Theory of Didactical Situations in Mathematics as one of the theoretical approaches to the LPS analysis of classroom data: the case of institutionalization
Abstract
The Learner's Perspective Study (LPS) offers an extremely rich source of data for analyses of classroom situations. In this paper we focus on events in mathematics classrooms through the lens of the Theory of Didactical Situations in Mathematics, namely, on the situation of institutionalization.
During the phase of institutionalization, the teacher tends to help pupils to transform a piece of their knowledge from the means of resolving a problem to a reference for further uses in new situations. A detailed analysis of transcripts of communication between a Czech teacher and her 14 to 15-year-old pupils resulted in the classification of institutionalization into four types, as follows: asking additional questions referring to statements from the stage of validation with the aim of adding new knowledge to the repertoire; presenting a mathematical proof of a statement from validation; asking pupils to solve a similar problem; and setting problems for pupils, whose solution will allow them to apply the acquired knowledge.
These are presented and illustrated in the paper. The combination of video-recordings from three cameras (one recording the teacher, one a pair of pupils and one the whole class), together with interviews with the teacher and the pair of pupils, materials prepared by the teacher, and pupils' productions, allows us to gain a deeper understanding of the role of institutionalization in mathematics education.