• Education of Primary School Mathematics
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• v.7 no.2
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• pp.101-116
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• 2003

In recent days, it is stressed that problem solving ability and inference ability to get a higer accomplishment are very important. The purpose of this research is to explore the affective factors related the problem solving ability and reasoning ability. Also, we explored the difference between the two affective factors focusing on 6th graders in primary school.

• 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.25 no.3
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• pp.537-556
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• 2011

This paper focuses on proportional reasoning being emphasized in today's elementary math, and analyzes the way students use their proportional reasoning abilities and strategies according to their academic achievement levels in solving proportional problems. For this purpose, various types of proportional problems were presented to 173 sixth-grade elementary school students and they were asked to use a maximum of three types of proportional reasoning strategies to solve those problems. The experiment results showed that upper-ranking students had better ability to use, express and perceive more types of proportional reasoning than their lower-ranking counterparts. In addition, the proportional reasoning strategies preferred by students were shown to be independent of academic achievement. But there was a difference in the proportional reasoning strategy according to the types of the problems and the ratio of the numbers given in the problem. As a result of this study, we emphasize that there is necessity of the suitable proportional reasoning instruction which reflected on the difference of ability according to student's academic achievement.

• 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.

• Journal of Elementary Mathematics Education in Korea
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• v.21 no.3
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• pp.461-483
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• 2017

The ability to think mathematically and to reason inductively are basics of logical reasoning and the most important skill which students need to acquire through their Math curriculum in elementary school. For these reasons, we need to conduct an analysis in their procedure in inductive reasoning and find difficulties thereof. Therefore, through this study, I found parts which covered inductive reasoning in their Math curriculum and analyzed the abilities and characteristics of students in solving a problem through inductive reasoning.

• Journal of Elementary Mathematics Education in Korea
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• v.18 no.1
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• pp.123-148
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• 2014

The purpose of this study is to figure out the perceptional characteristics of mathematically gifted elementary students by comparing the mathematical reasoning ability and errors between mathematically gifted elementary students and non-gifted students. This research has been targeted at 63 gifted students from 5 elementary schools and 63 non-gifted students from 4 elementary schools. The result of this research is as follows. First, mathematically gifted elementary students have higher inductive reasoning ability compared to non-gifted students. Mathematically gifted elementary students collected proper, accurate, systematic data. Second, mathematically gifted elementary students have higher inductive analogical ability compared to non-gifted students. Mathematically gifted elementary students figure out structural similarity and background better than non-gifted students. Third, mathematically gifted elementary students have higher deductive reasoning ability compared to non-gifted students. Zero error ratio was significantly low for both mathematically gifted elementary students and non-gifted students in deductive reasoning, however, mathematically gifted elementary students presented more general and appropriate data compared to non-gifted students and less reasoning step was achieved. Also, thinking process was well delivered compared to non-gifted students. Fourth, mathematically gifted elementary students committed fewer errors in comparison with non-gifted students. Both mathematically gifted elementary students and non-gifted students made the most mistakes in solving process, however, the number of the errors was less in mathematically gifted elementary students.

• Journal of the Korean School Mathematics Society
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• v.16 no.1
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• pp.31-61
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• 2013

The purpose of this study is to confirm constructivists' assumption that when a little low level learners are taken in learner-centered instruction based on a constructivism they can also construct knowledge by themselves. To achieve this purpose, the researchers compare the effects of learner-centered instruction based on the constructivism and teacher-centered instruction based on the objective epistemology where second graders learn multiplication facts through the each treatment on learners' reasoning ability and achievement. Some conclusions are drawn from results as follows. First, learner-centered instruction based on a constructivism has significant effect on learners' reasoning ability. Second, learner-centered instruction has slightly positive effect on learners' deductive reasoning ability. Third, learner-centered instruction has more an positive influence on understanding concepts and principles of not-presented mathematical knowledge than teacher-centered instruction when implementing it with a little low level learners.

• East Asian mathematical journal
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• v.31 no.2
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• pp.145-165
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• 2015

The purpose of this study is to suggest how to go about teaching and learning secondary school algebra by analyzing problem-solving ability and problem-solving process through algebraic reasoning. In doing this, 393 students' data were thoroughly analyzed after setting up the exam questions and analytic standards. As with the test conducted with technical school students, the students scored low achievement in the algebraic reasoning test and even worse the majority tried to answer the questions by substituting arbitrary numbers. The students with high problem-solving abilities tended to utilize conceptual strategies as well as procedural strategies, whereas those with low problem-solving abilities were more keen on utilizing procedural strategies. All the subject groups mentioned above frequently utilized equations in solving the questions, and when that utilization failed they were left with the unanswered questions. When solving algebraic reasoning questions, students need to be guided to utilize both strategies based on the questions.

• The Mathematical Education
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• v.59 no.2
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• pp.113-130
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• 2020

The purpose of this study is to analyze how well middle school students understand space geometrical concept related to a cylinder. To this end, we developed the test tool based on prior research and examined 433 middle school students in November and December, 2018. And in March 2019, we interviewed 4 students who showed some type of errors. The difference in the correct answer rate of the questions by the grade and gender was tested, and the error type was analyzed based on the student's responses to the questions to evaluate the spatial reasoning ability. The results of this study are as follows. First, the difference by graders was not statistically significant in the questions evaluating spatial visual ability. On the other hand, in the case of the two questions for evaluating spatial measurement ability and spatial reasoning ability, the difference in the correct answer rate between the 7th graders and 8th is not significant, but the difference between lower graders and 9th was significant. Second, there was no significant difference in the spatial geometric ability of all girls and boys participating in this study. Third, analyzing the student's error type for an item which assessed spatial reasoning ability, we found that there are various error types in relation to visual, manipulative, and reasoning errors.

• East Asian mathematical journal
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• v.24 no.5
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• pp.527-545
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• 2008

One of the education purpose of the section "Figures" in the eighth grade is to develop students' deductive reasoning ability, which is basic and essential for living in a democratic society. However, most or middle school students feel much more difficulty or even frustration in the study of formal arguments for geometric situations than any other mathematical fields. It is owing to the big gap between inductive reasoning in elementary school education and deductive reasoning, which is not intuitive, in middle school education. Also, it is very burden for students to describe geometric statements exactly by using various appropriate symbols. Moreover, Usage of the same symbols for angle and angle measurement or segments and segments measurement makes students more confused. Since geometric relations is mainly determined by the measurements of geometric objects, students should be able to interpret the geometric properties to the algebraic properties, and vice verse. In this paper, we first compare and contrast inductive and deductive reasoning approaches to justify geometric facts and relations in school curricula. Convincing arguments are based on experiment and experience, then are developed from inductive reasoning to deductive proofs. We introduce teaching methods to help students's understanding for deductive reasoning in the textbook by using stepwise visualization materials. It is desirable that an effective proof instruction should be able to provide teaching methods and visual materials suitable for students' intellectual level and their own intuition.