• Journal for History of Mathematics
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• v.34 no.6
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• pp.195-204
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• 2021

Mathematical induction is one of the deductive methods used for proving mathematical theorems, and also used as an inductive method for investigating and discovering patterns and mathematical formula. Proper understanding of the mathematical induction provides an understanding of deductive logic and inductive logic and helps the developments of algorithm and data science including artificial intelligence. We look at the origin of mathematical induction and its usage and educational aspects.

• Journal of the Korean School Mathematics Society
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• v.20 no.4
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• pp.405-422
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• 2017

Nim games were divided into three stages : one file, two files and three files game, and inquiry activities were conducted for middle school mathematically gifted students. In the first stage, students easily found a winning strategy through deductive reasoning. In the second stage, students found a winning strategy with deductive reasoning or inductive reasoning, but found an error in inductive reasoning. In the third stage, no students found a winning strategy with deductive reasoning and errors were found in the induction reasoning process. It is found that the tendency to unconditionally generalize the pattern that is formed in the finite number of cases is the cause of the error. As a result of visually presenting the binary boxes to students, students were able to easily identify the pattern of victory and defeat, recognize the winning strategy through game activities, and some students could reach a stage of justifying the winning strategy.

• Journal of The Korean Association of Information Education
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• v.22 no.5
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• pp.575-583
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• 2018

This study approached EPL learning with deductive teaching and learning methods and inductive teaching and learning methods which are grammar teaching and learning methods. In the entry site, lectures provided for elementary school students in grades 5 to 6 were set as deductive learning courses. Based on this, inductive learning process was developed and each learning process was composed of 12 periods. After conducting the research, EPL utilization evaluation, learning satisfaction and immersion test were conducted between the two groups. It was difficult to obtain statistically meaningful results between the two groups. However, in the three tests, the mean value of groups using inductive teaching and learning methods was high. If we construct a long-term learning process and conduct research, we think that statistically meaningful results are produced between the two groups.

• The KIPS Transactions:PartC
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• v.10C no.6
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• pp.717-726
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• 2003

In this paper, we analyze the associated rule based deductive algorithm which creates the rules automatically for intrusion detection from the vast packet data. Based on the result, we also suggest the deductive algorithm which creates the rules of intrusion pattern fast in order to apply the intrusion detection systems. The deductive algorithm proposed is designed suitable to the concept of clustering which classifies and deletes the large data. This algorithm has direct relation with the method of pattern generation and analyzing module of the intrusion detection system. This can also extend the appication range and increase the detection speed of exiting intrusion detection system as the rule database is constructed for the pattern management of the intrusion detection system. The proposed pattern generation technique of the deductive algorithm is used to the algorithm is used to the algorithm which can be changed by the supporting rate of the data created from the intrusion detection system. Fanally, we analyze the possibility of the speed improvement of the rule generation with the algorithm simulation.

• Journal of Science Education
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• v.43 no.1
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• pp.79-93
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• 2019

There have been great concerns on induction, deduction, abduction, and hypothetical deductive method as scientific method and logic behind the method. However, as seen from the similar logic structure of abduction and hypothetical deductive method logic, distinction of those four terms could be unclear. This study investigates statements of science instruction textbooks concerning those terms to analyze their meaning as scientific method or in the context of inquiry. For this purpose, related statements are extracted from seven textbooks to investigate the definitions and examples of those terms and relation among these terms by focusing on coherence of usage of the terms and the possibility of clear distinction among the terms. We find that those terms do not have coherent meanings in the textbooks and many statements make it hard to distinguish the meanings of the terms. Finally the origin of the confusion and educational implication is discussed.

• Journal of the Korean School Mathematics Society
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• v.24 no.3
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• pp.261-282
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• 2021

This study identified the meaning of mathematical justification and its characteristics for middle school math gifted students. 17 middle school math gifted students participated in questionnaires and written exams. Results show that the gifted students recognized justification in various meanings such as proof, systematization, discovery, intellectual challenge of mathematical justification, and the preference for deductive justification. As a result of justification exams, there was a difference in algebra and geometry. While there were many deductive justifications in both algebra and geometry questionnaires, the difference exists in empirical justifications: there were many empirical justifications in algebra, but there were few in geometry questions. When deductive justification was completed, the students showed satisfaction with their own justification. However, they showed dissatisfaction when they could not deductively justify the generality of the proposition using mathematical symbols. From the results of the study, it was found that justification education that can improve algebraic translation ability is necessary so that gifted students can realize the limitations and usefulness of empirical reasoning and make deductive justification.

