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The research aims at investigating the process of acquiring a theoretical perception of the Cartesian plane by Grade 1 children. We are using a dual theoretical lens of Husserlian phenomenology and Vygotsky’s cultural-historical approach, in order to highlight the crucial interplay of cultural practice and the learner’s intentionality in the learning process. A dual eye-tracker is used in order to track moments of joint attention that occurred during the shared activity of a child and an adult. Additionally, external video exposes the subtle interplay of embodied and reflective perceptions in the child’s intentional synthesis, which includes what the adult intends. Hence the paper takes further Radford’s ‘poetic moment’ in merging opposed theoretical perspectives in the study of the emergence of mathematical perception.