge structure is the most important. However, as expertise increases, the latter two stages of making connections and selection become more important.

• Journal of Digital Contents Society
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• v.8 no.2
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• pp.235-243
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• 2007

Students develop mathematical concepts through concrete operations in the area of mathematics. However, most of the learning contents provided on the web are not interactive and limit interactions with learners. To overcome the limitations, there have been needs to develop learning contents to support active interactions with students according to their cognitive levels. In this study, the curriculum of numbers and number operations in elementary mathematics was analyzed. Based on the object-oriented design principle, "Number Classes" on numbers and number operations were designed and implemented. A class-based learning applet was developed with theses "Number Classes". It was developed in small unit programs based on learning themes of mathematics in elementary schools. With this learning applet, the active explorations through easy operations will help students to learn concepts and principles of numbers and number operations. It will strengthen active interactions of students with computer.

• Journal of Elementary Mathematics Education in Korea
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• v.13 no.1
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• pp.75-95
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• 2009

The purpose of the study was to investigate the scaffolding processes of children in mathematical problem solving. 3 groups of 4th grade students participated in the study and the researchers proceeded the study for 4 months. The procedures of this research were as followings. First, when the learners solved the problems, the categories of scaffolding processes(by way of unit line coding belong in open codings, the categories were made 25 concepts and integrated 20 subcategories) were produced the 7 results: invite to the learning, set the problems, affective aids, attempt self learning, re-ordering between learners and affirmation self learning. Second, the processes of scaffolding in mathematic problem solving resulted in condition, the present condition, action/interaction and the outcomes. Third, the cognitive and affective aids that discovered in the scaffolding processes were considered the main categories of learner's scaffolding processes in solving the mathematic problems. In conclusion, first, the learners' scaffolding processes, based on Vygotsky's "the zone of proximal development" in selection and presentation of mathematic problems, are very diverse. Peers' affective aids are very important in solving the problems. Second, learners in the scaffolding processes exchange the cognitive and affective aids with each other with joy and earnestness, and the aids can give assistance to all the participants. Third, in the results of observation and analysis in learners' scaffolding processes, it is meaningful to know how they think. Finally, the learners' scaffolding processes are a little unsystematic and illogical compared to those of adults, but those of scaffolders are so similar to those of learners' cognitive and affective systems that they can provide teachers with many merits in understanding and teaching learners.

• Journal of The Korean Association For Science Education
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• v.24 no.3
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• pp.417-428
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• 2004

Conservation reasoning makes operational thought possible as a functional tool and it is the essential concept not only in the area of science and mathematics but also in several aspects of daily life. The abilities to solve mathematical problems and that of scientific reasoning and abstract way of thinking depend on whether thereis conservation reasoning or not and they are critical concepts that enables us to confirm the steps of cognitive development. Therefor in the study, we emphasized the issue that is the ways to speed up the scientific era by analyzing the correlation between the formation of conservation reasoning and neuro-cognitive variables. About 50% of 1-3 grade students did not had conservation reasoning skills. The formation of conservations was not linear. Scientific reasoning ability, planing and inhibiting ability were significantly different in levels of conservation, And, conservation reasonings were significantly correlated with cognitive variables. Scientific reasoning and planning ability significantly explained about 20% of the conservation reasoning ability of 1-3 grades.