• Journal of Educational Research in Mathematics
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• v.12 no.2
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• pp.181-192
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• 2002

There are various methods of proving a proposition. Among these, 'mathematical induction' is treated in school mathematics weightly. But many students have difficulty with the proof by 'mathematical induction'. To solve this problem, analysis needs to be attempted in various aspects This study attempts to compare the teaching methods of 'mathematical induction' in South and North Korea and to acquire the implication. In fact, many differences between South and North Korea are found. These differences are caused by epistemological and psychological premise. Therefore this study investigates the epistemological and psychological aspects in North Korea and compares the textbooks in South and North Korea. Through this study, some implications are found. First, the sequence of introducing the 'mathematical Induction' needs to be considered. Second, the rich context of applying the 'mathematical induction' is needed. Finally, disagreement between curriculum and textbook in South Korea needs to be reconsidered.

• Journal of Educational Research in Mathematics
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• v.9 no.1
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• pp.217-228
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• 1999

The fundamental theorem of calculus is the most 'fundamental' content in teaching calculus. Since the aim of teaching the theorem goes beyond simple application of it, it is difficult to teach it meaningfully. Hence, for the meaningful teaching of the fundamental theorem of calculus, this article seeks to find the educational implication of the fundamental theorem of calculus through reviewing the genetic history of it. A genetic history of the fundamental theorem of calculus can be divided into the following five phases: 1. The deductive discovery of the fundamental theorem of calculus 2. Galileo's Law of falling body and the idea of the fundamental theorem of calculus 3. The discovery of the fundamental theorem of calculus and Barrow's proof 4. Newton's mensuration 5. the development of calculus in 19th century and the fundamental theorem of calculus The developmental phases of the fundamental theorem of calculus discussed above provides the three educational implications. first, we can rediscover this theorem through deductive methods and get the ideas of it in relation to kinetic problems. Second, the developmental phases of the fundamental theorem of calculus shows that the value of this theorem lies in the harmony of its theoretical beauty and practicality. Third, Newton's dynamic image of this theorem can be a typical way of understanding the theorem. We have different aims of teaching the fundamental theorem of calculus, according to which the teaching methods can be adopted. But it is self-evident that the simple application of the theorem is just a part of teaching the fundamental theorem of calculus. Hence we must try to put the educational implications reviewed above into practice.

• 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.

• Communications of Mathematical Education
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• v.19 no.4 s.24
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• pp.699-713
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• 2005

In this paper, we attempted to find out the meaning of several means and inequalities, their relationships and proposed the effective ways to teach them in college mathematics classes. That is, we introduced 8 proofs of arithmetic-geometric mean equality to explain the fact that there exist diverse ways of proof. The students learned the diverseproof-methods and applied them to other theorems and projects. From this, we found out that the attempt to develop the students' logical thinking ability by encouraging them to find out diverse solutions of a problem could be a very effective education method in college mathematics classes.

• School Mathematics
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• v.11 no.1
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• pp.39-53
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• 2009

This study was conducted in 2008 with 80 in-service mathematics teachers. We took a course that was consisted of a lecture and a practice on Socrates' method. In our study, mathematics teachers conducted making a teaching plan by using Socrates' method. But we became know that we need to offer concrete ideas or examples for mathematics teachers in order to apply Socrates' method effectively. Therefore we tried to search for educational methods in using Socrates' method to teach school mathematics. After investigating of preceding researches, we selected some examples. On the basis of these examples, we suggested concrete methods in using Socrates' method. That is as follows. Socrates' method need to be used in the context mathematical problem solving. Socrates' method can be applied in the process of overcoming cognitive obstacles. A question in using Socrates' method have to guide mathematical thinking (or attitude). When we use Socrates' method in the teaching of a proof, student need to have an opportunity to guess the conclusion of a proposition. The process of reflection revision-improvement can be connected to using Socrates' method.

