• School Mathematics
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• v.8 no.4
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• pp.417-439
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• 2006

Many studies indicate the emerging crisis of education of calculus even though the emphasis of calculus have been widely recognized. In our classrooms, the education of calculus also has been faced with its bounds. Most instructions of calculus is too much emphasis on the algebraic approach, thus students solve mathematical problems without truly understanding the underlying concept. The purpose of this study is to develop mathematization teaching and learning materials and methods in caculus based on the mathematization teaching and learning theories by Freudenthal and the variability principles of conceptual learning by Dienes, In order to this purpose, first, we analyzed the high school mathematics II textbook of 7th curriculum in Korea. Second, we developed mathematization teaching and learning materials and methods in highschool calculus. Consequently, the following conclusions have been drawn: we have reorganized and reconstructed the context problem in calculus based on concepts of tangent line and instantaneous rate of change.

• Journal of Elementary Mathematics Education in Korea
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• v.1 no.1
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• pp.123-140
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• 1997

Researchers have insisted that mathematics should be learned not as a product but as a process. Nevertheless school mathematics has chosen ‘top-down’ method and has usually instilled into the mind of students the mathematical concepts in the form of product. Consequently school mathematics has been teamed by students without the process of inquiring and mathematical thinking. According to Freudenthal, it is a major source of all problems of mathematics education. He suggested mathematising as the method for 'teaching to think mathematically' 'Teaching to think mathematically' through the process of mathematization, interpreting and analysing mathematics as an activity, is a means to embody the purpose of mathematics education.

• The Mathematical Education
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• v.61 no.3
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• pp.419-439
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• 2022

This study is based on Freudenthal's mathmatising process and the didactical phenomenology of linear function concept, I have described and examined the process in which students represent the constant rate of change into tables, graphs and equations and, in this way, how they construct mental objects and essence of the linear function concept. The students used the proportionality as composite units, when they represented the phenomenon with constant rate of change into tables. When representing in graphs, all but one student represented it into a line. There were differences among the students in the level they were using the given conditions, co-variation perspective, and corresponding rules when formulating equations. The students compared the relationship between two variables in a multiplicative way, and under the guidance of teachers they reached to the understanding that its relationship becomes a constant. Moreover, they could construct mental objects of a constant rate of change, understanding the situation where the relationship between time difference and distance difference becomes one value, namely speed. The students had difficulties in connecting the rate of change with the inclination of a line. The students constructed the essence (concept) of linear functions, after building and organizing the image that the rate of change is constant, the graph is linear, and the equation is formulated as y=ax+b (a: inclination, b: intercept).

• The Mathematical Education
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• v.44 no.2 s.109
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• pp.159-167
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• 2005

As the 7th mathematics curriculum reform in Korea was implemented with its goal based on Freudenthal's perspectives on mathematization theory, the research on the effect of mathematization has been become more significant. The purpose of this thesis is not only to find whether this foreign theory would be also applied effectively into our educational practice in Korea, but also to investigate how much important role teachers should play in their teaching students, in order that students accomplish the process of mathematization more effectively. Two case studies were carried out with two groups of middle-school students using qualitative-research method with the research instrument designed by the researcher. It was found that we could get the possibility of being able to apply effectively this theory even to our educational practice since the students engaged in their mathematization using the horizontal mathematization and the vertical mathematization in geometry. Also, it was mentioned that teachers' role was so important in guiding students' processes of mathematization, although mathematization is the teaching-learning theory, stimulating students' activities. Since the Freudenthal's mathematization applied in the thesis is so meaningful in our educational practice, we need more various research about this theory that helps students develope their mathematical thinking.