• Title/Summary/Keyword: general mathematics

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A Survey on the Proportional Reasoning Ability of Fifth, Sixth, and Seventh Graders (5, 6, 7학년 학생들의 비례추론 능력 실태 조사)

  • Ahn, Suk-Hyun;Pang, Jeong-Suk
    • Journal of Educational Research in Mathematics
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    • v.18 no.1
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    • pp.103-121
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    • 2008
  • The primary purpose of this study was to gather knowledge about $5^{th},\;6^{th},\;and\;7^{th}$ graders' proportional reasoning ability by investigating their reactions and use of strategies when encounting proportional or nonproportional problems, and then to raise issues concerning instructional methods related to proportion. A descriptive study through pencil-and-paper tests was conducted. The tests consisted of 12 questions, which included 8 proportional questions and 4 nonproportional questions. The following conclusions were drawn from the results obtained in this study. First, for a deeper understanding of the ratio, textbooks should treat numerical comparison problems and qualitative prediction and comparison problems together with missing-value problems. Second, when solving missing-value problems, students correctly answered direct-proportion questions but failed to correctly answer inverse-proportion questions. This result highlights the need for a more intensive curriculum to handle inverse-proportion. In particular, students need to experience inverse-relationships more often. Third, qualitative reasoning tends to be a more general norm than quantitative reasoning. Moreover, the former could be the cornerstone of proportional reasoning, and for this reason, qualitative reasoning should be emphasized before proportional reasoning. Forth, when dealing with nonproportional problems about 34% of students made proportional errors because they focused on numerical structure instead of comprehending the overall relationship. In order to overcome such errors, qualitative reasoning should be emphasized. Before solving proportional problems, students must be enriched by experiences that include dealing with direct and inverse proportion problems as well as nonproportional situational problems. This will result in the ability to accurately recognize a proportional situation.

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Case Study on Meaningful use of Parameter - One Classroom of Third Grade in Middle School - (매개변수개념의 의미충실한 사용에 관한 사례연구 -중학교 3학년 한 교실을 대상으로-)

  • Jee, Young Myong;Yoo, Yun Joo
    • School Mathematics
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    • v.16 no.2
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    • pp.355-386
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    • 2014
  • Algebraic generalization of patterns is based on the capability of grasping a structure inherent in several objects with awareness that this structure applies to general cases and ability to use it to provide an algebraic expression. The purpose of this study is to investigate how students generalize patterns using an algebraic object such as parameters and what are difficulties in geometric-arithmetic pattern tasks related to algebraic generalization and to determine whether the students can use parameters meaningfully through pattern generalization tasks that this researcher designed. During performing tasks of pattern generalization we designed, students differentiated parameters from letter 'n' that is used to denote a variable. Also, the students understood the relations between numbers used in several linear equations and algebraically expressed the generalized relation using a letter that was functions as a parameter. Some difficulties have been identified such that the students could not distinguish parameters from variables and could not transfer from arithmetical procedure to algebra in this process. While trying to resolve these difficulties, generic examples helped the students to meaningfully use parameters in pattern generalization.

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Study on the Levels of Informal Statistical Inference of the Middle and High School Students (중·고등학생들의 비형식적 통계적 추리의 수준 연구)

  • Lee, Jung Yeon;Lee, Kyeong Hwa
    • School Mathematics
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    • v.19 no.3
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    • pp.533-551
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    • 2017
  • The statistical education researchers advise instructors to educate informal statistical inference and they are paying close attention to the progress of the statistical inference in general. This study was conducted by analyzing the levels and the traits of each levels of the informal statistical inference of the middle and high school students for comparing the samples of data and estimating the graph of a population. Research has shown that five levels of the informal statistical inference were identified for comparing the samples of data: responses that are distracted or misled by an irrelevant aspect, responses that focus on frequencies of individual data points and hold a local view of the sample data sets, responses that the student's view of the data is transitioning from local to global, responses that hold a global view but do not clearly integrate multiple aspects of the distribution, and responses that integrate multiple aspects of the distribution. Another five levels of the informal statistical inference were identified for estimating the graph of a population: responses that are distracted or misled by an irrelevant aspect, responses that focus only on representativeness, responses that consider both representativeness and variability and focus on one particular aspect of the distribution, responses that focus on multiple aspects of distribution but do not clearly integrate them, and responses that integrate multiple aspects of the distribution.

