• School Mathematics
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• v.5 no.1
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• pp.135-149
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• 2003

We present an understanding about students' conceptual model of differential equations, based on the discourse data that were collected in a differential equations course at a university in Korea. An interpretive approach is taken to analyze classroom discourse. This paper consists of three main parts. First, we completely analyze the students' use of conceptual metaphor in a university differential equations class. Secondly, we identify conceptual metaphors representing students' conceptual model of differential equations. Finally, we describe the mathematical characteristics of the conceptual metaphors identified in detail. Among other things, this paper reveals that there exists dual aspects of the students' conceptual model of differential equations. In other words, in the differential equations course observed we found that the students very often used two kinds of conceptual metaphor,“machine metaphor”and“fictive motion metaphor”, that have contrastingly different mathematical characteristics. In order to interpret the duality, we take a sociocultural perspective, and this perspective suggests and helps us to realize the significance of understanding of cognitive diversity in mathematics classroom.

• 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.

• 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.

• Research in Mathematical Education
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• v.1 no.1
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• pp.13-22
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• 1997

Cognitive psychology has provided valuable theoretical perspectives on learning mathematics. Based on the metaphor of the mind as an information processing device, educators and psychologists have developed detailed models of competence in a variety of areas of mathematical skill and understanding. Unquestionably, these models are an asset in thinking about the curriculum we want our students to follow. But any psychological paradigm has aspects of learning and knowledge that it accounts for well, and others that it accounts for less well. For instance, the paradigm of cognitive science gives us valuable models of the knowledge we want our students to acquire; but in picturing the mind as a computational device it reduces us to conceiving of learning in individualist terms. It is less useful in helping us develop effective learning communities in our classrooms. In this paper I review some of the significant accomplishments of cognitive psychology for mathematics education, and some of the directions that situated cognition theorists are taking in trying to understand knowing and learning in terms that blend individual and social perspectives.