• The Mathematical Education
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• v.58 no.4
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• pp.519-530
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• 2019

According to previous studies, meta-affect based on the interaction between cognitive and affective elements in mathematics learning activities maintains a close mechanical relationship with the learner's mathematical ability in a similar way to meta-cognition. In this study, in order to grasp these characteristics phenomenologically, small group problem-solving cases of 5th grade elementary mathematically gifted children were analyzed from a meta-affective perspective. As a result, the two types of problem-solving cases of mathematically gifted children were relatively frequent in the types of meta-affect in which cognitive element related to the cognitive characteristics of mathematically gifted children appeared first. Meta-affects were actively acted as the meta-function of evaluation and attitude types. In the case of successful problem-solving, it was largely biased by the meta-function of evaluation type. In the case of unsuccessful problem-solving, it was largely biased by the meta-function of the monitoring type. It could be seen that the cognitive and affective characteristics of mathematically gifted children appear in problem solving activities through meta-affective activities. In particular, it was found that the affective competence of the problem solver acted on problem-solving activities by meta-affect in the form of emotion or attitude. The meta-affecive characteristics of mathematically gifted children and their working principles will provide implications in terms of emotions and attitudes related to mathematics learning.

• School Mathematics
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• v.18 no.3
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• pp.503-526
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• 2016

The study aimed at determining the identity of mathematics essay test in the university entrance examination. For this purpose, a document research was conducted for higher order thinking and mathematics essay ability and it analyzed the goal of assessment and the tendency of problem settings and looked into mathematics essay problems of twenty-five universities. As a result, the study found out that evaluation factors of mathematics essay test requires higher order thinking ability including mathematical knowledge and essay ability such as mathematical knowledge, understanding, problem solving, logical and critical thinking, creative ability, power of expression, argument skills. Also, problems from previous mathematics essay tests were set mainly to assess mathematical knowledge, understanding and problem solving. Based on the findings, the past mathematics essay tests in university entrance examination in Korea that require logical and critical thinking, creative ability, power of expression, argument skills were a rather small percentage of questions.

• Communications of Mathematical Education
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• v.31 no.1
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• pp.125-147
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• 2017

The purpose of this study was to investigate the effects of mathematics-centered STEAM program which was operated in free semester system classes on middle school students' interest in science, technology/engineering, and mathematics(STEM) career and integrated problem solving ability. The study was conducted with 40 first graders in a middle school for 12 weeks using mathematics-centered STEAM program developed for the use of free semester system classes by the support of the Ministry of Education/KOFAC in 2016. According to the results of STEM career interest survey, mathematics-centered STEAM program was effective for improving middle school students' interest in STEM career. And it was also effective in the development of students' integrated problem solving ability.

• Education of Primary School Mathematics
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• v.18 no.2
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• pp.123-139
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• 2015

The purpose of this study was to investigate the effects of the experiences of productive failures on students' mathematical problem solving abilities and mathematical dispositions. The experiment was conducted with two groups. The treatment group was applied with the productive mathematics failure program, and the comparative group was taught with traditional mathematics lessons. In this study, for quantitative analysis, the students were tested their understanding of mathematical concepts, mathematical reasoning abilities, students' various strategies and mathematical dispositions before and after using the program. For qualitative analysis, the researchers analyzed the discussion processes of the students, students's activity worksheets, and conducted interviews with selected students. The results showed the followings. First, use of productive failures showed students' enhancement in problem solving abilities. Second, the students who experienced productive failures positively affected the changes in students' mathematical dispositions. Along with the more detailed research on productive mathematical failures, the research results should be included in the development of mathematics textbooks and teaching and learning mathematics.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.3
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• pp.619-640
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• 2011

The study aims the introducing the items for the assessment of mathematical thinking including mathematical reasoning, problem solving, and communication and the analyzing on the responses of the 5th grade pupils. We categorized the area of mathematical reasoning into deductive reasoning, inductive reasoning, and analogy; problem solving into external problem solving and internal one; and communication into speaking, reading, writing, and listening. And we proposed the examples of our items for each area and the 5th grade pupils' responses. When we assess on pupil's mathematical reasoning, we need to develop very appropriate items needing the very ability of each kind of mathematical reasoning. When pupils solve items requesting communication, the impact of the form of each communication seem to be smaller than that of the mathematical situation or sturucture of the item. We suggested that we need to continue the studies on mathematical assessment and on the constitution and utilization of cognitive areas, and we also need to in-service teacher education on the development of mathematical assessments, based on this study.

