• Education of Primary School Mathematics
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• v.2 no.2
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• pp.113-131
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• 1998

The purpose of this study is to investigate the relationships among affective characteristics, mathematical problem-solving abilities, and reasoning abilities of the 6th graders for mathematics, and to analyze whether the relationships have any differences according to the regions, which the subjects live. The results are as follows： First, self-awareness is the most important factor which is related mathematical problem-solving abilities and reasoning abilities, and learning habit and deductive reasoning ability have the most strong relationships. Second, for the relationships between problem-solving abilities and reasoning abilities, inductive reasoning ability is more related to problem-solving ability than deductive reasoning ability Third, for the regions, there is a significant difference between mathematical abilities and deductive reasoning abilities of the subjects.

• Education of Primary School Mathematics
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• v.19 no.2
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• pp.161-175
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• 2016

The purpose of this study is to measure the differences in affective characteristics and mathematical reasoning ability between gifted students and non-gifted students. This study compares and analyzes on the relations between the affective characteristics and mathematical reasoning ability. The study subjects are comprised of 97 gifted fifth grade students and 144 non-gifted fifth grade students. The criterion is based on the questionnaire of the affective characteristics and mathematical reasoning ability. To analyze the data, t-test and multiple regression analysis were adopted. The conclusions of the study are synthetically summarized as follows. First, the mathematically gifted students show a positive response to subelement of the affective characteristics, self-conception, attitude, interest, study habits. As a result of analysis of correlation between the affective characteristic and mathematical reasoning ability, the study found a positive correlation between self-conception, attitude, interest, study habits but a negative correlation with mathematical anxieties. Therefore the more an affective characteristics are positive, the higher the mathematical reasoning ability are built. These results show the mathematically gifted students should be educated to be positive and self-confident. Second, the mathematically gifted students was influenced with mathematical anxieties to mathematical reasoning ability. Therefore we seek for solution to reduce mathematical anxieties to improve to the mathematical reasoning ability. Third, the non-gifted students that are influenced of interest of the affective characteristics will improve mathematical reasoning ability, if we make the methods to be interested math curriculum.

• Journal of Elementary Mathematics Education in Korea
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• v.22 no.4
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• pp.497-516
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• 2018

The purpose of this study is to compare the process of mathematical modeling in mathematical modeling class according to group organization, and to investigate whether it shows improvement in mathematical reasoning ability. A total of 24 classes with 3 mathematical modeling activities were designed to investigate the research problem. The result of this study showed that the heterogeneous groups performed better than the homogeneous groups in terms of both the performance ability of mathematical modeling and mathematical reasoning ability. This study implies that, with respect to group design for applying mathematical modeling in teaching mathematics, heterogeneous group design would be more efficient than homogeneous group design.

• The Mathematical Education
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• v.60 no.2
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• pp.133-157
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• 2021

Ill-structured problems have drawn attention in that they can enhance problem-solving skills, which are essential in future societies. The purpose of this study is to analyze and evaluate students' spatial reasoning(Intrinsic-Static, Intrinsic-Dynamic, Extrinsic-Static, and Extrinsic-Dynamic reasoning) and problem solving abilities(understanding problems and exploring strategies, executing plans and reflecting, collaborative problem-solving, mathematical modeling) that appear in ill-structured problem-solving. To solve the research questions, two ill-structured problems based on the geometry domain were created and 11 lessons were given. The results are as follows. First, spatial reasoning ability of sixth-graders was mainly distributed at the mid-upper level. Students solved the extrinsic reasoning activities more easily than the intrinsic reasoning activities. Also, more analytical and higher level of spatial reasoning are shown when students applied functions of other mathematical domains, such as computation and measurement. This shows that geometric learning with high connectivity is valuable. Second, the 'problem-solving ability' was mainly distributed at the median level. A number of errors were found in the strategy exploration and the reflection processes. Also, students exchanged there opinion well, but the decision making was not. There were differences in participation and quality of interaction depending on the face-to-face and web-based environment. Furthermore, mathematical modeling element was generally performed successfully.

• Education of Primary School Mathematics
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• v.9 no.1 s.17
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• pp.43-58
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• 2005

The objective of the present study was designed to examine that metacognition education had any promoting effects on the development of students' reasoning ability. Two classes in the 5th grade were asked to participated for the present study. Prior to the metacognition teaching, both the experimental and control group classes were given to the preliminary test in which students' basic ability for mathematical reasoning was graded. Then, the students in the experimental group were given 8hour teaching for the topics on the symmetric properties of geometric figures. The present findings indicate that educational application which motivates metacognition can improve mathematical reasoning ability in elementary students. It is widely accepted that metacognition is an active and conscious mental activity, helps the students perceive voluntarily the study items, and further plays an important role in constructing independent and active thinking processes. Accordingly, the present results implicate that the practical performance of metacognition education into the class indeed contributes to build up or strengthen students' voluntary ways of reasoning.

