• Title/Summary/Keyword: mathematical conception

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A Study on De Morgan's Perspectives on Mathematics Education (수학교육에 관한 드모르간의 관점 조명)

  • Choi, Ji-Sun;Yu, Mi-Kyung;Park, Sun-Yong;Kwon, Seok-Il;Park, Kyo-Sik
    • Journal of Educational Research in Mathematics
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    • v.18 no.2
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    • pp.223-237
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    • 2008
  • In this paper, We focus on grasping De Morgan's perspectives on mathematics education systematically. His perspectives can be summarized as followings. First, historico-genesis of mathematics must be considered in the teaching and learning of mathematics. Second, mathematical conception of students must be formulated progressively. Third, it is important to use errors which come out continually in the process of passing from inductive stage to deductive stage. Fourth, personal knowledge of students is important in the teaching and learning of mathematics. These De Morgan's four perspectives are the way of approach for experiencing moral certainty first of all to get to mathematical certainty. Moral certainty which he presented is a combination of rationality and humanity to fill up gaps between Platonism and general public education.

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A Numerical Analysis of River-bed Variation in Alluvial Stream (충적하천(沖積河川)의 하상변동(河床變動)에 관한 수치해석(數値解析))

  • Park, Jung Eng
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.4 no.1
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    • pp.49-58
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    • 1984
  • This paper is to exhibit the numerical analysis of sediment transport in the slowly varing flow and the sediment transport relation between the steady and the unsteady flow in the alluvial stream. The gradually varied flow of alluvial stream and the sediment transport are very complicated physical phenomen. Therefore the mathematical modeling is needed to be established. Linear implicit means of modified indirect method are applied to sediment transport by numerical analysis instead of the conception of steady flow in order to decrease errors. Further more, this study has purpose on reasonable prediction of the river-bed variation by way of this numerical method.

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A Study of River-Bed Variation from Goan to Indogyo due to Flood in Han River (홍수시 한강 하류부의 하상변동에 관한 연구)

  • 박정응;김경수
    • Water for future
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    • v.24 no.2
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    • pp.109-119
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    • 1991
  • The river-bed variation and the sediment transport in an alluvial stream are very complicated physical phenomena, especially in a stream where the dam construction prevents the supply of earth and sand from upper tributaries Therefore, the mathematical modeling is needed to establish. The purpose of this study is to apply river-bed variation to the Han River downstream by the conception of gradually varied unsteady flow instead of that of steady flow in order to decrease errors. For the variation and forecast of river-bed, the numerical analysis has been made in this study by way of discharge variation and river-bed variation. In conclusion, the numerical analysis shows that river-bed variation, sediment transport , and their forecast have similarity to natural phenomena and that river-bed variation is greatly affected in sediment transport by discharge variation and retention time(duration). Therefore, the errors of numerical analysis can be reduced by the application of flood data instead of continuous discharge data.

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The Changes of postgraduate Students' Conceptions towards the Nature of Science through the Course related to Philosophy of Science (과학 철학을 수강하는 대학원생의 과학의 본성에 대한 인식의 변화)

  • Song, Jin-Woong;Kwon, Sung-Gi
    • Journal of The Korean Association For Science Education
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    • v.12 no.1
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    • pp.1-9
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    • 1992
  • This study investigated 15 Postgraduate students' conception toward the nature of science and the changes of those conceptions through the course called 'Philosophy of Science and Science Education', And another 8 postgrauate students who took the course called 'Mathematical Physics' were also investigated for comparison. A survey questionnaire involving 9 items was developed and administered before and after the course to both groups. Individual interviews with students taking 'Philosophy of Science and Science Education' were carried out in a small scale for obtaining additional information about their background knowledge. The results of this study showed that the students' traditional views of philosophy of science including the objective observation and the inductive method were reduced after the course, 'Philosophy of Science and Science Education'. On the other hand. views of modem philosophy of science including the theory-laden observation, the tentativeness of scientific knowledge and science as human activities became more popular. It was also found that their conceptions towards Science were different according to their previous knowledges on the philosophy of science and their majors.

