• Research in Mathematical Education
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• v.12 no.1
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• pp.1-26
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• 2008

The concept field is defined as the schema of all equivalent definitions of a mathematics concept. Concept system is defined as the schema of a group concept network where there are mathematics relations. Proposition field is defined as the schema of all equivalent proposition sets. Proposition system is defined as a schema of proposition sets where one mathematics proposition at least is "derived" from the other proposition. CPFS structure that consists of concept field, concept system proposition field, proposition system describes more precisely mathematics cognitive structure, and reveals the unique psychological phenomena and laws in mathematics learning.

• Research in Mathematical Education
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• v.7 no.1
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• pp.59-67
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• 2003

In linear algebra course, the theory of vector space is usually presented in a very formal setting, which causes severe difficulties to many students. In this study, the effect of teaching the theory of vector space in linear algebra from the geometrical point of view on students' learning was investigated. It was found that the teaching of the theory of vector space in linear algebra from the geometrical point of view increases the meaningful loaming since it increases the visualization.

• Research in Mathematical Education
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• v.12 no.2
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• pp.85-108
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• 2008

In this study, we created, implemented, and evaluated the impact of proportional reasoning authentic investigative activities on the mathematical content and pedagogical knowledge and attitudes of pre-service elementary and middle school mathematics teachers. For this purpose, a special teaching model was developed, implemented, and tested as part of the pre-service mathematics teacher training programs conducted in Israeli teacher colleges. The model was developed following pilot studies investigating the change in mathematical and pedagogical knowledge of pre- and in-service mathematics teachers, due to experience in authentic proportional reasoning activities. The conclusion of the study is that application of the model, through which the pre-service teachers gain experience and are exposed to authentic proportional reasoning activities with incorporation of theory (reading and analyzing relevant research reports) and practice, leads to a significant positive change in the pre-service teachers' mathematical content and pedagogical knowledge. In addition, improvement occurred in their attitudes and beliefs towards learning and teaching mathematics in general, and ratio and proportion in particular.

• Journal of Elementary Mathematics Education in Korea
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• v.11 no.2
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• pp.117-136
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• 2007

The purpose of this study was to analyze the effects of mathematics learning through tessellation activities on the improvement of spatial sense and to find out a better mathematics teaching method that could further develop spatial sense. For this purpose, the following questions were attempted; Can mathematics learning using tessellation activities develop spatial sense? In odor to test this hypothesis, twenty-four fifth graders of a class were selected at random. And the experimental group was divided into four groups according to gender and academic performance. The groups were protested and post-tested to determine results based on the quasi-experimental design(i.e. one-group pretest-post test design). The process of this study was checking spatial sense for a common evaluation of experimental group. In this study, tangram, pattern block, and GSP was used for mathematics learning through tessellation activities during each independent-study, discretion-activity, and math class. The instrument used in this study was a spatial sense test and pretest and post-test were implemented with the same instrument(i.e. K-WISC-III Activity Test). In conclusion, mathematics learning through tessellation activities with tangram, pattern block, and GSP is an effective teaching and learning method for the improvement of the spatial sense.

• Journal of the Korean School Mathematics Society
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• v.18 no.2
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• pp.203-221
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• 2015

The purpose of this study is to analyze how a peer mentoring method affects students' problem solving abilities and class satisfaction in the context of high school quadratic curves and provide implications for teaching and learning mathematics. For this study, seventy six 11th graders in the natural sciences track participated in the peer mentoring method. After finishing the teaching method, Problem Solving Abilities Questionnaire was collected for analysis of pre-test/post-test experiments and Class Satisfaction Questionnaire was also gathered. The results show that the mentoring method positively impacts on participants' problem solving abilities and class satisfaction because its comfortable learning environments, individualized learning contents, and unconstrained learning processes motivate them through ways to improve their communication. According to the results, it is to address practical implications applied in teaching quadratic curves in high school with the value and importance of mentoring methods.

• Journal of Elementary Mathematics Education in Korea
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• v.3 no.1
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• pp.21-39
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• 1999

In this paper, we first exam the relation between Piaget's theory of cognitive development and cognitive constructivism. With it's outcome We find three principles of constructivist teaching-learning methods for primary mathematics These are as follows 1) active learning based on self-regulatory process 2) empirical learning by self initiated activities 3) individual learning derived from present cognitive structure and fits of new experiences. Finally we introduce several examples for classroom practice applied the above principles in primary mathematics.

• Journal of the Korean School Mathematics Society
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• v.3 no.1
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• pp.31-45
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• 2000

The idea to be changed first among the general ideas of mathematics is that, from the standpoint of teachers, one-sided teaching is efficient due to the progress of classwork of excessive quantity, and, from the standpoint of students, they say they gave up mathematics publicly feeling uneasiness in every class because of the deficiency of previous learning and interest, and they think all problems are due to the educational system, neglecting their studies, not participating actively in lessons. Therefore this study is, after giving learning points and problem papers of which the degree of difficulty differs to the groups of students divided into the advanced, intermediate, and elementary by personal abilities of learning and concerns, tried out to remove uniformity and integrity of lessons through solving the problems students can, to convert lessons to the learner-oriented that learners take part in voluntarily through discussing, solving the problems, and correcting the errors of them by group-cooperative actions, for the students to realize that they can solve everything only by their own endeavors.

• Journal of Educational Research in Mathematics
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• v.25 no.4
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• pp.549-569
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• 2015

Reflecting on own beliefs about teaching and learning, developed during "the apprenticeship of observation", is a central task for pre-service years. This case study analysed a lesson observation course which could identify, challenge pre-service teachers' folk pedagogy about classroom communications and induce to change of beliefs about teaching and learning. Our analysis shows that targeting and refuting pre-service teachers' specific belief may be an effective strategy for teacher educators to foster new teaching practice.

• Journal for History of Mathematics
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• v.28 no.6
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• pp.333-348
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• 2015

Problem sovling skill is one of the core skills in mathematics education. To improve students' problem solving skill, the project approach or project based learning has been developed and applied. A teaching and learning strategy utilizing 'project' encourages students to understand the problem embedded in the project, find and reflect the solution, which might be effective in improving students' problem solving skill. The present study systematically reviews literature regarding project based learning and analyzes the characteristics of project. The findings from the systematic review illuminate an appropriate approach to apply project based learning in mathematics classrooms.

• Communications of Mathematical Education
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• v.38 no.1
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• pp.1-26
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• 2024

As the limitations of professional development programs and individual attempts to improve teaching expertise have been reported, mathematics teachers have operated various types of teacher learning communities as alternative teacher professional programs. A teacher learning community can be considered a Community of Practice(CoP) in that it satisfies three factors of Cop, which are common purpose, mutual participation, and shared repertoire, so the 'learning' of a teacher community can be interpreted based on the theory of CoP. The purpose of this study is to investigate the process of identity development of five mathematics teachers who have been continuously involved in teacher communities. For this, the researcher collected data on the entire process of community activities through participant observation and conducted individual follow-up interviews to explore mathematics teachers' narratives and personal experiences. Results indicated that mathematics teachers experienced the development of practical knowledge related to mathematics teaching and learning, improvement of teaching practice through continuous reflection and introspection, and recognization the shared value of togethering through community immersion. Based on these experiences, implications for the effective operation of learning communities such as national support of teacher learning communities and horizontal and cooperative teacher norms were discussed, and follow-up research was proposed.