• School Mathematics
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• v.7 no.4
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• pp.445-467
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• 2005

The purpose of this study was to investigate mathematics teaching of an elementary school teacher and to understand the meaning of it. This study was a qualitative case study using by analyzing metaphors. The notion of metaphors was newly set up. Traditionally, it had been regarded as a mere tool for better understanding, but it was recognized as the primary source of all of our concept(Sfard, 1998). The subject of this case study was a researcher 'I' and also an elementary school teacher. The three selves named Mee1, Mee2, Mee3, respectively. Mee1 was the 'I' who developed the 4th graders' activities on mathematical patterns in 1996 and wrote mathematics textbook for the 4th graders in 1998-1999. Mee2 was the 'I' who taught mathematical patterns to her students in 2002. Mee3 was the 'I' who criticized the teaching of Mee2 in 2005. [ADVENTURE], [HIDE-AND-SEEK], and [FIREWORKS DISPLAY] were deter-mined to be key metaphors of mathematics teaching. [ADVENTURE] of Mee] was focused on profound understanding of mathematics, [HIDE-AND-SEEK] of Mee2 on construction of mathematics, and [FIRE-WORKS DISPLAY] of Mee3 on making meaning and participating in communities. Studies of metaphors give us the power of understanding mathematics teaching and also generate it. And viewing mathematics teaching via metaphors makes teaching studies open to new ways.

• Journal for History of Mathematics
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• v.30 no.4
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• pp.247-258
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• 2017

The goal of this essay is to examine metaphors for mathematics and to discuss philosophical problems related to them. Two metaphors for mathematics are well known. One is a tree and the other is a building. The former was proposed by Pasch, and the latter by Hilbert. The difference between these metaphors comes from different philosophies. Pasch's philosophy is a combination of empiricism and deductivism, and Hilbert's is formalism whose final task is to prove the consistency of mathematics. In this essay, I try to combine two metaphors from the standpoint that 'mathematics is a part of the ecosystem of science', because each of them is not good enough to reflect the holistic mathematics. In order to understand mathematics holistically, I suggest the criteria of the desirable philosophy of mathematics. The criteria consists of three categories: philosophy, history, and practice. According to the criteria, I argue that it is necessary to pay attention to Pasch's philosophy of mathematics as having more explanatory power than Hilbert's, though formalism is the dominant paradigm of modern mathematics. The reason why Pasch's philosophy is more explanatory is that it contains empirical nature. Modern philosophy of mathematics also tends to emphasize the empirical nature, and the synthesis of forms with contents agrees with the ecological analogy for mathematics.

• Journal of the Ergonomics Society of Korea
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• v.28 no.2
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• pp.57-67
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• 2009

This study proposed a practical metaphor development process that consisted of three steps: 1) identifying major functions, 2) developing metaphor candidates, and 3) evaluating appropriateness of the candidates. In the first step, a total of 27 functions might be implemented in a driver information system (DIS) in the near future. Then, three metaphor candidates were selected from existing metaphors, which were reported to be more practical than others by previous studies. Finally, the candidates were evaluated on their appropriateness for driver information systems by using a quick and simple survey. As a result, two metaphors (a PC and a secretary) were identified as the most appropriate ones. The two metaphors can be used to design a variety of interfaces and interactions for driver information systems. In addition, the development process proposed in this study could be applied to developing metaphors for emerging devices with a variety of functions (e.g. PMPs, MP3s, and electronic dictionaries) as well as driver information systems.

• Cross-Cultural Studies
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• v.28
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• pp.67-86
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• 2012

Metaphors were conceived of as a figure of speech whose role consisted in merely ornamenting the language. However, with their seminal book Metaphors we live by (1980), Lakoff and Johnson have revolutionized the conception of metaphors by placing them as central to human language, thought and action. Cognitive linguists argue that humans tend to conceptualize abstract concepts, such as time, through more experiential and tangible concepts. For instance, it has been observed that the abstract concept of time is conceptualized as space in several unrelated languages. According to the Conceptual Metaphor Theory (CMT), TIME AS SPACE metaphor covers two more specific metaphors: (1) The MOVING TIME metaphor wherein the observer is conceived as a stationary entity, as in The end of the academic year is getting closer; and (2) The TIME AS A LOCATION metaphor wherein times are conceived as stationary points and the observer is conceived as moving relative to these locations, as in We are first approaching the end of the year. This paper aims at probing the validity of the CMT representations of time on the basis of an analysis of time metaphors in two languages: English and French. This analysis is conducted within the framework of CMT. The results corroborate the CMT representations of time, suggesting that in both languages the abstract concept of time is expressed in spatial terms. In English, as in French, time is conceptualized as a moving entity and as having extension in space. In both languages, time can be seen as bounded; therefore, one can perform actions within defined limits of time.

• Education of Primary School Mathematics
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• v.27 no.3
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• pp.321-331
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• 2024

This study aims to analyze the difficulties encountered in the process of conceptualizing fractions from the perspective of metaphor. To achieve this, metaphors in mathematics education were examined by dividing them into natural conceptualizations through metaphor and their extension to educational metaphors. Subsequently, the difficulties in learning fractions through metaphorical conceptualization were analyzed from three aspects: the integration of multiple metaphors, interference from previously formed grounding metaphors, and the paradoxes of metaphor. Through this analysis, the study highlights the need for careful attention to how metaphors function during fraction learning and aims to provide insights for devising instructional strategies for teaching fractions.

