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Analysis of the Algebraic Thinking Factors and Search for the Direction of Its Learning and Teaching (대수의 사고 요소 분석 및 학습-지도 방안의 탐색)

  • Woo, Jeong-Ho;Kim, Sung-Joon
    • Journal of Educational Research in Mathematics
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    • v.17 no.4
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    • pp.453-475
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    • 2007
  • School algebra starts with introducing algebraic expressions which have been one of the cognitive obstacles to the students in the transfer from arithmetic to algebra. In the recent studies on the teaching school algebra, algebraic thinking is getting much more attention together with algebraic expressions. In this paper, we examined the processes of the transfer from arithmetic to algebra and ways for teaching early algebra through algebraic thinking factors. Issues about algebraic thinking have continued since 1980's. But the theoretic foundations for algebraic thinking have not been founded in the previous studies. In this paper, we analyzed the algebraic thinking in school algebra from historico-genetic, epistemological, and symbolic-linguistic points of view, and identified algebraic thinking factors, i.e. the principle of permanence of formal laws, the concept of variable, quantitative reasoning, algebraic interpretation - constructing algebraic expressions, trans formational reasoning - changing algebraic expressions, operational senses - operating algebraic expressions, substitution, etc. We also identified these algebraic thinking factors through analyzing mathematics textbooks of elementary and middle school, and showed the middle school students' low achievement relating to these factors through the algebraic thinking ability test. Based upon these analyses, we argued that the readiness for algebra learning should be made through the processes including algebraic thinking factors in the elementary school and that the transfer from arithmetic to algebra should be accomplished naturally through the pre-algebra course. And we searched for alternative ways to improve algebra curriculums, emphasizing algebraic thinking factors. In summary, we identified the problems of school algebra relating to the transfer from arithmetic to algebra with the problem of teaching algebraic thinking and analyzed the algebraic thinking factors of school algebra, and searched for alternative ways for improving the transfer from arithmetic to algebra and the teaching of early algebra.

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An analysis on the development processes of mathematics and the results by dialectical materialism (수학의 발달과정과 그 결과에 대한 변증법적 유물론에 의한 분석)

  • 조윤동
    • Journal of Educational Research in Mathematics
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    • v.13 no.3
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    • pp.329-349
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    • 2003
  • Mathematics education is accomplished by systems such as mathematical curriculum and tools such as a textbook which reflects such systems. Human beings make such systems and tools. Therefore, a viewpoint of mathematics of those who make them is an important factor. The view point of mathematics is formed during doing and learning mathematics, but the already formed viewpoint of mathematics affects doing and teaching mathematics. Hence, it will be a factor which affects basically that those who employ themselves on mathematics education have a certain viewpoint of mathematics. This article presents dialectical materialistic viewpoint as the viewpoint of mathematics which affects fundamentally on mathematical teaching-learning practice. The dialectical materialism is carried through the process and result of mathematics development. This shows that mathematical knowledge is objective. Mathematical knowledge has developed according to three basic rules of dialectical materialism i.e. the transformation of quantity into quality, the unification of antagonistic objects, and the negation of negation. This viewpoint of mathematics should offer the viewpoint of mathematics education which is different from the view point of absolutism, relativism or formal logic. In this article I considered mathematics separating standpoint of mathematics into materialistic viewpoint and dialectical viewpoint. 1 did so for the convenience of analysis, but you will be able to look at the unified viewpoint of dialectical materialism. 1 will make mention of teaching-learning method on another occasion.

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High School Students' Mathematics Learning Style and Its Characteristics According to Their MBTI Personality Disposition Types (고등학생들의 수학 학습양식과 MBTI 성격기질별 특징)

  • Kang, Yun Soo
    • Communications of Mathematical Education
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    • v.34 no.3
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    • pp.299-324
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    • 2020
  • The purpose of this study was to identify high school students' mathematics learning style and its characteristics according to their personality disposition types and to propose mathematics learning strategies fit into each personality disposition type. For this purpose, MBTI personality test and survey to find mathematics learning style for 375 high school students were executed. The results were as follows. First, many students highly evaluated the effects of private education and prefer reference book to textbook. Second, there were significant differences on following variable domains of mathematics learning style such as learning attitude, learning habit(concentrativeness to concept understanding), problem solving strategies(effort for problem comprehension, use of various strategies), self management(metacognition) by MBTI personality disposition types(SJ, SP, NT, NF groups). Third, based on the results, the following mathematics learning strategies fit into each personality disposition type were recommended. SJ type students are needed to effort creative approach for open problem and to use mindmap as mathematics learning strategy. SP type students are needed to fulfill stepwise problem solving process and to effort constantly practice long/short term learning objectives. NT type students are needed to expand opportunity to study with friends and to use SRN(self reflection note) or mathematics journal writings as mathematics learning strategy. NF type students are needed to use mathematics learning note writing activity which include logical basis for each step of problem solving and to invest more time on learning algebra which need meticulous calculation.