An Analysis on Behavior Characteristics between Gifted Students and Talented Students in Open-end Mathematical Problem Solving (개방형 문제 해결과정에서 수학 영재아와 수학 우수아의 행동특성 분석)

  • Shin In-Sun;Kim See-Myung
    • Communications of Mathematical Education
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    • v.20 no.1 s.25
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    • pp.33-59
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    • 2006
  • This study is intended to reconsider the meaning of the education for gifted/talented children, the foundation object of science high school by examining the behavior characteristics between gifted students and talented students in open-end mathematical problem solving and to provide the basis for realization of 'meaningful teaming' tailored to the learner's level, the essential of school education. For the study, 8 students (4 gifted students and 4 talented students) were selected out of the 1 st grade students in science high school through the distinction procedure of 3 steps and the behavior characteristics between these two groups were analyzed according to the basis established through the literature survey. As the results of this study, the following were founded. (1) It must be recognized that the constituent members of science high school were not the same excellent group and divided into the two groups, gifted students who showed excellence in overall field of mathematical behavior characteristics and talented students who had excellence in learning ability of mathematics. (2) The behavior characteristics between gifted students and talented students, members of science high school is understood and a curriculum of science high school must include a lesson for improving the creativity as the educational institutions for gifted/talented students, unlike general high school. Based on these results, it is necessary to try to find a support plan that it reduces the case which gifted students are generalized with common talented students by the same curriculum and induces the meaningful loaming to learners, the essential of school education.

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An Exploration of Cognitive Demand Level in MiC Textbook based on the Tasks of 'Data Analysis and Probability' (MiC 교과서의 과제에 대한 인지적 요구 수준 탐색 -'자료 분석과 확률' 영역을 중심으로-)

  • Hwang, Hye Jeang;Jeong, Ji hye
    • Communications of Mathematical Education
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    • v.31 no.1
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    • pp.103-123
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    • 2017
  • Mathematical tasks in general introduce and deal with real-life situations, and they derive to students' thinking fluently in solving the given tasks. The tasks might be considered as an important and significant factor to lead a successful mathematical teaching and learning situation. MiC Textbook is a representative one showing such good examples and tasks. This study explores concretely and in detail the cognitive demand level of mathematical tasks, by the subject of MiC Textbook. To accomplish this, this study is to reconstruct more elaborately the analysis framework developed by Hwang and Park in 2013. The framework basically was set up utilizing 'the cognitive demand level' suggested by Stein, et, al. The cognitive demand level is divided into two levels such as low level and high level. The low level is comprized of two elements such as Memorization Tasks(MT), Procedures Without Connections Tasks(PNCT), and high level is Procedures With Connections Tasks(PWCT), and Doing Mathematics Tasks(DMT). This study deals with the tasks on the area of 'data analysis and statistics' in MiC 1, 2, 3 level Textbook. As a result, mathematical tasks of MiC Textbook led learners to deal with and understand mathematical content for themselves, and furthermore to do leading roles for checking and reinforcing the content. Also, mathematical tasks of MiC Textbook are comprized of the tasks suitable to enhance mathematical thinking ability through communication. In addition, mathematical tasks of MiC Textbook tend to offer more learning opportunity to learners' themselves while the level of MiC Textbook is going up.

