• Journal of Educational Research in Mathematics
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• v.26 no.4
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• pp.731-754
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• 2016

The purpose of the study is to identify the point of knowing. The point of knowing is the time, which indicates that 'knowing' occurs in the recognition process. To understand recognition process, the researchers analyzed the questions in units of lessons presented in elementary mathematics textbooks. The researchers analyzed the validity of the point of knowing and found out the basis of the point of knowing. The results are as follows. First, the point of knowing is time to expect to change from a leaner's 'not-knowing' to 'knowing'. Second, the point of knowing can be identified with the questions on textbooks to ask students to do practical action. Third, the point of knowing is closely related to instructional objective in a class. Fourth, in relation to subsidiary awareness and focal awareness, the point of knowing corresponds to focal awareness. Fifth, the point of knowing is equivalent to the inflection point at which personalization/contextualization is changed into depersonalization/decontextualization.

• Journal of Educational Research in Mathematics
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• v.26 no.2
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• pp.173-188
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• 2016

Research on didactic transposition in mathematics education has about 25-year and about 35-year long history in and out of Korea, respectively. This study attempts to investigate in trends of those research and to suggest tasks needed to be tackled. Major findings are followed. First, studies done in Korea tended to focus on the application of the didactic transposition theory for proving its effectiveness in understanding mathematics textbooks and mathematics lessons in-depth. It is suggested to conduct meta-analysis of the accumulated results or analysis of further applications of the didactic transposition theory to improve theoretical aspects of didactic transposition. Second, new categories for extreme teaching phenomenon were found and new typology in knowledge to be considered in the didactic transposition was developed in a few studies done in other subject matter education. Application of these to mathematics education may enhance research in didactic transposition of mathematical knowledge. Third, praxeology or a complex of praxeology for Korean school mathematics should be explored as did in other countries. Fourth, there have been rich attempts to link perspectives in didactic transposition to other perspectives or fields such as anthropology, human and education in technology era, praxeology theory in economics, epistemology in other countries but not in Korea. It is suggested to extend the scope of discussion on didactic transposition and to relate various concepts given in other disciplines. Fifth, clarification or negotiation of meaning for the main terms used in the discussion on didactic transposition such as personalization, contextualization, depersonalization, decontextualization, Topaze Effect, Meta-Cognitive Shift is suggested by comparing researchers' various descriptions or uses of the terms.

• Communications of Mathematical Education
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• v.21 no.3
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• pp.407-430
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• 2007

The extreme didactic phenomena that occur by ignoring or overemphasizing the process of personalization/contextualization, depersonalization/decontextualization of mathematical knowledge is always in our teaching practice and in fact, seems to be a kind of phenomena that suppress teachers psychologically or didactically. The study of the problems on error, misconception or obstacles revealed by students has been done continuously, but that of the extreme didactic phenomena revealed by teachers has not. In this study, I will explain four extreme didactic phenomena and help you understand them by giving various examples from several case studies and analyzing them. And also, I will discuss the way to overcome the extreme didactic phenomena in the mathematical class, based on this analysis. This thesis will become a standard of didactic phenomena that are proceeded extremely by having teachers reconsider their own classes and furthemore, will offer the research data for considering better didactic situation.