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Conception and Performance Analysis of Efficient CDMA-Based Full-Duplex Anti-collision Scheme

  • Cao, Xiaohua;Li, Tiffany
    • ETRI Journal
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    • v.37 no.5
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    • pp.929-939
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    • 2015
  • Ultra-high-frequency radio-frequency identification (UHF RFID) is widely applied in different industries. The Frame Slotted ALOHA in EPC C1G2 suffers severe collisions that limit the efficiency of tag recognition. An efficient full-duplex anti-collision scheme is proposed to reduce the rate of collision by coordinating the transmitting process of CDMA UWB uplink and UHF downlink. The relevant mathematical models are built to analyze the performance of the proposed scheme. Through simulation, some important findings are gained. The maximum number of identified tags in one slot is g/e (g is the number of PN codes and e is Euler's constant) when the number of tags is equal to mg (m is the number of slots). Unlike the Frame Slotted ALOHA, even if the frame size is small and the number of tags is large, there aren't too many collisions if the number of PN codes is large enough. Our approach with 7-bit Gold codes, 15-bit Gold codes, or 31-bit Gold codes operates 1.4 times, 1.7 times, or 3 times faster than the CDMA Slotted ALOHA, respectively, and 14.5 times, 16.2 times, or 18.5 times faster than the EPC C1 G2 system, respectively. More than 2,000 tags can be processed within 300 ms in our approach.

The Perception of the Professors and Teachers about the Education on Quadratic Curves in Various Universities (사범대학의 이차곡선 영역 교육에 대한 교수 및 교사의 인식)

  • Yi, Seunghun;Cho, Wan Young
    • School Mathematics
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    • v.16 no.4
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    • pp.827-845
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    • 2014
  • This study aims to investigate how the university educational programs about quadratic curves are operated in relation to the high school curriculum and what their effects may be, and the degree of understanding for the prospective and current teachers of the mathematical content knowledge about quadratic curves. To solve this research questions, we randomly selected three universities and one high school. Then we investigated the curricula of each department of mathematics education, compared them with the high school curricula, and conducted surveys of the professors' and students' conception on how much mathematical content knowledge they need to know about quadratic curves. The study resulted in the following conclusions. First, the curriculum on the subject of quadratic curves in the college of education is closely connected to the high school programs. This study's results showed that the college of education's curriculum includes a series of lectures regarding quadratic curves, and that within them, the mathematical content about quadratic curves associated with high school mathematics was thoroughly covered. Also, a large number of students who attended the lecture reported a significant increase in their understanding in regards to the quadratic curves. Second, it is strongly recommended to strengthen the connection between the college of education's curriculum and the actual high school education field. The prospective teachers think that there is a substantial need to learn about the quadratic curves because it is closely connected with the high school curriculum. But they find it challenging to put what they were taught into practical use in the high school education field, and feel that an improvement in this area is much needed. Third, it is necessary to promote, encourage and support the voluntary efforts to expand the range of the content knowledge in quadratic curves to cover the academic content associated with the high school mathematics.

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Student Understanding of Scale: From Additive to Multiplicative Reasoning in the Constriction of Scale Representation by Ordering Objects in a Number Line (척도개념의 이해: 수학적 구조 조사로 과학교과에 나오는 물질의 크기를 표현하는 학생들의 이해도 분석)

