• Journal of Educational Research in Mathematics
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• v.12 no.4
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• pp.557-579
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• 2002

The purpose of this study is to find out the problems which are caused when the limit concept of sequences is learned through an intuitive definition and to suggest a way of solving those problems. Students in Korea study the limit concept of sequences through an intuitive definition. They fail to apply the intuitive definition properly to the problems and they are apt to have misconception even though the Intuitive definition is applied properly. To solve these problems, this study examined the develop- mental process of the limit concept of sequences from the Intuitive definition to the formal definition, and looked into the way of students' internalization of the process through a field study. In this study, the levels of the limit concept of sequences possessed by the students at ZPD are as follows; level 0 : Students understand the limit concept of sequences through the intuitive definition. level 1 : Students understand the limit concept of sequences as 'The difference between $\alpha$$_{n}$ and $\alpha$ approaches 0' rather than 'The sequence approaches $\alpha$ infinitely.' level 2 : Students understand the limit concept of sequences through the formal definition. The levels of students' limit concept development were analysed by those criteria. Almost of the students who studied the limit concept of sequences through the intuitive defition stayed at level 0, whereas almost of the students who studied through the formal definition stayed at level 1. Through the study, I found that it was difficult for the students to develop the higher level of understanding for themselves but the teachers and peers could help the students to progress to the higher level. Students' learning ability was one of major factors that make the students progress to the higher level of understanding as the concept was developed hierarchically from Level 0 to Level 2. If you want to see your students get to the higher level of understanding in the limit concept, you need to facilitate them to fully develop understanding in lower levels through enough experiences so that they can be promoted to the highest level.

• School Mathematics
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• v.4 no.2
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• pp.247-260
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• 2002

In recent elementary school mathematics a word 'stipulation' newly appears. The word is used instead of definition. However, there seems to be some differences between definition and stipulation. So, in this paper we investigate those differences through the concept 'function of definition'. In school mathematics textbooks there are definitions which carry out special functions In mathematical contexts or situations. We can say that we understand those definitions, only if we also understand the functions of definitions in those contexts or situations. Functions of definition are classified as, stipulation-function, discrimination-function, analysis-function, demonstration-function, improvement-function. With these analyses we made a frame for investigating the characteristics of the definitions in recent elementary school mathematics textbooks. As a result of analysing functions of definition we found that generally speaking, stipulation-function is excessively emphasized and the other functions of definition are not explained adequately in school mathematics textbooks. So it is required that the textbook authors should be careful not to miss an opportunity for the functional understanding and the mathematics teachers should be aware of the functions of definitions. Finally, we comment that textbook author, teacher, and researcher should be careful in using the word 'stipulation' instead of definition, because, although there are various functions of definitions, students might ream only stipulation-function.

• Journal of Educational Research in Mathematics
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• v.11 no.2
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• pp.363-384
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• 2001

The purpose of this thesis is, through analysing the characteristics of the definitions in Korean school mathematics textbooks, to explore the levels of them and to make suggestions for definition - teaching as a mathematising activity, Definitions used in academic mathematics are rigorous. But they should be transformed into various types, which are presented in school mathematics textbooks, with didactical purposes. In this thesis we investigated such types of transformation. With the result of this investigation we tried to identify the levels of the definitions in school mathematics textbooks. And in school mathematics textbooks there are definitions which carry out special functions in mathematical contexts or situations. We can say that we understand those definitions, only if we also understand the functions of definitions in those contexts or situations. In this thesis we investigated the cases in school mathematics textbooks, when such functions of definition are accompanied. With the result of this investigation we tried to make suggestions for definition-teaching as an intellectual activity. To begin with we considered definition from two aspects, methods of definition and functions of definition. We tried to construct, with consideration about methods of definition, frame for analysing the types of the definitions in school mathematics and search for a method for definition-teaching through mathematization. Methods of definition are classified as connotative method, denotative method, and synonymous method. Especially we identified that connotative method contains logical definition, genetic definition, relational definition, operational definition, and axiomatic definition. Functions of definition are classified as, description-function, stipulation-function, discrimination-function, analysis-function, demonstration-function, improvement-function. With these analyses we made a frame for investigating the characteristics of the definitions in school mathematics textbooks. With this frame we identified concrete types of transformations of methods of definition. We tried to analyse this result with van Hieles' theory about levels of geometry learning and the mathematical language levels described by Freudenthal, and identify the levels of definitions in school mathematics. We showed the levels of definitions in the geometry area of the Korean school mathematics. And as a result of analysing functions of definition we found that functions of definition appear more often in geometry than in algebra or analysis and that improvement-function, demonstration-function appear regularly after demonstrative geometry while other functions appear before demonstrative geometry. Also, we found that generally speaking, the functions of definition are not explained adequately in school mathematics textbooks. So it is required that the textbook authors should be careful not to miss an opportunity for the functional understanding. And the mathematics teachers should be aware of the functions of definitions. As mentioned above, in this thesis we analysed definitions in school mathematics, identified various types of didactical transformations of definitions, and presented a basis for future researches on definition teaching in school mathematics.