Practical Guide to the Characterization of Piezoelectric Properties (압전재료의 기초 물성 측정)

  • Kang, Woo-Seok;Lee, Geon-Ju;Jo, Wook
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.34 no.5
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    • pp.301-313
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    • 2021
  • Theoretical background for the meaning of various piezoelectric properties can be easily found in a number of textbooks and academic papers. In contrast, how they are actually measured and characterized are rarely described, though this information would be the most important especially to the researchers who just started working on the field. It follows that this report was intended to provide a practical guidance for measuring basic but essential properties of ferroelectric-based piezoelectric materials. The discussion begins with how to measurement dielectric properties such as dielectric permittivity and loss (dissipation factor), followed by piezoelectric properties such as piezoelectric constants, electromechanical coupling factor, and quality factor as well as ferroelectric features, i.e., electric field dependent polarization hysteresis. Though our discussion here is limited to the techniques that are already well-standardized, it is expected to make a seed to be developed into more challenging and creative ones.

The Effect of Interleaved-practice by the Discriminative-contrast hypothesis in Mathematics (수학학습에서 구분-대조 가설에 의한 교차연습의 효과)

  • Ryu, Jimin;Park, Mijeong
    • Communications of Mathematical Education
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    • v.37 no.2
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    • pp.199-212
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    • 2023
  • The purpose of this study is to find out whether there is a difference in achievement between blocked practice and interleaved practice according to the difference in domain and type of learning content in mathematics subject, and through this result, it is to confirm whether the effect of interleaved practice in mathematics learning is due to the 'Discriminative-contrast Hypothesis' or the 'Distributed-practice Hypothesis'. Although interleaved practice is more effective than blocked practice, previous studies have not shown consistent results regarding the cause. Therefore, in this study, 103 first-year middle school students were randomly assigned to blocked practice, interleaved practice, remote blocked practice, and remote interleaved practice groups had learning activities over 4 times. The results reveals that the effect of interleaved practice appeared in similar types in the same domain, but the effect of interleaved practice did not appear in different types in different domain. In addition, through this result, it was confirmed that the effect of interleaved practice was due to the 'Discriminative-contrast hypothesis' rather than the 'Distributed-practice hypothesis'. Further research topics were suggested after the issues on the research method and the findings were discussed.

A Case Study on the Growth of Learners through the Changemaker TEMPS Program (체인지메이커(Changemaker) TEMPS 프로그램을 통한 학습자의 성장에 대한 사례연구)

  • Kim, Nam Eun;Heo, Young Sun
    • Journal of Korean Home Economics Education Association
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    • v.31 no.3
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    • pp.91-116
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    • 2019
  • The purpose of this study is to examine the meaning of Changemaker education and to investigate the significance of Changemaker education in home economics education through a study of growth of learners applying the TEMPS program. To this end, first, the concept of Changemaker education was defined. Changemaker education is an education that changes society in a positive direction through a process of thinking about, learning about, making, and participating(playing) in various problems that we face in real life and drawing out solutions and share he solutions with others. Second, in this reasearch, the direction of Changemaker education is to make them interested in social problems and solve it and to make both the family and the career life happy and healthy by collaborating with other people. The scope of the contents is defined as "the selection of the content elements of the five domains of the child family, diet nutrition, clothing, housing and consumer life". As a way of teaching, we suggested that the TEMPS phase is followed so that the session purpose is achieved. Third, the Changemaker program consists of five steps of TEMPS among the five key ideas of Changemaker education. T(Thinking) is the step of understanding the problem and thinking about how to solve it, and E(Education) is getting the background for the next step. M(Making) is a step to create a target for problem solving, and P(Participation) and P(Play) are steps to Participation and enjoy. S(Share) is a step of changing the society through the result display, SNS sharing, and class presentation. In this study, 12 programs for middle school and 15 programs for high school were developed on the basis of TEMPS level. Each of the programs consists of 2 to 12 unit hours, which add up to 68 hours in the middle school program and 68 in high school. The learners who participated in the Changemaker program for one year (March 2, 2018~December 31, 2018) will experience improvement in many aspects including the linkage of life and education, practical ability, self-directed learning, self-esteem, sense of achievement and self-reflection, sensory observation, and so on.