• Safety and Health at Work
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• v.4 no.2
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• pp.100-104
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• 2013

Background: The aim of this study was to assess public and private medical diagnostic laboratories in Nigeria for the presence of biosafety equipment, devices, and measures. Methods: A total of 80 diagnostic laboratories in biosafety level 3 were assessed for the presence of biosafety equipment, devices, and compliance rate with biosafety practices. A detailed questionnaire and checklist was used to obtain the relevant information from enlisted laboratories. Results: The results showed the presence of an isolated unit for microbiological work, leak-proof working benches, self-closing doors, emergency exits, fire extinguisher(s), autoclaves, and hand washing sinks in 21.3%, 71.3%, 15.0%, 1.3%, 11.3%, 82.5%, and 67.5%, respectively, of all laboratories surveyed. It was observed that public diagnostic laboratories were significantly more likely to have an isolated unit for microbiological work (p = 0.001), hand washing sink (p = 0.003), and an autoclave ($p{\leq}0.001$) than private ones. Routine use of hand gloves, biosafety cabinet, and a first aid box was observed in 35.0%, 20.0%, and 2.5%, respectively, of all laboratories examined. Written standard operating procedures, biosafety manuals, and biohazard signs on door entrances were observed in 6.3%, 1.3%, and 3.8%, respectively, of all audited laboratories. No biosafety officer(s) or records of previous spills, or injuries and accidents, were observed in all diagnostic laboratories studied. Conclusion: In all laboratories (public and private) surveyed, marked deficiencies were observed in the area of administrative control responsible for implementing biosafety. Increased emphasis on provision of biosafety devices and compliance with standard codes of practices issued by relevant authorities is strongly advocated.

• Journal of Educational Research in Mathematics
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• v.11 no.2
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• pp.307-320
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• 2001

Traditionally, there are many inherent restrictions in highschool mathematics textbooks. They are restricted in its contents and inevitably resorted to reader's ability of intuition. So they are usually lacked logical precisions and have various differences in expressions. We are mainly concerned with the definite integral and its applications in current highschool mathematics II textbooks according to 6th curriculum. We choose 6 of them arbitrarily and survey by comparison to deduce some controversial topics among them as follows. 1) absurd metaphors in formula process 2) confusions in important notations and too much choices in terms and statements. 3) lack of precisions in - teaching hierarchy (between some contents of Physics and the applications of definite integral) - introducing a proof of theorem (fundamental theorem of Calculus I) - introducing the methods (integral substitutions 1, ll) 4) adopting small topics such as - mean value theorem of integral - integrals with variable limits. In coming 7th curriculum, highschool students in Korea are supposed to choose calculus as a whole, independent course. So we hope that the suggested controversial topics are to be referred by authors to improve the preceding Mathematics ll textbooks and for teachers to use them for better mathematics education.

• International Journal of Computer Science & Network Security
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• v.23 no.12
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• pp.167-174
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• 2023

Electronic educational environments in the conditions of quarantine restrictions of COVID-19 have become a common phenomenon for the organization of distance educational activities. Under the conditions of Russian aggression, Ukrainian proof of their use is unique. The purpose of the article is to analyze the role of electronic educational environments in the process of training applicants for higher education in Ukraine in the realities of a large-scale war. General scientific methods (analysis, synthesis, deduction, and induction) and special pedagogical prognostic methods, modeling, and SWOT analysis methods were used. In the results, the general properties of the Internet educational platforms common in Ukraine, the peculiarities of using the Moodle and Prometheus platforms, and an approximate model of the electronic learning environment were discussed. The reasons for the popularity of Moodle among Ukrainian universities are analyzed, but vulnerable elements related to security are emphasized. It was also determined that the high cost of Prometheus software and less functionality made this learning environment less relevant. The conclusions state that the military actions drew the attention of universities in Ukraine to the formation of their own educational platforms. This is especially relevant for technical and military institutions of higher education.

• Journal of The Korean Association For Science Education
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• v.27 no.9
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• pp.809-817
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• 2007

The purpose of this research was to investigate the nature of the science views of science teachers and high school students as well as the views expressed in 10th grade science textbooks. The subjects were a high school science teacher, 18 male students and 11 female students in a 10th grade class located in Gyeongbuk Province, Korea. The data were analyzed in terms of three main categories of the nature of the science: the definition of science, the development of science, and the method of science. In the results, it was found that the textbook had an inductivism point of view, and that the teacher had a falsificationism point of view in terms of the definition of science. However, the teacher presented the inductive point of view of the textbook in the class. After the class, the students showed an inductive point of view. In terms of scientific development, the textbook represented a relativism point of view briefly, and the viewpoint of the teacher also expressed relativism. The teacher taught briefly from the relativism point of view, as in the textbook. The viewpoints of the students were inductivism and were not affected by the textbook or the explanations of the teacher. In terms of scientific methods, the viewpoints of the textbook and the teacher were falsificationism, and the teacher represented falsificationism views in her classes. The views of the students also showed falsificationism after their classes. However, before conclusions can be made, it is necessary to find concrete proof of the teaching effect on the viewpoints of the students in continuing research.