• The Mathematical Education
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• v.42 no.5
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• pp.697-706
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• 2003

In this paper we consider the equality sign as a mathematical concept and investigate its meaning, errors made by students, and subject matter knowledge of mathematics teacher in view of The Model of Mathematic al Concept Analysis, arithmetic-algebraic thinking, and some examples. The equality sign = is a symbol most frequently used in school mathematics. But its meanings vary accor ding to situations where it is used, say, objects placed on both sides, and involve not only ordinary meanings but also mathematical ideas. The Model of Mathematical Concept Analysis in school mathematics consists of Ordinary meaning, Mathematical idea, Representation, and their relationships. To understand a mathematical concept means to understand its ordinary meanings, mathematical ideas immanent in it, its various representations, and their relationships. Like other concepts in school mathematics, the equality sign should be also understood and analysed in vie w of a mathematical concept.

• Research in Mathematical Education
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• v.14 no.1
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• pp.33-50
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• 2010

The mathematical thinking which transforms important mathematical content and developed into mathematical structure is a vital process in building up mathematical ability as mathematical knowledge based on structure. Such process based on students' recognition of mathematical concept. Developing mathematical thinking into mathematical structure happens when different cognitive units are connected and compressed to form schema of solution, which could happen through some guided problems. The effort of arithmetic approach in problem solving did not necessarily provide students the structure schema of solution. The using of equation to solve the problem is based on the schema of building equation, and is not necessary recognizing the structure of the solution, as the recognition of structure may be lost in the process of simplification of algebraic expressions, leaving only the final numeric answer of the problem.

• Research in Mathematical Education
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• v.15 no.2
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• pp.181-196
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• 2011

In mathematical modeling tasks, where students are exposed to model-eliciting for real and open problems, students are supposed to formulate and use a variety of mathematical skills and tools at hand to achieve feasible and meaningful solutions using appropriate problem solving strategies. In contrast to problem solving activities in conventional math classes, math modeling tasks call for varieties of mathematical ability including mathematical creativity. Mathematical creativity encompasses complex and compound traits. Many researchers suggest the exhaustive list of criterions of mathematical creativity. With regard to the research considering the possibility of enhancing creativity via math modeling instruction, a quantitative scheme to scale and calibrate the creativity was investigated and the assessment of math modeling activity was suggested for practical purposes.

• Journal for History of Mathematics
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• v.34 no.6
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• pp.195-204
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• 2021

Mathematical induction is one of the deductive methods used for proving mathematical theorems, and also used as an inductive method for investigating and discovering patterns and mathematical formula. Proper understanding of the mathematical induction provides an understanding of deductive logic and inductive logic and helps the developments of algorithm and data science including artificial intelligence. We look at the origin of mathematical induction and its usage and educational aspects.

• The Mathematical Education
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• v.47 no.2
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• pp.135-154
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• 2008

The purpose of this study is to help to improve the method of math teaching by analysing how learner-centered teaching method offsets mathematical creativity and mathematical disposition. For this purpose, research questions are established as follows; (1) Mathematical creativity between open-ended learning activity approach(OLAA) and general classroom-based instruction(GCI) shows any difference? (2) Mathematical disposition between OLAA and GCI shows any difference? The results obtained through this study were as follows: (1) There was significant difference between OLAA group and CCI group in mathematical creativity. This means that open-ended learning activity approach was generally more effective in improving mathematical creativity than general classroom-based instruction. (2) There was no significant difference between OLAA group and GCI group in mathematical disposition. But the average scores of mathematical disposition except mathematical confidence improved a little. So we can say that open-ended learning activity approach brought an positive influence on students' mathematical disposition. The results obtained in this study suggest that the OLAA can be used to cultivate the children's mathematical creativity and disposition. Therefore, I suggest that teachers should use the OLAA to improve the children's mathematical creativity and disposition.

• Korean Journal of Child Studies
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• v.34 no.1
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• pp.123-140
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• 2013

The purpose of this study was to examine the effects of counting ability on young children's mathematical ability and mathematical learning potential. The subjects in this study were 75 young children of 4 & 5 years old who attended kindergartens and child care center in the city of B. They were evaluated in terms of counting ability, mathematical ability and mathematical learning potential(training and transfer) and the correlation between sub-factors and their relative influence on the partipants' mathematical ability was then analyzed. The findings of the study were as follows : First, there was a close correlation between the sub-factors of counting and those of mathematical ability. As a result of checking the relative influence of the sub-factors of counting on mathematical ability, reverse counting was revealed to have the largest impact on total mathematical ability scores and each sub-factors including algebra, number and calculation, geometry and measurement. Second, the results revealed a strong correlation between counting ability and mathematical learning ability. Regarding the size of the relative influence of the sub-factors of counting ability on training scores, reverse counting was found to be most influential, followed by continuous counting. While in relation to transfer scores, reverse counting was found to exert the greatest influence.