A study on the contents related to the plane figures of Joseon-Sanhak in the late 18th century (18세기 후반 조선산학서에 나타난 평면도형 관련 내용 분석)

  • Choi, Eunah
    • The Mathematical Education
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    • v.61 no.1
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    • pp.47-62
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    • 2022
  • This study investigated the contents related to the plane figures in the geometry domains of Joseon-Sanhak in the late 18th century and focused on changes in explanations and calculation methods related to plane figures, the rigor of mathematical logic in the problem-solving process, and the newly emerged mathematical topics. For this purpose, We analyzed , and written in the late 18th century and and written in the previous period. The results of this study are as follows. First, an explanation that pays attention to the figures as an object of inquiry, not as a measurement object, and a case of additional presentation or replacing the existing solution method was found. Second, descriptions of the validity of calculations in some problems, explanations through diagrams with figure diagrams, clear perceptions of approximations and explanations of more precise approximation were representative examples of pursuing the rigor of mathematical logic. Lastly, the new geometric domain theme in the late 18th century was Palsun corresponding to today's trigonometric functions and example of extending the relationship between the components of the triangle to a general triangle. Joseon-Sanhak cases in the late 18th century are the meaningful materials which explain the gradual acceptance of the theoretical and argumentative style of Western mathematics

Relationships between thinking styles and the Components of Mathematical Ability of the Elementary Math Gifted Children and General Students (초등 수학영재와 일반학생의 사고양식 및 수학적 능력 구성 요소)

  • Hong, Hyejin;Kang, Wan;Lim, Dawon
    • Education of Primary School Mathematics
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    • v.17 no.2
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    • pp.77-93
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    • 2014
  • The purpose of this study was to investigate the relationships between thinking styles and the components of mathematical ability of elementary math gifted children. The results of this study were as follows: First, there were differences in thinking styles: The gifted students prefer legislative, judical, hierarchic, global, internal and liberal thinking styles. General students prefer oligarchic and conservative thinking styles. Second, there were differences in components of mathematical ability: The gifted students scored high in all sections. And if when they scored high in one section, then they most likely scored high in the other sections as well. But the spacial related lowly to the generalization and memorization. There is no significant relationship between memorization and calculation Third, there was a correlation between thinking styles and components of mathematical ability: Some thinking styles were related to components of mathematical ability. In functions of thinking styles, legislative style have higher effect on calculation. And executive, judical styles related negatively to the inference ability. In forms of thinking styles monarchic style had higher effect on space ability, hierarchic style had higher effect on calculation. Monarchic, hierarchic styles related negatively to inference ability. In level of thinking styles global, local styles have higher effect on calculation. Local styles related negatively to the inference ability. In the scope of thinking styles, internal style had a higher effect on generalization, and external style had a higher effect on calculation. And there is no significant relationship leaning of thinking styles.

Language and Symbolic Reference in Whitehead′s Philosophy (화이트헤드의 언어 이해와 상징적 연관)

  • 문창옥
    • Lingua Humanitatis
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    • v.6
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    • pp.147-166
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    • 2004
  • Whitehead's discussion of language is not to be found in any one book or article. It is interwoven with his discussion of many other questions. He was, however, greatly concerned with the problem of symbolism in general and the uses of language. He regards language, spoken or written, as an instrument devised by men to aid them in their adjustment to the environment in which they live Language is used for many specific purposes in the process of this adjustment. Words are employed not only to refer to data and to express emotions. They may be used also to record experiences, and thoughts about these experiences. Worts also function as instruments in the organization of experiences as they are considered in retrospect. Thus words free us from the bondage of the immediate. And Whitehead's theory of meaning is implicit in his discussion of the functions of language. According to him, the human mind is functioning symbolically when some components of its experience elicit consciousness, beliefs, emotions, and usages, respecting other components of its experiences. The former set of components are the 'symbols', and the latter set constitute the 'meaning' of the symbols. Whitehead points out that one word may have several meanings, i.e. refer to several different data. In order to understand, thus, the meaning to which a word refers, it is sometimes very important to appreciate the system of thought within which a person is operating. Further, Whitehead's discussion of language includes a number of cogent warning the deficiencies of language, and hence the need for great care in the use of words. In fact, language developed gradually. For the most part we have created words designed to deal with practical problems. Attention focuses on the prominent features in a situation, in particular the changing aspects of things. With reference to such data our words are relatively adequate. However, this issues in an unfortunate superficiality. The enduring, the subtle, the complex and the general aspects of the universe do not have adequate verbal representation. for this reason, Whitehead's position concerning the uses of language in speculative philosophy is stated with pungent directness. The uncritical trust in the adequacy of language is one of the main errors to which philosophy is liable. Since ordinary language does not do justice to the generalities, profundities and complexities of life, it is obvious that philosophy requires new words and phrases, or at least the revision of familiar words and phrases. Proceeding to develop the theme Whitehead contends that words and phrases must be stretched towards a generality foreign to their ordinary usage. In the same vein Whitehead refers to the need to realize that language which is the tool of philosophy needs to be redesigned just as in physical science available physical apparatus needs to be redesigned. But even these words and phrases, stretched or redesigned, are never completely adequate in philosophical speculations. They are, in his opinion, merely a great improvement over ordinary language or the language science, mathematics or symbolic logic.