• Education of Primary School Mathematics
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• v.9 no.2 s.18
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• pp.75-87
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• 2005

For Probabilistic Reasoning Ability is useful to predict uncertain fact from information, it's getting more important. But when we consider the actual condition of teaching Probabilistic Reasoning Ability, it doesn't correspond with its importance. So the purpose of this study is, by developing Basic Contents of Probabilistic Reasoning Teaching; by developing and applying Probabilistic Reasoning Teaching Program, to study how the application of it effects the progress of the student's Probabilistic Reasoning Ability.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.2
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• pp.401-420
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• 2010

The purpose of this research is to find out effectiveness of geometry learning through spatial reasoning activities on mathematical problem solving ability and mathematical attitude. In order to proof this research problem, the controlled experiment was done on two groups of 6th graders in N elementary school; one group went through the geometry learning style through spatial reasoning activities, and the other group went through the general geometry learning style. As a result, the experimental group and the comparing group on mathematical problem solving ability have statistically meaningful difference. However, the experimental group and the comparing group have not statistically meaningful difference on mathematical attitude. But the mathematical attitude in the experimental group has improved clearly after all the process of experiment. With these results we came up with this conclusion. First, the geometry learning through spatial reasoning activities enhances the ability of analyzing, spatial sensibility and logical ability, which is effective in increasing the mathematical problem solving ability. Second, the geometry learning through spatial reasoning activities enhances confidence in problem solving and an interest in mathematics, which has a positive influence on the mathematical attitude.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.1
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• pp.105-129
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• 2016

The elements of mathematical processes include mathematical reasoning, mathematical problem-solving, and mathematical communications. Proportion reasoning is a kind of mathematical reasoning which is closely related to the ratio and percent concepts. Proportion reasoning is the essence of primary mathematics, and a basic mathematical concept required for the following more-complicated concepts. Therefore, the study aims to analyze the proportion reasoning ability of sixth graders of primary school who have already learned the ratio and percent concepts. To allow teachers to quickly recognize and help students who have difficulty solving a proportion reasoning problem, this study analyzed the characteristics and patterns of proportion reasoning of sixth graders of primary school. The purpose of this study is to provide implications for learning and teaching of future proportion reasoning of higher levels. In order to solve these study tasks, proportion reasoning problems were developed, and a total of 22 sixth graders of primary school were asked to solve these questions for a total of twice, once before and after they learned the ratio and percent concepts included in the 2009 revised mathematical curricula. Students' strategies and levels of proportional reasoning were analyzed by setting up the four different sections and classifying and analyzing the patterns of correct and wrong answers to the questions of each section. The results are followings; First, the 6th graders of primary school were able to utilize various proportion reasoning strategies depending on the conditions and patterns of mathematical assignments given to them. Second, most of the sixth graders of primary school remained at three levels of multiplicative reasoning. The most frequently adopted strategies by these sixth graders were the fraction strategy, the between-comparison strategy, and the within-comparison strategy. Third, the sixth graders of primary school often showed difficulty doing relative comparison. Fourth, the sixth graders of primary school placed the greatest concentration on the numbers given in the mathematical questions.

• Education of Primary School Mathematics
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• v.24 no.1
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• pp.43-69
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• 2021

The purpose of this study is to confirm the influences of learner-centered instruction on learners' achievement and reason ability. In order to accomplish them, the fraction unit and the polygonal unit in the fourth grade were implemented with teaching methods and materials suitable for learner-centered mathematics instruction. Some conclusions could be drawn from the results as follows: First, learner-centered mathematics instruction has a more positive effect on learning of learned knowledge and generating unlearned knowledge in the experimental period than teacher-centered instructions. Second, learner-centered instruction makes an influence of low learning ability on getting achievement positively. Third, as the experimental treatment is repeated, learner-centered instruction has a positive effect on students' reasoning ability. The reasoning ability of students showed a difference in the comparison between the experimental group and the comparative group, and within the experimental group, there was a positive effect of the extension of the positive reasoning ability. Fourth, it can be estimated that the development of students' reasoning ability interchangeably affected their generation test results.

• School Mathematics
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• v.15 no.4
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• pp.785-799
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• 2013

The researchers developed the teaching-learning materials for 9th grade mathematically gifted students in terms of the hypothesis that the students would have opportunity for problem solving and develop various mathematical thinking through the mathematical modeling lessons. The researchers analyzed what mathematical thinking abilities were shown on each stage of modeling process through the application of the materials. Organization of information ability appears in the real-world exploratory stage. Intuition insight ability, spatialization/visualization ability, mathematical reasoning ability and reflective thinking ability appears in the pre-mathematical model development stage. Mathematical abstraction ability, spatialization/visualization ability, mathematical reasoning ability and reflective thinking ability appears in the mathematical model development stage. Generalization and application ability and reflective thinking ability appears in the model application stage. The developed modeling assignments have provided the opportunities for mathematically-gifted students' mathematical thinking ability to develop and expand.