• School Mathematics
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• v.13 no.1
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• pp.19-36
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• 2011

This study provides middle school students with an opportunity to construct elementary functions with dynamic geometry based on the proportion between lengths of triangle to activate students' intuition in handling elementary algebraic functions and their geometric properties. In addition, this study emphasizes the process of justification about the choice of students' construction method to improve students' deductive reasoning ability. As a result of the pilot lesson study, this paper shows the characteristics of the students' construction process of elementary functions and the roles the teacher plays in the process.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.1
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• pp.65-80
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• 2010

The aims of our study are to investigate the nature of mathematical reasoning and the teaching of mathematical reasoning in school mathematics. We analysed the process of shaping deduction in ancient Greek based on Netz's study, and discussed on the comparison between his study and Freudenthal's local organization. The result of our analysis shows that mathematical reasoning in elementary school has to be based on children's natural language and their intuitions, and then the mathematical necessity has to be formed. And we discussed on the sequences and implications of teaching of the sum of interior angles of polygon composed the discovery by induction, justification by intuition and logical reasoning, and generalization toward polygons.

• Journal of Korean Elementary Science Education
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• v.23 no.1
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• pp.61-73
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• 2004

The purpose of this study was to suggest a grounded theory on the process of undergraduate students' generating pattern-knowledge about scientific episodes. The pattern-discovery tasks were administered to seven college students majoring in elementary education. The present study found that college students show five types of procedural knowledge represented in the process of pattern-discovery, such as element, elementary variation, relative prior knowledge, predictive-pattern, and final pattern-knowledge. Furthermore, subjects used seven types of thinking ways, such as recognizing objects, recalling knowledges, searching elementary variation, predictive-pattern discovery, confirming a predictive-pattern, combining patterns, and selecting a pattern. In addition, pattern-discovering process involves a systemic process of element, elementary variation, relative prior knowledge, generating and confirming predictive-pattern, and selecting final pattern-knowledge. The processes were shown the abductive and deductive reasoning as well as inductive reasoning. This study also discussed the implications of these findings for teaching and evaluating in science education.

• Korean Journal of Logic
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• v.13 no.2
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• pp.83-116
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• 2010

In this paper we provide a teaching learning method for logic in debate, in particular, in debate of engineers. First we criticize the concept of argument and the Toulmin model on argument used in education for debate. We next provide a general method for learning arguments needed in debate. Finally, we suggest the hypothetico-inferential method and the model for inference to the best choice as argument methods coming in useful in debate education for engineers.

• Journal of The Korean Association For Science Education
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• v.41 no.5
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• pp.371-390
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• 2021

The purpose of this study is to develop a neuropsychological model for the spatial ability factor and to divide the brain active area involved in the light & shadow problem solving process into the domain-general ability and the domain-specific ability based on the neuropsychological model. Twenty-four male college students participated in the study to measure the synchronized eye movement and electroencephalograms (EEG) while they performed the spatial ability test and the light & shadow tasks. Neuropsychological model for the spatial ability factor and light & shadow problem solving process was developed by integrating the measurements of the participants' eye movements, brain activity areas, and the interview findings regarding their thoughts and strategies. The results of this study are as follows; first, the spatial visualization and mental rotation factors mainly required activation of the parietal lobe, and the spatial orientation factor required activation of the frontal lobe. Second, in the light & shadow problem solving process, participants use both their spatial ability as a domain-general thought, and the application of scientific principles as a domain-specific thought. The brain activity patterns resulting from a participants' inferring the shadow by parallel light source and inferring the shadow when the direction of the light changed were similar to the neuropsychological model for the spatial visualization factor. The brain activity pattern from inferring an object from its shadow by light from multiple directions was similar to the neuropsychological model for the spatial orientation factor. The brain activity pattern from inferring a shadow with a point source of light was similar to the neuropsychological model for the spatial visualization factor. In addition, when solving the light & shadow tasks, the brain's middle temporal gyrus, precentral gyrus, inferior frontal gyrus, middle frontal gyrus were additionally activated, which are responsible for deductive reasoning, working memory, and planning for action.

• 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 Korean Elementary Science Education
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• v.17 no.1
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• pp.47-60
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• 1998

The purpose of this study was to analyze the problem solving strategies of elementary school students and to find out correlations between the functional mental capacity, the perseveration error and the Creature Card Task solving ability. To study this purpose, four categories were selected through pilot test. The sample consisted of 231, the 4th grade students and the 5th grade students in Inchon, Korea and selected 32 students among them. Three instruments were used in this study, Creature Card Task, FIT(Figural Intersection Test) and WCST(Wisconsin Card Sorting Test). Researcher interviewed 32 students about Creature Card Task solving strategies and tests with FIT, WCST. Major findings of the study are as follows: 1. Creature Card Task solving strategies of the selected 4th & 5th grade students were different. Some students solved problems during individual interviews. 2. Creature Card Task solving abilities were significantly correlated with the functional mental capacity and the perseveration error.

• Journal of the Korean School Mathematics Society
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• v.15 no.3
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• pp.565-584
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• 2012

This study investigates how the GSP helps gifted and talented students understand geometric principles and concepts during the inquiry process in the generalization of the internal triangle, and how the students logically proceeded to visualize the content during the process of generalization. Four mathematically gifted students were chosen for the study. They investigated the pattern between the area of the original triangle and the area of the internal triangle with the ratio of each sides on m:n respectively. Digital audio, video and written data were collected and analyzed. From the analysis the researcher found four results. First, the visualization used the GSP helps the students to understand the geometric principles and concepts intuitively. Second, the GSP helps the students to develop their inductive reasoning skills by proving the various cases. Third, the lessons used GSP increases interest in apathetic students and improves their mathematical communication and self-efficiency.

• School Mathematics
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• v.19 no.1
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• pp.153-170
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• 2017

This study conducted an analysis of types of reasoning shown in students' solving a problem and processes of students' reasoning according to type of problem by posing an open-ended problem where students' reasoning activity is expected to be vigorous and a multiple-choice problem with which students are familiar. And it examined teacher's role of promoting the reasoning in solving an open-ended problem. Students showed more various types of reasoning in solving an open-ended problem compared with multiple-choice problem, and showed a process of extending the reasoning as chains of reasoning are performed. Abduction, a type of students' probable reasoning, was active in the open-ended problem, accordingly teacher played a role of encouragement, prompt and guidance. Teachers posed a problem after varying it from previous problem type to open-ended problem in teaching and evaluation, and played a role of helping students' reasoning become more vigorous by proper questioning when students had difficulty reasoning.

• Journal of the Korean earth science society
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• v.26 no.8
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• pp.751-758
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• 2005

The purpose of this study was to develop an inquiry analysis framework based on the features of earth science inquiry methodology and to analyze inquiry activities in the 8th grade 'Earth History and Diastrophism' unit by using this framework. The framework classified earth science methods as logical inference, hermeneutic, and historical methods, each of which was subdivided in consideration of its subordinate methods and characteristics. The analysis revealed that the logical inference method reflected in the unit as the 'abductive method' (70%) was used more frequently than the 'inductive' (23%) and 'deductive' (22%) methods. The hermeneutic method was found in terms of the 'forestructures of understanding' (92%), 'circular reasoning' (9%). and 'historical nature of human understanding' (17%). The historical method also used as the 'constructing proper taxonomy' (53%), 'adhering to the modem principle of uniformitarianism' (47%), and 'relic interpretation' (41%) were identified with ratios more fester than those for the 'place substituting for time in stage theorizing' (3%) and 'evaluating independent lines of inquiry for convergence' (3%).