• 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.