• East Asian mathematical journal
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• v.35 no.2
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• pp.239-257
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• 2019

The purpose of this study is to show that the topology is closely related to some subjects learned in school mathematics and then to give motivations for learning of the topology. To do this, it is showed that the topology is an abstracted device that deal with structure of limit and continuity introduced in school mathematics. This study took a literature study. The results of this study are as follows. First, the formal definition of general topology to structure open sets was examined. The nearness relation together with the closure operation was introduced and used to characterize for construction of general topology. Second, as definitions for continuity of function, we considered the intuitive definition, definition, structured definitions using open intervals and definition using open sets and then we investigated their roles. We also examined equivalent definition using the nearness relation which is helpful to understand continuity of function. Third, the sequence and its limit are treated in terms of continuous functions having the set of natural numbers and its extended set as domains. From these, it can be concluded that the convergence of sequence and the continuity of function are identified as functions that preserve the nearness relation and that the topology is a specialized tool for dealing with convergence and continuity.

• Journal of Korean Medical classics
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• v.27 no.2
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• pp.77-95
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• 2014

Objectives : This study was to analyze the definitions of herbs, herbal drugs, crude drugs and natural products in the relevant laws and regulations, understand the related problems, and propose directions for improvement. Methods : I analyzed the legal definitions in respect of herbs, herbal drugs, crude drugs and natural products in relevant laws and regulations since 1945, explained the problems, and suggested the solution-considering the academic stance of Traditional Korean Medicine and the dualistic medical and pharmaceutical system. Results : Herbs are defined as "refined things that are cut and dried in their most original state". The definition of crude drugs includes herbs and the "cell contents, secretion, extracts, minerals and other parts of animals and plants that are used medicinally". The concept of natural products is expanded to adding tissue cultures to the definition of crude drugs. Conclusions : The definition of herbs should at least include all products that are "processed, extracted and prepared" as well as contents that consist of various forms of hospital-prepared herbs. The term "herbal drug" corresponds to a traditional term of "drug", and this should be established as a concept to explain "drugs in raw materials that are used to prepare herbs and/or manufacture herbal medicine". The legal definition of herbs should include the concept of crude drugs. Herbal drug preparations and crude drugs should be included in the definition of herbal drugs.

• Journal for History of Mathematics
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• v.32 no.3
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• pp.135-155
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• 2019

One of the reasons students have difficulty in studying probability is that they do not understand the meaning of mathematical terms precisely. One such term is a continuous random variable. Students tend not to think of the accurate definition of continuous random variables but to understand the definition of continuity of functions and the meaning of continuity in probability as equal. In this study, we try to explore the degree of pre-service teachers' understanding on the concept of continuation of functions and continuous random variables. To do this, the questionnaire items related to continuous random variables and continuity of functions were developed by experts and examined by pre-service teachers. Based on this, we make suggestions on implications for teaching and learning about continuous random variables.