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A study on the left/right brain utilization tendency of information prodigies (정보영재 학생의 좌·우뇌 활용 성향 연구)

  • Nam, Seun Kwon;Choi, Won Sik;Lim, Byoung Ung
    • 대한공업교육학회지
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    • v.33 no.1
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    • pp.23-43
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    • 2008
  • The purpose of this study is to provide some necessary baseline data to the information prodigy related research through the study on the brain left/right tendency of information prodigies. Subjects were 298 gifted students(59 information, 79 mathematics, 80 science, 40 invention, 40 social science) and 114 general students summing up 412 in the schools of Daejeon metropolitan area. 'Brain Tendency Test' developed by Torrance and modified by Ko in Korean was used as a tool to measure the prodigies' brain tendencies. Data analysis has been done with the $x^2$ test of frequency with the alpha = .05. The results of this study are as follows. 1) The information gifted students have tendencies of utilizing right brain hemisphere at the most, both left/right brain(whole brain) utilization at the second, and left brain utilization at the last. 2) There was statistically no difference between information prodigies and general students in the left/right brain tendency. 3) There was statistically mild evidence to support the notion that there are some differences in the brain tendency between the group of information prodigies and the group of other area of the prodigies. The degree of inclination to utilize the whole brain hemisphere for the prodigies of the other area was the highest compare to other left/right brain utilization while the information prodigies tend to utilize the right brain hemisphere at the most. 4) The female information prodigies have tendencies of utilizing while brain area at the most, right brain utilization at the second, and left brain utilization at the last contrary to the brain utilization tendencies in the male information prodigies which are the same as the brain utilization tendencies of the information prodigies. However there was no difference in brain tendencies statistically between the two groups since the female subjects were too small.

A Case Study on the Effect of the Artificial Intelligence Storytelling(AI+ST) Learning Method (인공지능 스토리텔링(AI+ST) 학습 효과에 관한 사례연구)

  • Yeo, Hyeon Deok;Kang, Hye-Kyung
    • Journal of The Korean Association of Information Education
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    • v.24 no.5
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    • pp.495-509
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    • 2020
  • This study is a theoretical research to explore ways to effectively learn AI in the age of intelligent information driven by artificial intelligence (hereinafter referred to as AI). The emphasis is on presenting a teaching method to make AI education accessible not only to students majoring in mathematics, statistics, or computer science, but also to other majors such as humanities and social sciences and the general public. Given the need for 'Explainable AI(XAI: eXplainable AI)' and 'the importance of storytelling for a sensible and intelligent machine(AI)' by Patrick Winston at the MIT AI Institute [33], we can find the significance of research on AI storytelling learning model. To this end, we discuss the possibility through a pilot study targeting general students of an university in Daegu. First, we introduce the AI storytelling(AI+ST) learning method[30], and review the educational goals, the system of contents, the learning methodology and the use of new AI tools in the method. Then, the results of the learners are compared and analyzed, focusing on research questions: 1) Can the AI+ST learning method complement algorithm-driven or developer-centered learning methods? 2) Whether the AI+ST learning method is effective for students and thus help them to develop their AI comprehension, interest and application skills.