  • Park, Eun-Jung
    • Journal of The Korean Association For Science Education
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    • v.34 no.4
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    • pp.335-347
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    • 2014
  • Size/scale is a central idea in the science curriculum, providing explanations for various phenomena. However, few studies have been conducted to explore student understanding of this concept and to suggest instructional approaches in scientific contexts. In contrast, there have been more studies in mathematics, regarding the use of number lines to relate the nature of numbers to operation and representation of magnitude. In order to better understand variations in student conceptions of size/scale in scientific contexts and explain learning difficulties including alternative conceptions, this study suggests an approach that links mathematics with the analysis of student conceptions of size/scale, i.e. the analysis of mathematical structure and reasoning for a number line. In addition, data ranging from high school to college students facilitate the interpretation of conceptual complexity in terms of mathematical development of a number line. In this sense, findings from this study better explain the following by mathematical reasoning: (1) varied student conceptions, (2) key aspects of each conception, and (3) potential cognitive dimensions interpreting the size/scale concepts. Results of this study help us to understand the troublesomeness of learning size/scale and provide a direction for developing curriculum and instruction for better understanding.

Mathematics Preservice Teachers' Conception of Teacher Discourse (예비 수학 교사의 교사 담화에 대한 인식 분석)

  • Lee, Jihyun
    • Journal of the Korean School Mathematics Society
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    • v.20 no.4
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    • pp.465-494
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    • 2017
  • Teachers' conceptions about teaching are important driving and also interfering forces which might affect their actual practice and training. This research explores preservice mathematics teachers' conceptions of teacher discourse, through tasks analyzing and evaluating teachers' moment-to-moment discourse moves which occur in authoritative and dialogical classroom discourse. Some facets of the preservice teachers' conceptions were congruent with dialogical discourse: they criticized teacher's one-way communication and ignoring students' voices; they supported teacher's questions probing students' thinking and receptive attitude to ward students' wrong answers. However, some deep and subtle facets of their conceptions were more congruent with authoritative discourse rather than dialogical discourse: they positively perceived teacher's closed, information seeking questions that funnel students' thinking to the predetermined procedure; they emotionally resisted teacher's questions which might facilitate dialogical engagement by allowing students to judge mathematical correctness of ideas from their peers. Preservice teachers' conceptions of teacher discourse explored in this research provide useful foundations on which to build continuous and coherent teacher professional development programs about classroom discourse.

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An Analysis of Effective on Using Calculators in Elementary Mathematics (초등수학에서 계산기 활용에 대한 효과 분석)

  • Ahn Byoung Gon
    • School Mathematics
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    • v.7 no.1
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    • pp.17-32
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    • 2005
  • The purpose of this study is to analyze the effects of calculator use, which is drawing more attention in elementary mathematics, on students' learning of mathematics and to suggest effective ways of using calculators. The present study examined appropriate items commonly used in other papers in the areas of number sense and concepts, problem solving, pattern exploration and reasoning ability. The process of item selection about calculator use were investigated through preservice elementary school teachers' responses to the Questionnaire. The use of calculators In elementary school should be based on teachers' under-standing about why calculators are useful tools for learning mathematics. For more effective use of calculators, more sophisticated experimental studies need to be conducted about selected questions.

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Analysis of the Error-Remedial Effect and Change of the Students' Misconception on the Learning of Linear Function (교수학적 처방에 따른 중학생들의 일차함수 오개념의 변화와 그 효과 분석)

  • 이종희;김부미
    • School Mathematics
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    • v.5 no.1
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    • pp.115-133
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    • 2003
  • Investigation of the students' mathematical misconceptions is very important for improvement in the school mathematics teach]ng and basis of curriculum. In this study, we categorize second-grade middle school students' misconceptions on the learning of linear function and make a comparative study of the error-remedial effect of students' collaborative learning vs explanatory leaching. We also investigate how to change and advance students' self-diagnosis and treatment of the milton ceptions through the collaborative learning about linear function. The result of the study shows that there are three main kinds of students' misconceptions in algebraic setting like this: (1) linear function misconception in relation with number concept, (2) misconception of the variables, (3) tenacity of specific perspective. Types of misconception in graphical setting are classified into misconception of graph Interpretation and prediction and that of variables as the objects of function. Two different remedies have a distinctive effect on treatment of the students' misconception under the each category. We also find that a misconception can develop into a correct conception as a result of interaction with other students.

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