• East Asian mathematical journal
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• v.36 no.2
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• pp.253-271
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• 2020

The purpose of this study was to see the effects of a learning method of the multiplication play activities on improving the mathematical thinking ability and mathematical attitude of 2nd grade students in elementary school. We chose 19 students of the 2nd grade experimental group of D elementary school in the D city to conduct this research. The result of this study are as follows. First, Classes using multiplicative play activities have a positive effect on students' mathematical thinking ability. When analyzing transcripts and activities, students were able to think of strategies that could solve the problem according to the situation. Second, Classes using multiplicative play activities, in result of this they have positive effect mathematical attitude than using textbook in terms of attitude about mathematical subject and habits of study. In conclusion, the multiplication play activities are effective to improve mathematical thinking ability and attitude of second elementary school students. It can be a implication for the method of improving mathematical thinking ability and attitude.

• East Asian mathematical journal
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• v.33 no.4
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• pp.381-411
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• 2017

The purpose of this study is to investigate how students' mathematical creativity changes through problem-solving instruction using problem-posing for elementary school students and to explore instructional methods to improve students' mathematical creativity in school curriculum. In this study, nonequivalent control group design was adopted, and the followings are main results. First, problem-solving lessons with problem-posing had a significant effect on students' mathematical creativity, and all three factors of mathematical creativity(fluency, flexibility, originality) were also significant. Second, the lessons showed meaningful results for all upper, middle, and lower groups of pupils according to the level of mathematical creativity. When analyzing the effects of sub-factors of mathematical creativity, there was no significant effect on fluency in the upper and middle groups. Based on the results, we suggest followings: First, there is a need for a systematic guidance plan that combines problem-solving and problem-posing, Second, a long-term lesson plan to help students cultivate novel mathematical problem-solving ability through insights. Third, research on teaching and learning methods that can improve mathematical creativity even for students with relatively high mathematical creativity is necessary. Lastly, various student-centered activities in math classes are important to enhance creativity.

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.557-580
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• 2012

Common Core State Standards for Mathematics(CCSSM) is a blueprint for school mathematics in 2010s of the United States. CCSSM can be divided into two major parts, the standards for mathematical content and the standards for mathematical practice. This study focused on the latter. Mathematical practice comes from the mathematical process in 'Principles and standards for school mathematics(NCTM, 2000)' as well as the mathematical proficiency in 'Adding it up(NRC, 2001)'. It is composed of eight standards which mathematically proficient students are expected to do. From Korean perspective, it can also be comparable with the mathematical process which contains mathematical problem solving, mathematical reasoning, and mathematical communication and was provided by the 2009 revised national curriculum for mathematics in Korea. However, few focused the standards for mathematical practice among the studies related to CCSSM in Korea. Moreover, there is a study that even ignores the existence of the standards for mathematical practice itself. This study aims to understand the standards for mathematical practice through analysing the document of CCSSM and its successive materials for implementing the CCSSM. This understanding will help effective implementation of the mathematical process in Korea.

• Journal of Elementary Mathematics Education in Korea
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• v.13 no.1
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• pp.31-49
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• 2009

Utilizing the mathematical materials in elementary mathematics education is known to increase the learners' creativity and interests for mathematics. Although the effects of mathematical materials have been frequently researched, a practical plan and a process to utilize the mathematical materials has been rarely researched. The dependence on the mathematical materials is tested by the students' responses to the mathematical problems in the class that allowed to use mathematical materials. The activities in the text book are reorganized to seven chapters for utilizing the mathematical materials. The dependence on the mathematical materials when solving the mathematical problems is investigated by the textbook, students' answers, and handouts. The conclusions of this study are: First of all, the activities using mathematical materials are reorganized within the mathematics education curriculum. The high interests are also investigated in all the learning level of learners. Second, the learners in the high learning level use the mathematical materials for their needs and the correction of their mistakes. The dependence on mathematical materials is lowest compared to the other level learners. Third, the learners in the mid learning level also use the mathematical materials for their needs and their mistakes, but are often confused when utilizing the materials. Fourth, the learners in the low learning level show their interests, and enthusiasm in the mathematical materials themselves. Their interests help to solve mathematical problems. The dependence on the materials is higher than the other level learners, but the dependence is not shown only for the low level learners.