• Journal of Educational Research in Mathematics
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• v.23 no.2
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• pp.237-252
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• 2013

The philosophy of science of Bachelard is introduced mainly with epistemological obstacles in the discussions within mathematics education. In his philosophy, epistemological obstacles are connected with the dialectical developments of science. Science progresses through generalization of concepts and theories by negating things which were recognized as obvious. These processes start with ruptures against the existing knowledge. Epistemological obstacles are failure in keeping distance with the existing knowledge when reorganization is needed. This concept means that there are the inherent difficulties in the processes of concept formation. Finally I compare the view of Bachelard on the developments of science and the 'interiorization-condensation-objectification' scheme of reflexive abstraction in mathematics education and discuss the inherent difficulties in the learning mathematics.

• The Journal of the Korea Contents Association
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• v.21 no.9
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• pp.493-501
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• 2021

This study started to examine the understanding and perception of 'disabled people' and 'non-disabled people', one of the dichotomous elements in the 21st century social integration era. In particular, for the analysis, Q-methodology, which should respond based on the respondent's inner self and perception, was used. For the analysis, 32 Q-statements were secured, and as a result of targeting 20 P-sample respondents, three types were derived as follows. In , statements such as 'A correct awareness of disability is necessary' and 'Disability can occur to anyone' are emphasized, so it was named 「Correct Perception Emphasis Type」. emphasized 'The life of the disabled is not easy' and 'The disabled need an opportunity to participate in society' and was named 「The Life of the Disabled Understanding Type」. emphasized statements such as 'Economic support is necessary for the disabled' and 'The welfare budget for the disabled must be sufficiently secured', and was named 「Institutional Support Emphasis Type」. Therefore, in addition to the necessity of correct recognition of disability and disability in our society, we expect this study result is to be priming water for improving the recognition of the disabled.

• Journal of the Korean School Mathematics Society
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• v.19 no.1
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• pp.63-82
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• 2016

Mathematical notation is the main means to realize the power of mathematics. Under this perspective, this study analyzed the difficulties of learning an irrational number concept in terms of notation. I tried to find ways to overcome the difficulties arising from the notation. There are two primary ideas in the notation of irrational number using root. The first is that an irrational number should be represented by letter because it can not be expressed by decimal or fraction. The second is that $\sqrt{2}$ is a notation added the number in order to highlight the features that it can be 2 when it is squared. However it is difficult for learner to notice the reasons for using the root because the textbook does not provide the opportunity to discover. Furthermore, the reduction of the transparency for the letter in the development of history is more difficult to access from the conceptual aspects. Thus 'epistemological obstacles resulting from the double context' and 'epistemological obstacles originated by strengthening the transparency of the number' is expected. To overcome such epistemological obstacles, it is necessary to premise 'providing opportunities for development of notation' and 'an experience using the notation enhanced the transparency of the letter that the existing'. Based on these principles, this study proposed a plan consisting of six steps.

• Education of Primary School Mathematics
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• v.15 no.2
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• pp.159-170
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• 2012

Many obstacles have been found in the learning of ratio and rate. The types of epistemological obstacles concern 'terms', 'calculations' and 'symbols'. It is important to identify the epistemological obstacles that students must overcome to understand the learning of ratio and rate. In this respect, the present study attempts to figure out what types of epistemological obstacles emerge in the area of learning ratio and rate and where these obstacles are generated from and to search for the teaching implications to correct them. The research questions were to analyze this concepts as follow; A. How do elementary students show the epistemological obstacles in ratio and rate? B. What is the reason for epistemological obstacles of elementary students in the learning of ratio and rate? C. What are the teaching implications to correct epistemological obstacles of elementary students in the learning of ratio and rate? In order to analyze the epistemological obstacles of elementary students in the learning of ratio and rate, the present study was conducted in five different elementary schools in Seoul. The test was administered to 138 fifth grade students who learned ratio and rate. The test was performed three times during six weeks. In case of necessity, additional interviews were carried out for thorough examination. The final results of the study are summarized as follows. The epistemological obstacles in the learning of ratio and rate can be categorized into three types. The first type concerns 'terms'. The reason is that realistic context is not sufficient, a definition is too formal. The second type of epistemological obstacle concerns 'calculations'. This second obstacle is caused by the lack of multiplication thought in mathematical problems. As a result of this study, the following conclusions have been made. The epistemological obstacles cannot be helped. They are part of the natural learning process. It is necessary to understand the reasons and search for the teaching implications. Every teacher must try to develop the teaching method.

