• Communications of Mathematical Education
• /
• v.24 no.2
• /
• pp.325-344
• /
• 2010

The purpose of this study is to investigate what influences students' preferences on empirical and deductive proofs and find their relations. Although empirical and deductive proofs have been seen as a significant aspect of school mathematics, literatures have indicated that students tend to have a preference for empirical proof when they are convinced a mathematical statement. Several studies highlighted students'views about empirical and deductive proof. However, there are few attempts to find the relations of their views about these two proofs. The study was conducted to 47 students in 7~9 grades in the transition from empirical proof to deductive proof according to their mathematics curriculum. The data was collected on the written questionnaire asking students to choose one between empirical and deductive proofs in verifying that the sum of angles in any triangles is $180^{\circ}$. Further, they were asked to provide explanations for their preferences. Students' responses were coded and these codes were categorized to find the relations. As a result, students' responses could be categorized by 3 factors; accuracy of measurement, representative of triangles, and mathematics principles. First, the preferences on empirical proof were derived from considering the measurement as an accurate method, while conceiving the possibility of errors in measurement derived the preferences on deductive proof. Second, a number of students thought that verifying the statement for three different types of triangles -acute, right, obtuse triangles - in empirical proof was enough to convince the statement, while other students regarded these different types of triangles merely as partial examples of triangles and so they preferred deductive proof. Finally, students preferring empirical proof thought that using mathematical principles such as the properties of alternate or corresponding angles made proof more difficult to understand. Students preferring deductive proof, on the other hand, explained roles of these mathematical principles as verification, explanation, and application to other problems. The results indicated that students' preferences were due to their different perceptions of these common factors.

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

• Journal of Science Education
• /
• v.43 no.1
• /
• pp.79-93
• /
• 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 Association For Science Education
• /
• v.25 no.3
• /
• pp.327-335
• /
• 2005

This study investigates student achievement and science-related attitudes on STS hypothetical deductive instruction strategy in the water section of high school chemistry. Two 11th grade co-ed high school classes participated in the study; one control group and one treatment group. After being taught for 10 class periods during the second semester. ANCOVA analysis revealled no significant difference (p>.05) between two groups' achievement tests. However, analysis by ANCOVA did show that the scores for science-related attitudes in the treatment group were significantly higher than those of the control group (p<.05). In particular, the scores of science learning contents and science value about science-related attitude were significantly higher in the treatment group.

• Korean Journal of Logic
• /
• v.3
• /
• pp.53-93
• /
• 2000

프레게의 논리주의 프로그램은 기본적인 산수 법칙 혹은 가장 단순한 수의 법칙을 논리적 원리로부터 유도해 냄으로써 달성된다. 프레게는 이른바 외연 공리를 포함하는 논리적 원리로부터 흄의 원리로 지칭되는 원리를 거쳐 '기본적인' 산수 법칙을 이끌어내고 있다. 외연 공리가 흄의 원리를 연역하는 과정에서만 사용되고 인다는 사실은 프레게가 말하는 기본적인 산수 법칙을 외연 공리 대신 흄의 원리를 공리로 채택함으로써 유도해낼 수 있음을 암시한다. 여기서는 흄의 원리로부터 페아노의 다섯 가지 공리를 연역해 내는 프레게의 과정을 조상 관계에 대한 일반적인 고찰에 기초하여 보다 단순화하고 있다.

• Journal for History of Mathematics
• /
• v.20 no.2
• /
• pp.47-58
• /
• 2007

In this paper, we shall try to give a comparative study of mathematics developments in ancient Greece and ancient Oriental mathematics. We have found that the Oriental Mathematics. is quantitative, computational and algorithmetic, but the ancient Greece is axiomatic and deductive mathematics in character. The two region mathematics should be unified to give impetus to further development of mathematics in future times.

• Journal of The Korean Association For Science Education
• /
• v.33 no.1
• /
• pp.181-192
• /
• 2013

This study aims to explore scientific reasoning that students and their teachers constructed in elementary science classroom discourses in terms of basic reasoning types; deduction, induction, and abduction. For this research, data were collected from 13 classes of 4th grade science activities during a period of three months and analyzed three types of scientific reasoning in elementary school science discourses. We found that deduction (one discourse segment), induction (one discourse segment), and deduction-abduction (two discourse segments) were presented in the discourses. They showed that: first, scientific reasoning proceeded explicitly or implicitly in elementary science discourses; second, the students and their teachers have potentials to increase the quality of reasoning depending on their inter-subjectivity; and last, the students' background knowledge were very important in the development of their reasoning. Implication and remarks on science education and research were presented based on this results as well.

• Journal of Korean Elementary Science Education
• /
• v.42 no.1
• /
• pp.109-126
• /
• 2023

In this study, I took the evidence-explanation (E-E) continuum perspective to examine the epistemological implications of scientific reasoning cases designed by preservice elementary teachers during their simulation teaching. The participants were four preservice teachers who conducted simulation instruction on the seasons and high/low air pressure and wind. The selected discourse episodes, which included cases of inductive, deductive, or abductive reasoning, were analyzed for their epistemological implications-specifically, the role played by the reasoning cases in the E-E continuum. The two preservice teachers conducting seasons classes used hypothetical-deductive reasoning when they identified evidence by comparing student-group data and tested a hypothesis by comparing the evidence with the hypothetical statement. However, they did not adopt explicit reasoning for creating the hypothesis or constructing a model from the evidence. The two preservice teachers conducting air pressure and wind classes applied inductive reasoning to find evidence by summarizing the student-group data and adopted linear logic-structured deductive reasoning to construct the final explanation. In teaching similar topics, the preservice teachers showed similar epistemic processes in their scientific reasoning cases. However, the epistemological implications of the instruction were not similar in terms of the E-E continuum. In addition, except in one case, the teachers were neither good at abductive reasoning for creating a hypothesis or an explanatory model, nor good at using reasoning to construct a model from the evidence. The E-E continuum helps in examining the epistemological implications of scientific reasoning and can be an alternative way of transmitting scientific reasoning.

• School Mathematics
• /
• v.15 no.4
• /
• pp.667-682
• /
• 2013

Though teachers' lesson plays, this article analysed teachers' knowledge for mathematical teaching about mathematical definitions and their pedagogical difficulties in teaching defining. Although the participant teachers didn't transmit definitions to students and suggested possible definitions of the given geometric figure in their imaginary lessons, they didn't teach defining as deductive organization of properties of the geometric figure. They considered mathematical definition as a mere linguistic convention of a word, so they couldn't appreciate the necessity of deductive organization in teaching definitions, and the arbitrary nature of mathematical definitions. Therefore, for learning to teach definitions differently, it is necessary for teachers to reflect the gap between the everyday and mathematical definitions in teachers'education.

• The KIPS Transactions:PartD
• /
• v.9D no.6
• /
• pp.991-998
• /
• 2002

With the advent of XML and database languages armed with the object-oriented concept and deductive logic, the problem of efficient query processing for them has become a major issue. We describe a way of processing semi-structured XML data through an implementation of a Deductive and Object-oriented Database (DOODB) language with the explanation of query processing. We have shown how to convert an XML data model to a DOODB data model. We have then presented an efficient query processing method based on Connection Graph Resolution. We also present a knowledge-based query processing method that uses the homomorphism of objects in the database and the associative rule of substitutions.