• The Mathematical Education
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• v.40 no.2
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• pp.253-263
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• 2001

Developing mathematical thinking skills is one of the most important goals of school mathematics. In particular, recent performance based on assessment has focused on the teaching and learning environment in school, emphasizing student's self construction of their learning and its process. Because of this reason, people related to mathematics education including math teachers are taught to recognize the fact that the degree of students'acquisition of mathematical thinking skills and strategies(for example, inductive and deductive thinking, critical thinking, creative thinking) should be estimated formally in math class. However, due to the lack of an evaluation tool for estimating the degree of their thinking skills, efforts at evaluating student's degree of mathematics thinking skills and strategy acquisition failed. Therefore, in this paper, mathematical thinking was studied, and using the results of study as the fundamental basis, mathematical thinking process model was developed according to three types of mathematical thinking - fundamental thinking skill, developing thinking skill, and advanced thinking strategies. Finally, based on the model, evaluation factors related to essential thinking skills such as analogy, deductive thinking, generalization, creative thinking requested in the situation of solving mathematical problems were developed.

• Research in Mathematical Education
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• v.12 no.2
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• pp.127-142
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• 2008

The most important aim of mathematics education is to promote mathematical thinking. In the Hong Kong primary school, mathematical thinking is usually conducted through the use of formula and working on "application problem" or "word problems". However, there are many other ways that can promote mathematical thinking, and investigation on mathematical structure by using counting is one important source for promoting mathematical thinking for primary school children, as every children can count and hence a well designed question that can be solved by counting can enable children of different abilities to work together and obtain different results.

• Research in Mathematical Education
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• v.14 no.1
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• pp.79-98
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• 2010

To analyze the relationships between self-control, thinking quality and mathematical academic achievement, 197 senior school students were asked to complete questionnaires called "self-control ability on mathematics for middle school students" and "thinking quality for senior school students." The results were as follows: (1) There was strongly positive relevance between self-control ability, thinking quality and mathematical academic achievement. (2) A model was presented in which self-control ability had a direct impact on mathematical academic achievement, meanwhile had indirectly influenced mathematical academic achievement by thinking quality which acted as the intermediate variable. Thinking quality had a direct impact on mathematical academic achievement, too. (3) There's no significant difference between the two groups of boys and girls on the structural weights.

• East Asian mathematical journal
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• v.38 no.4
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• pp.463-496
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• 2022

The purpose of this study is to analyze the mathematical creativity and computational thinking of mathematically gifted elementary students through a convergence class using programming and to identify what it means to provide the convergence class using Python for the mathematical creativity and computational thinking of mathematically gifted elementary students. To this end, the content of the nine sessions of the Python-applied convergence programs were developed, exploratory and heuristic case study was conducted to observe and analyze the mathematical creativity and computational thinking of mathematically gifted elementary students. The subject of this study was a single group of sixteen students from the mathematics and science gifted class, and the content of the nine sessions of the Python convergence class was recorded on their tablets. Additional data was collected through audio recording, observation. In fact, in order to solve a given problem creatively, students not only naturally organized and formalized existing mathematical concepts, mathematical symbols, and programming instructions, but also showed divergent thinking to solve problems flexibly from various perspectives. In addition, students experienced abstraction, iterative thinking, and critical thinking through activities to remove unnecessary elements, extract key elements, analyze mathematical concepts, and decompose problems into small components, and math gifted students showed a sense of achievement and challenge.

• 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.

• The Mathematical Education
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• v.47 no.2
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• pp.169-180
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• 2008

The purpose of this study was to analyze the elementary students' mathematical thinking, which is found during mathematical problem solving processes based on mathematical knowledge, heuristics, control, and mathematical disposition. The participants were 8 fifth grade elementary students in Seoul. A qualitative case study was used for investigating the students' mathematical thinking. The data were coded according to the four components of the students' mathematical thinking. The results of the analyses concerning mathematical thinking of the elementary students were as follows: First, in terms of mathematical knowledge, the elementary students frequently used conceptual knowledge, procedural knowledge and informal knowledge during problem solving processes. Second, students tended not to find new heuristics or apply new one, but they only used the heuristics acquired from the experiences of the class and prior experiences. Third, control was found while students were solving problems. Last, mathematical disposition influenced on the mathematical problem solving processes. Teachers need to in-depth observations on the problem solving processes of students, which leads to teachers'effective assistance on facilitating students' problem solving skills.

• East Asian mathematical journal
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• v.27 no.4
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• pp.381-389
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• 2011

The flexible mathematical thinking - the ability to generate and connect various representations of concepts - is useful in understanding mathematical structure and variation in problem solving. In particular, the flexible mathematical thinking with the inventive mathematical thinking, the original mathematical problem solving ability and the mathematical invention is a core concept, which must be emphasized in all branches of mathematical education. In this paper, the author considered a case of flexible mathematical thinking with an inventive problem solving ability shown by his student via real analysis courses. The case is on the proofs of the equivalences of three different definitions on the concept of limit superior shown in three different real analysis books. Proving the equivalences of the three definitions, the student tried to keep the flexible mathematical thinking steadily.

• 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.

• The Mathematical Education
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• v.50 no.1
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• pp.69-87
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• 2011

The aim of this research is to develop a 'program which improves critical thinking' to improve elementary school students' mathematical thinking, and investigate the effect of program by applying and verifying the program. In order to achieve the objective, the author determined the factors of critical thinking capabilities matched to the discipline of mathematics, and accordingly designed relevant programs and test questions for critical thinking skills which contributes to improving the critical thinking of elementary school students, and thus applied the program the developed program of improving the critical thinking to both preliminary and main experiments, which verified the effects of the test method. The following results have been acquired through this research : In the preliminary inspection that this researcher has developed, it was able to predict that 'the program which improves critical thinking' would have a positive influence on the students' critical thinking. In the main experiment which was performed after modifying and supplementing it, the result showed that the program had a positive influence on the students' critical thinking.

• Communications of Mathematical Education
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• v.22 no.3
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• pp.383-397
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• 2008

In problem solving, the necessity of mathematical thinking is absolute. In this paper, with an established theory about mathematical thinking, we will try to observe how the students can form mathematical thinking through a mathematical example in mathematical class by using Lakatos' process of proofs and refutations.