• Journal of Elementary Mathematics Education in Korea
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• v.18 no.3
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• pp.475-492
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• 2014

The purpose of this study is to analyze the United States Elementary Mathematics textbooks "Everyday Mathematics", focused on area of the probability. The concept of probability as qualitative probability is taught from Kindergarten in EM curricula for progressive mathematising. EM have reflected both perspectives in probability which are a frequency perspective and a classical perspective. And EM includes abundant activities for remedying the misconceptions of probability. On the basis of the results from this analysis, we have five suggestions which are helpful for the revision of the Korean national curriculum.

• Journal of Educational Research in Mathematics
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• v.11 no.1
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• pp.157-177
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• 2001

Modern society's technological and economical changes require high-level education that involve critical thinking, problem solving, and communication with others. Thus, today's perspective of mathematics and mathematics learning recognizes a potential symbolic relationship between concrete and abstract mathematics. If the problems engage students' interests and aspiration, mathematical problems can serve as a source of their motivation. In addition, if the problems stimulate students'thinking, mathematical problems can also serve as a source of meaning and understanding. From these perspectives, the purpose of my study is to prove that mathematical modeling tasks can provide opportunities for students to attach meanings to mathematical calculations and procedures, and to manipulate symbols so that they may draw out the meanings out of the conclusion to which the symbolic manipulations lead. The review of related literature regarding mathematical modeling and model are performed as a theoretical study. I especially concentrated on the study results of Freudenthal, Fischbein, Lesh, Disessea, Blum, and Niss's model systems. We also investigate the emphasis of mathematising, the classified method of mathematical modeling, and the cognitive nature of mathematical model. And We investigate the purposes of model construction and the instructive meaning of mathematical modeling. In conclusion, we have presented the methods that promote students' effective model construction ability. First, the teaching and the learning begins with problems that reflect reality. Second, if students face problems that have too much or not enough information, they will construct useful models in the process of justifying important conjecture by attempting diverse models. Lastly, the teachers must understand the modeling cycle of the students and evaluate the effectiveness of the models that the students have constructed from their classroom observations, case study, and interaction between the learner and the teacher.

• Journal of the Korean School Mathematics Society
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• v.15 no.3
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• pp.511-533
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• 2012

In order to determine whether there is a significant correlation between relational understanding and creative math. problem finding ability, this study performed relational understanding and problem finding ability tests on a sample of 186 8th grade middle school students. According to the study results, we found a very significant positive correlation between relational understanding and the creativity of the mathematising ability and the combining ability of mathematical concepts in the problem finding ability. Although there was no statistically significant correlation between relational understanding and the extension ability of mathematical facts, the results from analyzing the students response rate and actual scores in each test showed that students with high relational understanding scores also had high response rate and high scores in analogical reasoning and inductive reasoning. Through this study, therefore, relational understanding is found to have a positive impact on the creative mathematics problem finding ability.

• 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.

• Communications of Mathematical Education
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• v.31 no.2
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• pp.223-239
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• 2017

In this paper, it is aimed to design the teaching units 'Inquiry into the isoperimetric problem of triangle and quadrilateral' to give elementary gifted students experience of mathematization. For this purpose, the teacher and the class observer (researcher) made a discussion about the design of the teaching unit through the analysis of the class based on the thought processes appearing during the problem solving process of each group of students. The following is a summary of the discussions that can give educational implications. First, it is necessary to use mathematical materials to reduce students' cognitive gap. Second, it is necessary to deeply study the relationship between the concept of side, which is an attribute of the triangle, and the abstract concept of height, which is not an attribute of the triangle. Third, we need a low-level deductive logic to justify reasoning, starting from inductive reasoning. Finally, there is a need to examine conceptual images related to geometric figure.

• Journal of Educational Research in Mathematics
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• v.11 no.2
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• pp.363-384
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• 2001

The purpose of this thesis is, through analysing the characteristics of the definitions in Korean school mathematics textbooks, to explore the levels of them and to make suggestions for definition - teaching as a mathematising activity, Definitions used in academic mathematics are rigorous. But they should be transformed into various types, which are presented in school mathematics textbooks, with didactical purposes. In this thesis we investigated such types of transformation. With the result of this investigation we tried to identify the levels of the definitions in school mathematics textbooks. And in school mathematics textbooks there are definitions which carry out special functions in mathematical contexts or situations. We can say that we understand those definitions, only if we also understand the functions of definitions in those contexts or situations. In this thesis we investigated the cases in school mathematics textbooks, when such functions of definition are accompanied. With the result of this investigation we tried to make suggestions for definition-teaching as an intellectual activity. To begin with we considered definition from two aspects, methods of definition and functions of definition. We tried to construct, with consideration about methods of definition, frame for analysing the types of the definitions in school mathematics and search for a method for definition-teaching through mathematization. Methods of definition are classified as connotative method, denotative method, and synonymous method. Especially we identified that connotative method contains logical definition, genetic definition, relational definition, operational definition, and axiomatic definition. Functions of definition are classified as, description-function, stipulation-function, discrimination-function, analysis-function, demonstration-function, improvement-function. With these analyses we made a frame for investigating the characteristics of the definitions in school mathematics textbooks. With this frame we identified concrete types of transformations of methods of definition. We tried to analyse this result with van Hieles' theory about levels of geometry learning and the mathematical language levels described by Freudenthal, and identify the levels of definitions in school mathematics. We showed the levels of definitions in the geometry area of the Korean school mathematics. And as a result of analysing functions of definition we found that functions of definition appear more often in geometry than in algebra or analysis and that improvement-function, demonstration-function appear regularly after demonstrative geometry while other functions appear before demonstrative geometry. Also, we found that generally speaking, the functions of definition are not explained adequately in school mathematics textbooks. So it is required that the textbook authors should be careful not to miss an opportunity for the functional understanding. And the mathematics teachers should be aware of the functions of definitions. As mentioned above, in this thesis we analysed definitions in school mathematics, identified various types of didactical transformations of definitions, and presented a basis for future researches on definition teaching in school mathematics.