• Journal of The Korean Association For Science Education
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• v.27 no.3
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• pp.169-179
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• 2007

We investigated the effects of hypothetical deductive experiment on students' views about the nature of science (NOS). Participants were 212 eighth graders from a middle school and they were assigned to a control group and an experimental group. Students of the control group did guided experiment in small group and students of the experimental group did hypothetical deductive experiment in small group. The results revealed that both students of the control group and the experimental group possessed similar views about NOS in a pretest. But the experimental group exhibited more sophisticated views about the theory of dependance of observation, scientific reasoning and hypothesis in the posttest. Students who used mainly surface learning strategy within the experimental group exhibited more sophisticated views about hypothesis in the posttest. On the other hand, students who used mainly deep learning strategy within the experimental group exhibited more sophisticated views about the theory of dependance of observation, scientific reasoning and hypothesis in the posttest.

• Journal of The Korean Association For Science Education
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• v.27 no.3
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• pp.225-234
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• 2007

This research was conducted with an intention to develop a teaching program that possesses a goal of elevating higher thinking ability within the science class and to investigate its effect. The hypothetico-deductive teaching model was developed and its' program was designed to be directly put into the practical use, and apply it in class. The application of the hypothetico-deductive teaching program had a positive effect in the improvement of students' creative thinking ability and critical thinking ability. And it had a positive influence on scientific attitudes. After completing the program the opinions of the students who participated in this research by a poll were gathered and analyzed. The students felt uneasy and had a lot of difficulties during the program activity because they had to keep on thinking newly, critically, and scientifically, but they admitted that they gained the ability to think on their own when the program was completed.

• Research in Mathematical Education
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• v.18 no.3
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• pp.171-185
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• 2014

Mathematically deductive reasoning skill is one of the major learning objectives stated in senior secondary curriculum (CDC & HKEAA, 2007, page 15). Ironically, student performance during routine assessments on geometric reasoning, such as proving geometric propositions and justifying geometric properties, is far below teacher expectations. One might argue that this is caused by teachers' lack of relevant subject content knowledge. However, recent research findings have revealed that teachers' knowledge of teaching (e.g., Ball et al., 2009) and their deductive reasoning skills also play a crucial role in student learning. Prior to a comprehensive investigation on teacher competency, we use a case study to investigate teachers' knowledge competency on how to teach their students to mathematically argue that, for example, two triangles are congruent. Deductive reasoning skill is essential to geometry. The initial findings indicate that both subject and pedagogical content knowledge are essential for effectively teaching this challenging topic. We conclude our study by suggesting a method that teachers can use to further improve their teaching effectiveness.

• Journal of The Korean Association For Science Education
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• v.38 no.6
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• pp.839-851
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• 2018

The purpose of this study is to analyze the science reasoning differences of elementary school students' science writing. For this purpose, science writing activities and analysis frameworks were developed. Science writing data were collected and analyzed. Third to sixth grade elementary students were selected from a middle high level elementary school in terms of a national achievement test in Seoul. A total of 320 writing materials were analyzed. The results of the analysis were as follows. Science writings show science reasoning at 52 % for $3^{rd}$ grade, 68% for $4^{th}$ grade, 85% for $5^{th}$ grade, and 89% for $6^{th}$ grade. Three types of scientific reasoning such as inductive reasoning, deductive reasoning, and abductive reasoning appeared in science writing of the third to sixth graders. The abductive reasoning appeared very low in comparing with inductive and deductive reasoning. Level three appeared the most frequently in the science writing of the elementary students. The levels of inductive and deductive reasoning in science writing increased according to increasing grade and showed statistical differences between grades. But the levels of abductive reasoning did not show an increasing aspect according to increasing grade and also did not show statistical differences between grades. The levels of inductive reasoning and deductive reasoning of the 3rd grade was very low in comparing with the other grades.