A Study on Necessity and Demands of Teachers and Students for Housing Contents in Technology.Home Economics Curriculum of the Middle School (중학교 기술.가정 교과의 주생활 영역 교과내용에 대한 교사와 학생의 필요성 및 요구도 -울산광역시를 중심으로-)

  • Choi, Hye-Mi;Kim, Sun-Joong
    • Journal of Korean Home Economics Education Association
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    • v.19 no.4
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    • pp.75-89
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    • 2007
  • This study has its aim at suggesting new direction of our education to search different ways in housing contents by comparing the necessity perception and demands between teachers and students for housing contents in Technology Home Economics curriculum of middle school. To achieve this aim, I chose middle school teachers in charge of Technology Home Economics and male and female students who are in the first grade in high school in Ulsan. I sent e-mail, mail, and visited researcher to gather the data. I used SPSS +12 statistical package for frequency, percentage, mean, standard deviation, and t-test to analyze the data. Here is the result. First, In the part of application of living place, teachers had necessity perception in use and placement of furniture, and arrangement of objects. Students had necessity perception in the use and placement of furniture, the kind and choice of furniture. Also in the indoor environment and equipment part, both teachers and students had necessity perception in controlling of ventilation, temperature, and humidity. In the part of maintenance repair of housing, teachers had necessity perception in the need for maintenance management but students had necessity perception in house equipments and repair had high necessity perception Second, In housing-related general part, teachers demanded housing for elderly, disabled people, information about future housing and students demanded environmentally friendly living environment, housing for elderly, disabled people. In interior design part, teachers demanded in the expression of interior places through computer, the kind and characteristic of housing material and students demanded the way to reuse old furniture, kind and characteristic of housing material. In the part of housing preparation and occupation, teachers demanded the kind of housing-related occupation and students demanded the housing tax and the process of house purchase or concerned matter. Third, there were some difference of necessity perception and degree of demand between teachers and students. Teachers had higher necessity perception and demand in all part except in demand for housing equipment, maintenance, and environmentally friendly living environment.

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An Analysis on the Understanding of High School Students about the Concept of a Differential Coefficient Based on Integrated Understanding (통합적 이해의 관점에서 본 고등학교 학생들의 미분계수 개념 이해 분석)

  • Lee, Hyun Ju;Ryu, Jung Hyeon;Cho, Wan Young
    • Communications of Mathematical Education
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    • v.29 no.1
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    • pp.131-155
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    • 2015
  • The purpose of this study is to investigate if top-ranked high school students do integrated understanding about the concept of a differential coefficient. For here, the meaning of integrated understanding about the concept of a differential coefficient is whether students understand tangent and velocity problems, which are occurrence contexts of a differential coefficient, by connecting with the concept of a differential coefficient and organically understand the concept, algebraic and geometrical expression of a differential coefficient and applied situations about a differential coefficient. For this, 38 top-ranked high school students, who are attending S high school, located in Cheongju, were selected as subjects of this analysis. The test was developed with high-school math II textbooks and various other books and revised and supplemented by practising teachers and experts. It is composed of 11 questions. Question 1 and 2-(1) are about the connection between the concept of a differential coefficient and algebraic and geometrical expression, question 2-(2) and 4 are about the connection between occurrence context of the concept and the concept itself, question 3 and 10 are about the connection between the expression with algebra and geometry. Question 5 to 9 are about applied situations. Question 6 is about the connection between the concept and application of a differential coefficient, question 8 is about the connection between application of a differential coefficient and expression with algebra, question 5 and 7 are about the connection between application of a differential coefficient, used besides math, and expression with geometry and question 9 is about the connection between application of a differential coefficient, used within math, and expression with geometry. The research shows the high rate of students, who organizationally understand the concept of a differential coefficient and algebraic and geometrical expression. However, for other connections, the rates of students are nearly half of it or lower than half.