• Journal of Educational Research in Mathematics
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• v.12 no.2
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• pp.275-290
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• 2002

This Study takes Peirce' abduction which is Phenomenology' first reasoning mode, as a part of mathematical reasoning with deduction and induction. Abduction(retroduction, hypothesis, presumption, and originary argument) leads a case through a result and a rule, while deduction leads a result through a rule and a case and induction leads a rule through a case and a result. Polya(1954) involved generalization, specialization, and analogy within induction, but this paper contain analogy in abduction. And metaphors and metonymies are also contained in abduction, in which metaphors are contained in analogy. Metaphors and metonymies are applied to semiosis i.e. the signification of mathematical signs. Semiotic analysis for a student's problem solving showed the semiosis with metaphors and metonimies. Thus, abductions should be regarded as a mathematical reasoning, and we must utilize abductions in mathematical teaming since abductions are thought as a natural reasoning by students.

• International Journal of CAD/CAM
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• v.9 no.1
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• pp.93-102
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• 2010

Shaping realistic hairstyles for digital characters is a difficult, long and tedious task. The lack of appropriate interaction metaphors enabling efficient and simple, yet accurate hair modeling further aggravates the situation. This paper presents 3D interaction metaphors for modeling virtual hair using haptic interfaces. We discuss user tasks, ergonomic aspects, as well as haptics-based styling and fine-tuning tools on an experimental prototype. In order to achieve faster haptic rates with respect to the hair simulation and obtain a transparent rendering, we adapt our simulation models to comply with the specific requirements of haptic hairstyling actions and decouple the simulation of the hair strand dynamics from the haptic rendering while relying on the same physiochemical hair constants. Besides the direct use of the discussed interaction metaphors in the 3D modeling area, the presented results have further application potential in hair modeling facilities for the entertainment industry and the cosmetic sciences.

• Lingua Humanitatis
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• v.8
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• pp.11-38
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• 2006

Laotzu's view of language is well expressed at the beginning stanza of "道可道 非常道" of Tao De Ching, the interpretation of which is pivotal for the proper interpretation of the entire text. Two lines of interpretation of this stanza have been proposed; The first view regards the letter "道" in "非常道" as representing that which is signified by a sign. The other takes the posture that the letter "道" is itself the signifier of the sign. I argue in this article that the second posture should be taken to interpret Tao De Ching properly, contrary to the traditional interpretation of this stanza, by pointing out the verses which inevitably contradict each other when interpreted according to the first view. The second view leads to the conclusion that everyday language is not sufficient enough to describe the supernatural beings, including Tao, accurately, and seeks a way to augment ordinary language for appropriate description of such supernatural beings. The strategy Laotzu adopts in Tao De Ching is to expand the expressive power of ordinary language by extensive use of metaphors. This paper discerns 4 conceptual metaphors in the sense of Johnson and Lakoff(1980) which underlie the metaphors used in Tao De Ching: (1) Tao is Void; (2) Tao is Mother; (3) Tao is Valley; and (4) Tao is Untrimmed Log.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.12 no.10
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• pp.4348-4353
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• 2011

This paper is based on the Cognitive Linguistics point of view on metaphor. Metaphors are not a matter of language use or rhetorics but of a conceptual frame, where thoughts work. The conceptual frames can highlight one aspect affecting our lives while hiding the other aspect of the facts. Politicians use metaphors to persuade people and justify their political decisions. Lakoff argues that the Republicans in the U.S. have their own conceptual framework based on the 'strict father model' of the conservatives, which can be found in important political speeches. Political metaphors supporting this view are found in the 'Attack on Iraq Speech' by G. H. Bush in 1991 and 'Operation Iraqi Freedom Address' by G. W. Bush in 2003.

• Journal of The Korean Association For Science Education
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• v.24 no.4
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• pp.748-757
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• 2004

When teachers for the gifted express metaphors about their teaching, they may develop better understanding and conceptualizing of teaching and enable to choose appropriate teaching strategies for optimizing individualized learning of the gifted. Therefore, the purpose of this study includes to explore metaphors about science teachers' teaching for the gifted in middle schools and classify into types of metaphors. The survey was administered and completed survey instruments by 66 science teachers for the gifted at gifted educational institutions affiliated with local offices of education and 18 science teachers at middle schools were analyzed. It was revealed that science teachers for the gifted described seven types of metaphors about their teaching with characteristics of student-centered (counsel, helper, etc.), teacher-centered (judge, captain, etc.), or student-teacher-interacted (painter, nurse, etc.) types. More than 60% of teachers described their teaching as either student-centered or student-teacher-interacted types. However, percentage of teachers for the teacher-centered and power-oriented type was higher for science teachers for the gifted (33%) than science teachers for regular students (22%). It was also found that female science teachers for the gifted showed higher percentage for teacher-centered and power-oriented (35%) than male teachers (28%) and teachers with BS degree showed higher percentage for student-centered and service-oriented type (33%) than teachers with MS degree (27%). In addition biology teachers for the gifted also were appeared to be more teacher-centered and power-oriented type (60%) than physics (21%), chemistry (6%), and earth science (33%).