• Education of Primary School Mathematics
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• v.20 no.1
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• pp.85-99
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• 2017

In order to improve mathematical problem-solving ability, there has been a need for research on practical application of meta-affect which is found to play an important role in problem-solving procedure. In this study, we analyzed the characteristics of the sociodynamical aspects of the meta-affective factor of the successful problem-solving procedure of small groups in the context of collaboration, which is known that it overcomes difficulties in research methods for meta-affect and activates positive meta-affect, and works effectively in actual problem-solving activities. For this purpose, meta-functional type of meta-affect and transact elements of collaboration were identified as the criterion for analysis. This study grasps the characteristics about sociodynamical function of meta-affect that results in successful problem solving by observing and analyzing the case of the transact structure associated with the meta-functional type of meta-affect appearing in actual episode unit of the collaborative mathematical problem-solving activity of elementary school students. The results of this study suggest that it provides practical implications for the implementation of teaching and learning methods of successful mathematical problem solving in the aspect of affective-sociodynamics.

• Journal for History of Mathematics
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• v.28 no.5
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• pp.263-278
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• 2015

As intuition is more unreliable than logic or reason, its studies in mathematics and mathematics education have not been done that much. But it has played an important role in the invention and development of mathematics with logic. So, it is necessary to recognize and explore the value of intuition in mathematics education. In this paper, I investigate the function and role of intuition in terms of mathematical learning and problem solving. Especially, I discuss the positive and negative aspects of intuition with its characters. The intuitive acceptance is decided by self-evidence and confidence. In relation to the intuitive acceptance, it is discussed about the pedagogical problems and the role of intuitive thinking in terms of creative problem solving perspectives. Intuition is recognized as an innate ability that all people have. So, we have to concentrate on the mathematics education via intuition and the complementary between intuition and logic. For further research, I suggest the studies for the mathematics education via intuition for students' mathematical development.

• Education of Primary School Mathematics
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• v.12 no.2
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• pp.81-97
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• 2009

Visual representations play an important role for students to understand the meaning of a given problem, devise problem-solving approaches, and implement them successfully. The purpose of this study was to investigate how 6th graders would use visual representations in solving mathematical problems and in what ways such use might affect successful problem solving. The results showed that many students preferred numerical expressions to visual representations. However, students who used visual representations, specifically schematic representations, performed better than those who employed numerical representations. Given this, this paper includes instructional implications to nurture students' use of visual representations in a way to increase their problem solving ability.

• Electronics and Telecommunications Trends
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• v.38 no.6
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• pp.1-11
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• 2023

Large language models seem promising for handling reasoning problems, but their underlying solving mechanisms remain unclear. Large language models will establish a new paradigm in artificial intelligence and the society as a whole. However, a major challenge of large language models is the massive resources required for training and operation. To address this issue, researchers are actively exploring compact large language models that retain the capabilities of large language models while notably reducing the model size. These research efforts are mainly focused on improving pretraining, instruction tuning, and alignment. On the other hand, chain-of-thought prompting is a technique aimed at enhancing the reasoning ability of large language models. It provides an answer through a series of intermediate reasoning steps when given a problem. By guiding the model through a multistep problem-solving process, chain-of-thought prompting may improve the model reasoning skills. Mathematical reasoning, which is a fundamental aspect of human intelligence, has played a crucial role in advancing large language models toward human-level performance. As a result, mathematical reasoning is being widely explored in the context of large language models. This type of research extends to various domains such as geometry problem solving, tabular mathematical reasoning, visual question answering, and other areas.

• Communications of Mathematical Education
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• v.32 no.3
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• pp.385-406
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• 2018

The purpose of this study is to investigate the effect of mathematics classes focused on mathematical problem posing activities on 10th grade students' mathematics achievement and affective characteristics of mathematics. This study was conducted in a total of 45 regular mathematics classrooms with 81 students from two classes through a nonequivalent control group design. The results of the study showed that the teaching method based on mathematical problem posing activities had a more positive effect on students' mathematics achievement and the affective characteristics of mathematics than the teaching method that focuses on problem solving. The teaching method based on problem posing activities proposed in this study could induce students' self-reflective learning motivation, which in turn gave them a more solid understanding of the mathematical concepts they had learned. In addition, it was found that students' problem solving ability, mathematical communication ability, and mathematical thinking ability were positively influenced by problem posing activities. Regarding the affective characteristics of mathematics, the mathematical problem-posing activity suggested in this study turned out to be a very effective strategy for improving students' interest in mathematics.