• Journal of Educational Research in Mathematics
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• v.20 no.3
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• pp.305-322
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• 2010

The epistemological obstacles in the area learning of plane figure can be categorized into two types that is closely related to an attribute of measurement and is strongly connected with unit square. First, reasons for the obstacle related to an attribute of measurement are that 'area' is in conflict. with 'length' and the definition of 'plane figure' is not accordance with that of 'measurement'. Second, the causes of epistemological obstacles related to unit square are that unit square is not a basic unit to students and students have little understanding of the conception of the two dimensions. Thus, To overcome the obstacle related to an attribute of measurement, students must be able to distinguish between 'area' and 'length' through a variety of measurement activities. And, the definition of area needs to be redefined with the conception of measurement. Also, the textbook should make it possible to help students to induce the formula with the conception of 'array' and facilitate the application of formula in an integrated way. Meanwhile, To overcome obstacles related to unit square, authentic subject matter of real life and the various shapes of area need to be introduced in order for students to practice sufficient activities of each measure stage. Furthermore, teachers should seek for the pedagogical ways such as concrete manipulable activities to help them to grasp the continuous feature of the conception of area. Finally, it must be study on epistemological obstacles for good understanding. As present the cause and the teaching implication of epistemological obstacles through the research of epistemological obstacles, it must be solved.

• The Journal of the Korea Contents Association
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• v.15 no.1
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• pp.197-210
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• 2015

The purpose of this study is to find out subjective perception types and needs of interested group on the employment supporting for students with disabilities in college by Q methodology, then to search for political measures to support employment for students with disabilities in the implication of the sorted subjective perception types. The result of the study showed that there are four major sorts of subjectivities on the employment supporting for students with disabilities in college : external dependence(Type1), disability-friendly (Type2), demand tailored(Type3), internal role emphasis(Type4). The result of the study could check that there was necessary reconstruction to disability-friendly infrastructure based on interset and willness on the employment supporting for students with disabilities in college. In addition to that there was necessary to job creation of government, to build network of industry to successful labor market entry of students with disabilities.

• Journal of Educational Research in Mathematics
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• v.18 no.4
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• pp.469-482
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• 2008

This study analysed difficult points on the understanding of infinity when the concept is considered as actual infinity or as potential infinity. And I consider examples that the concept of actual infinity is used in texts of elementary and middle school mathematics. For understanding of modem mathematics, the concept of actual infinity is required necessarily, and the intuition of potential infinity is an epistemological obstacle to get over. Even so, it might be an excessive requirement to make such epistemological rupture from the early school mathematics, since the concept of actual infinity is not intuitive, derives many paradoxes, and cannot offer any proper metaphor.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.2
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• pp.241-262
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• 2010

This study was carried out to identify the cognitive obstacles while using addition and subtraction with fractions, and to analyze the sources of cognitive obstacles. For this purpose, the following research questions were established : 1. What errors do elementary students make while performing the operations with fractions, and what cognitive obstacles do they have? 2. What sources cause the cognitive obstacles to occur? The results obtained in this study were as follows : First, the student's cognitive obstacles were classified as those operating with same denominators, different denominators, and both. Some common cognitive obstacles that occurred when operating with same denominators and with different denominators were: the students would use division instead of addition and subtraction to solve their problems, when adding fractions, the students would make a natural number as their answer, the students incorporated different solving methods when working with improper fractions, as well as, making errors when reducing fractions. Cognitive obstacles in operating with same denominators were: adding the natural number to the numerator, subtracting the small number from the big number without carrying over, and making errors when doing so. Cognitive obstacles while operating with different denominators were their understanding of how to work with the denominators and numerators, and they made errors when reducing fractions to common denominators. Second, the factors that affected these cognitive obstacles were classified as epistemological factors, psychological factors, and didactical factors. The epistemological factors that affected the cognitive obstacles when using addition and subtraction with fractions were focused on hasty generalizations, intuition, linguistic representation, portions. The psychological factors that affected the cognitive obstacles were focused on instrumental understanding, notion image, obsession with operation of natural numbers, and constraint satisfaction.

• 한국사회복지학회:학술대회논문집
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• 2003.10a
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• pp.161-179
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• 2003

• Journal for History of Mathematics
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• v.26 no.1
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• pp.85-101
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• 2013

This study is to analyse the characteristics of Barrow's theorem on the historical standpoint of hermeneutics and to discuss the teaching-learning sequence for guiding students to reinvent the calculus according to historico-genetic principle. By the historical analysis on the Barrow's theorem, we show the geometric feature of the theorem, conjecture the Barrow's intention in dealing with it, and consider the epistemological obstacles undergone by Barrow. On a basis of this result, we suggest a purposeful and meaning-oriented teaching-learning way for students to realize the sameness of the 'integration' and 'anti-differentiation', and point out the shortcomings and supplement point in current School Mathematic Calculus.