• The Mathematical Education
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• v.53 no.1
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• pp.147-162
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• 2014

The purpose of this study was to investigate the nature of pre-service elementary teachers' metaphors on mathematics textbooks. Their metaphors describe individual and collective patterns of thinking and action on mathematics teaching and learning. To analyze their metaphors, qualitative analysis method based on Lakoff and Johnson's theory of metaphor (1980) was adopted. Metaphors on mathematics textbooks were elicited from 161 pre-service elementary school teachers through writing prompts. The writing prompt responses revealed three types and thirteen categories: As Type I, there were (1) 'Principles', (2) 'Summary', (3) 'Manual', (4) 'Encyclopedia', (5) 'Code', (6) 'Guidelines', and (7) 'Example'. As TypeII, there were (9) 'Assistant', (10) 'Friend', (11) 'Scale', and (12) 'Ongoing'. As TypeIII, there was (13) 'Trap'. Among these categories, 'Guidelines', 'Assistant', and 'Ongoing' were the most frequently revealed. These results indicate that the relations of mathematics curriculum, textbooks, and classrooms are not a unilateral way but should communicate with each other.

• Communications of Mathematical Education
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• v.29 no.1
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• pp.51-72
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• 2015

This study aimed to analyze the characteristic of undergraduate students' perception and preference for mathematics. For this purpose, I surveyed 124 undergraduate students' metaphorical expressions about mathematics. I classified the expressions as four categories: a positive form, a negative form, a mixed form, an undecidable form. I investigated the proportion and characteristic of the metaphorical expressions according to the above four categories. Also, I surveyed the students' preference and nonpreference moments for mathematics and categorized them into 6-cases: elementary school, middle school, high school, university, always, and none. In addition, I examined the students' preference and nonpreference reasons for mathematics and classified them according to the 5-factors: grade factor, affective factor, content factor, teacher factor, and other factors. The results of this study as follows: First, the 27% of university students expressed their metaphorical expressions for mathematics as a positive form, 42% as a negative form, and 27% as a mixed form. Also, the preference rate for mathematics was higher as their school years increase and the main reasons of preference were grade and affective factors. The result of nonpreference rate was also higher as their school year increased. Students said that the contents and grade factor were the main factors among the 5-factors.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2006.05a
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• pp.17-31
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• 2006

• Communications of Mathematical Education
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• v.16
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• pp.175-180
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• 2003

• School Mathematics
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• v.18 no.1
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• pp.215-229
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• 2016

This study aims to identify Archimedes' idea used while proving proposition 23 in 'Quadrature of the Parabola' and to provide an alternative way for finding the sum of geometric series without applying the concept of limit by extending the idea though metaphor. This metaphorical model is characterized as static and thus can be complimentary to the dynamic aspect of limit concept adopted in Korean high school mathematics textbooks. In addition, middle school students can understand $0.999{\cdots}=1$ with this model in a structural way differently from the operative one suggested in Korean middle school mathematics textbooks. In this respect, I argue that the metaphorical model can be an useful educational tool for Korean secondary students to overcome epistemological obstacles inherent in the concepts of infinity and limit by making it possible to transfer from geometrical context to algebraic context.

• Journal of Educational Research in Mathematics
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• v.14 no.3
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• pp.221-237
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• 2004

This research analyzed mathematical discourse of the students in an RME-based differential equations course at a university in order to investigate the social transformation of the students' conceptual model of differential equations. The analysis focused on the change in the students' use of conceptual metaphor for differential equations and pedagogical factors promoting the change. The analysis shows that discrete and quantitative conceptual model was prevalent in the beginning of the semester However, continuous and qualitative conceptual model emerged through the negotiation of mathematical meaning based on the inquiry of context problems. The participation in the project class has a positive impact on the extension of the students' conceptual model of differential equations and increases the fluency of the students' problem solving in differential equations. Moreover, this paper provides a discussion to identify the pedagogical factors Involved with the transformation of the students' conceptual model. The discussion highlights the sociocultural aspect of teaching and learning of mathematics and provides implications to improve teaching of mathematics in school.

• Journal of Educational Research in Mathematics
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• v.12 no.4
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• pp.523-542
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• 2002

The matter of understanding mathematical concepts in learning mathematics is one of the most important issues in mathematics education. There have been so many studies about it but the more practical study has been asked. When we Think using intuitional models such as examples, figures of speech, situations and activities, it is supposed that the major elements of cognitive mechanism are prototypes, analogies, metaphors and metonymies. In this paper, we tried to examine Rosch's prototype theory, the studies about analogies in congnitive psychology, Lakoff and Johnson's metaphor theory from the viewpoint of teaching mathematics, and then tried to analyze examples, analogies, analogical transfers, metaphorical expressions, metonymies in middle school mathematics text books used in Korea now.

• 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.

• Education of Primary School Mathematics
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• v.25 no.4
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• pp.395-410
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• 2022

Nominalization is one of the grammatical metaphors, and it is the representation of verbal meaning through noun equivalent phrases. In mathematical word problems, texts using nominalization have both the advantage of clarifying the object to be noted in the mathematization stage, and the disadvantage of complicating sentence structure, making it difficult to understand the sentences and hindering the experience of the full steps in mathematical modelling. The purpose of this study is to analyze word problems in the textbooks from the perspective of nominalization, a linguistic element, and to derive implications in relation to students' difficulties during solving the word problems. To this end, the types of nominalization of 341 word problems from the content domain of 'Numbers and Operations' of elementary math textbooks according to the 2015 revised national curriculum were analyzed in four aspects: grade-band group, main class and unit assessment, specialized class, and mathematical expression required word problems. Based on the analysis results, didactical implications related to the linguistic expression of the mathematical word problems were derived.

• Education of Primary School Mathematics
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• v.19 no.4
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• pp.361-380
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• 2016

This study aims to reflect on mathematical imaginations in learning mathematics and elementary students' mathematical imaginations. This was approaching a study of imagination not as psychological problems but as objects and methods of mathematics learning. First, children's mathematical narratives were analysed in terms of Egan(2008)'s basic cognitive tools using imagination, that is, metaphor, binary opposites, rhyme rhythm pattern, jokes humor, mental imagery, gossip, play, mystery. Second, how children's imaginations change under different grades was addressed.