Reconsideration of the Formation Process of Current Nagyangchun (현행 낙양춘의 형성과정 재고)

  • Yim, Hyun-taek
    • (The) Research of the performance art and culture
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    • no.43
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    • pp.79-120
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    • 2021
  • Nagyangchun is a Dangak that has been handed down to the present time with Boheoja as a Saak of the Song Dynasty which was introduced in the Goryeo Dynasty. The title and lyrics of Nagyangchun are conveyed in the Dangakjo of Goryeosa-akji and the Jeungbomunheonbigo. The remaining scores containing Nagyangchun include Akjangyoram, Sogagwonbo Vol.4 and Vol.6 of the Joseon Dynasty and Aakbu-akbo, the 6th Aaksaeng-gyogwacheol, Leewangjikaakbu-oseonakbo during the Japanese colonial period. Besides, the current melody of Nagyangchun is based on Hangugeumak and Gugakjeonjib published by the National Gugak Center. This paper aims to examine how Nagyangchun, which is currently being performed at the National Gugak Center, went through the process of change to have the same structure and form as it is now using these scores as a research subject. The study results are summarized as follows. First, the song of Nagyangchun, which was originally Saak but transmitted as an instrumental piece without lyrics, first appeared in the Hangugeumak Vol.16 and Gugakjeonjib Vol.7 published by the National Gugak Center in 1978 and 1979. In this process, the Janggu added by Kim Ki-soo is now disappearing and is replaced by Jwago. Second, though the five notes of 黃, 太, 仲, 林, and 南 have been maintained unchanged since the Akjangyoram, the pitch of 無/應 and 夾/姑, which appear once each, gradually rises and is unified into 應 and 姑 during the period of Aaksaeng-gyogwacheol or at the latest Leewangjikaakbu-oseonakbo, and reached the present. Third, the current melody of Nagyangchun consists of a structure in which the tones and range of each phrase rises within the form of Mijeonsa (a·b·c·d) and Mihusa (e·b'·c'·d'). Particularly, except for the a-type and e-type melodies, which are the introduction for the Mijeonsa and Mihusa, the remaining melodic types show a gradually descending structure within the corresponding phrase, so the structure of ascending and descending is generally in harmony. Forth, the Ganeum that appeared from Aakbu-akbo are currently classified into seven types, and they appear in ascending pitches of 2nd, 3rd, 4th, and 5th and play a role in smoothly or fluently connecting melodic progression. Fifth, after Akjangyoram, Nagyangchun, which had been handed down as an instrumental piece without lyrics, was restored in 1960 by Lee Hye-gu, and is being passed down as the form of male and female vocals added to the instrumental accompaniment. As a result of examining the current Nagyangchun, which was formed through the process of change after Akjangyoram, it was found that there were tasks that required reconsideration of the current Nagyangchun, which is being played at the National Gugak Center, such as the arrangement of Janggu, the identification of the key, and the investigation of the lyrics. When follow-up studies are continued in the future, it will be able to contribute to the cultural transmission of Nagyangchun.

Features of Science Classes in Science Core Schools Identified through Semantic Network Analysis (언어네트워크분석을 통해 본 과학중점학교 과학수업의 특징)

  • Kim, Jinhee;Na, Jiyeon;Song, Jinwoong
    • Journal of The Korean Association For Science Education
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    • v.38 no.4
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    • pp.565-574
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    • 2018
  • The purpose of this study is to investigate the features of science classes of Science Core Schools (SCSs) perceived by students. 654 students from 14 SCSs were surveyed with two open-ended questions on the features of science classes. The students' responses were analyzed with NetMiner 4.5, in terms of the centrality (of betweenness and of degree) analysis and the community analysis. The results of the research are as follows: (1) the science classes of SCSs were perceived by students to be of the environment of free questioning, active participation and communication, caring teacher, more science experiments and advanced contents, and knowledge sharing; (2) science classes in SCSs were perceived to be different from those of ordinary high schools because SCSs provide more opportunities for science-related special courses (like project work, advanced science subjects), extra-curricular activities, inquiry and research activities, school supports, hard-working classroom environment, longer studying hours, R&E and club activities. The students' perceptions of SCS science classes appear to be in line with the characteristics of 'good' science lessons from previous studies. The SCS project itself and the features of SCS science classes would help us to see how we introduce educational innovations into actual schools.