• The Mathematical Education
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• v.61 no.2
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• pp.323-338
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• 2022

The purpose of this study are to analyze how well middle and high school students understand the concept definition of quadrangle and to explore the phenomenon about their concept image. A test tool was developed and 60 8th graders, 63 9^th graders and 65 10^th graders were tested, and some students who needed in-depth analysis were interviewed. The results are as follows. First, it cannot be said that understanding level of the concept definition of the quadrangle naturally improves as the grade level goes up. Particularly, it was found that the understanding of the definition of the rhombus is the lowest in all three grades compared to other quadrangle. Second, although female students understood the definition of square better than male students, the understanding level of the definition of trapezoid, parallelogram, rhombus, and rectangle did not differ by gender. Third, it was found that the students who did not understand the concept definition of the quadrangle were more and more influenced by the concept image as the grade level went up. Fourth, it showed that a tendency to be less influenced by the concept definition and more influenced by textbooks and teachers as the grades go up when students form a concept image.

• Journal of Society of Preventive Korean Medicine
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• v.18 no.1
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• pp.23-41
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• 2014

Objective : The purpose of this study was to lay the groundwork for understanding the details and scope of the legal definition of medicinal products, following the changes in the relevant laws and regulations. This will let readers properly understand the origins of the ongoing conflicts on herbal drugs and new drugs from natural products that are present in the medical field and the medical industry. Possible solutions are proposed in the end. Method : I analyzed the changes in definition of medicinal products since 1945 that have been used in relevant laws and regulations(i.e. Pharmaceutical Affairs Act) and drug approval process(i.e. New Drug Application and Investigational New Drug Application). Results : Legal definition of medicinal products has changed in accordance with the changes in the pharmaceutical industry, such as the establishment of dualistic medical and pharmaceutical System and the introduction of the substance patent. Due to those changes, boundaries of Western medicinal products and health food expanded, while those of herbal medicine products relatively downscaled. Conclusion : Legal definition of medicinal products-i.e. Herbal Drugs, Crude Drugs, and New Drugs from Natural Products-should be reestablished according to academic legitimacy and dualistic medical and pharmaceutical System.

• Journal of Educational Research in Mathematics
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• v.21 no.1
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• pp.57-65
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• 2011

The conceptions of definition and proof radically change in the transition from secondary to tertiary mathematics. Specifically this paper analyses the historical development of the axiomatic method from Greek to modern mathematics. To understand Greek and modern axiomatic method, it is important to know the different characteristics of the primitive terms, constant and variable. Especially this matter of primitive terms explains the change of conceptions of definition, proof and mathematics. This historical analysis is useful for introducing the meaning of formal definition and proof.

• Journal of the Korean Society of Physical Medicine
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• v.18 no.4
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• pp.109-119
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• 2023

PURPOSE: The definition and scope of biofeedback are broad and lack a clear framework. Therefore, efforts are needed to clearly understand the exact range and definition of biofeedback based on the research and development conducted to date. Thus, the purpose of this study was to arrive at the definition and scope of biofeedback through a literature review and analysis of its application methods. METHODS: This study is a systematic literature review conducted to understand the various types and effects of biofeedback. International databases such as Google Scholar and PubMed were used. Domestic databases utilized for keyword searches included the Research Information Sharing Service (RISS) and the National Digital Science Library (NDSL). Quality assessment of the selected studies in the selection process was done using the Cochrane risk of bias, and the research was analyzed according to the population, intervention, control, and outcomes (PICO) format. RESULTS: Studies conducted between 2019 and 2021 were selected, with 4 papers falling under physiological classifications and 7 under biomechanical classifications. The quality assessment results showed that random sequence generation, allocation concealment, performance bias, and reporting bias were unclear. Detection bias was moderate, and attrition bias and other biases were low. Out of the 11 papers, 9 dealt with physical function outcomes, 5 with daily life activities, and 3 with mental functions. CONCLUSION: Physiological biofeedback tended to influence psychological factors more than physical functions, while biomechanical biofeedback tended to have a positive impact on physical functions.