• 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.

• 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.

• Proceedings of the Safety Management and Science Conference
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• 2010.11a
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• pp.27-33
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• 2010

The paper proposes the guidelines of application and interpretation for quality and reliability methodologies using deductive or inductive reasoning. The research also reviews Bayesian quality and reliability tools by deductive prior function and inductive posterior function.

• 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.

• Journal of The Korean Association For Science Education
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• v.34 no.4
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• pp.375-383
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• 2014

The purpose of this study is to find out how middle school students evaluate scientific information in terms of hypothetico-deductive reasoning. A total of 66 middle school students completed a paper-and-pencil test on scientific information evaluation and 14 of them were individually interviewed for triangulation. The test includes six topics related to scientific or pseudoscientific information, and questions about each topic were sequenced based on a hypothetico-deductive reasoning. The hypothetico-deductive process consists of three steps: identifying predictions made by explanations in the information, identifying data actually obtained, and determining the fit between predictions and data to judge the validity of the explanations. Data analyses have focused on students' response types at each step, whether students used hypoethetico-deductive reasoning, and students' preference to evidence types in making decisions. The middle school students in this study answered the questions in various ways based on how they used the information given or personal knowledge and beliefs. A small portion of students evaluated information based on hypothetico-deductive reasoning. These students tended to give priority to scientific data in determining the validity of the information. On the other hand, students who did not use hypoethetico-deductive reasoning tended to prefer first-hand experience in the decision. The results provide implications for science lessons and the curriculum for scientific literacy. Further research should include student evaluation of the validity of data and other types of reasoning.

• 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 Korean Elementary Science Education
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• v.37 no.4
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• pp.372-390
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• 2018

The purpose of this research is to know the scientific reasoning ability of elementary students. In order to find it, 320 elementary students wrote a report about germination of the 700 or 2,000 years old seeds. Their writings were analyzed by scientific writing analysis frameworks, Scientific Reasoning Types and Scientific Reasoning Level Criteria developed by Lim (2018). Minto Pyramid Principles was used to show statements and relations of statements related to scientific reasoning. This paper showed scientific reasoning statements of elementary students about germination of seeds. The characteristics of scientific reasoning of elementary students were as follows. In the process of logical writing by the types of scientific reasoning, many students showed various characteristics and different levels. In the writings based on inductive reasoning, they did not distinguish between common features and differences of cases, and did not derive the rules based on common features and differences of the cases. In the writings based on deductive reasoning, there were cases where the major premise corresponding to the principle or rule was omitted and only the phenomenon was described, or the rule was presented but not connected with the case. In the writings based on abductive reasoning, the ability to selectively use the background knowledge related to the question situation was not sufficient, and borrowing of similar background knowledge, which was commonly used in other situations, was very rare.

• Journal of Educational Research in Mathematics
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• v.13 no.2
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• pp.159-178
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• 2003

This study analyzes on the reasoning in the process of justification and mathematical problem solving in our primary mathematics textbooks. In our analyses, we found that the inductive reasoning based on the paradima-tic example whose justification is founnded en a local deductive reasoning is the most important characteristics in our textbooks. We also found that some propositions on the properties of various quadrangles impose a deductive reasoning on primary students, which is very difficult to them. The inductive reasoning based on enumeration is used in a few cases, and analogies based on the similarity between the mathematical structures and the concrete materials are frequntly found. The exposition based en a paradigmatic example, which is the most important characteristics, have a problematic aspect that the level of reasoning is relatively low In Miyazaki's or Semadeni's respects. And some propositions on quadrangles is very difficult in Piagetian respects. As a result of our study, we propose that the level of reasoning in primary mathematics is leveled up by degrees, and the increasing levels are following: empirical justification on a paradigmatic example, construction of conjecture based on the example, examination on the various examples of the conjecture's validity, construction of schema on the generality, basic experiences for the relation of implication.

• Journal of Korean Elementary Science Education
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• v.25 no.spc5
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• pp.567-581
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• 2007

This study examined patterns of reasoning of both the scientifically-gifted and children of average ability as witnessed in their science problem solving skills. Science problem solving skills are one of the significant characteristics of scientifically gifted children, and by using methods such as individual interviews, inductive reasoning, abductive reasoning, and deductive reasoning, the characteristics of these children can be to be further explored and categorized. The study also compared the findings with those of average children. This study sought to determine efficient guidelines fur teaching the scientifically-gifted, to come up with basic materials for developing relevant programs, and to find suggestions for identifying such students. The results of the study are as follows: Firstly, the creative science problem solving skills of the scientifically-gifted were better than that of the average students. Secondly, all of the three reasoning patterns used revealed in creative science solving processes were different between the gifted and the average, especially in terms of abductive reasoning, which was proved to reveal the greatest distinction between the two groups.

• 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.