期刊名称：Bolema: Mathematics Education Bulletin = Bolema: Boletim de Educação Matemática
印刷版ISSN：1980-4415
出版年度：2012
卷号：26
期号：44
页码：1345-1366
语种：Portuguese
出版社：UNESP - Campus de Rio Claro - Instituto de Geociências e Ciências Exatas
摘要：This study provides support to the characteristics of participatory and anticipatory stages in secondary school pupils’ abstraction of mathematical conceptions. We carried out clinical task-based interviews with 71 secondary-school pupils to obtain evidence of the different constructed mathematical conceptions (Participatory Stage) and how they were used (Anticipatory Stage). We distinguish two moments in the Participatory Stage based on the coordination of information from particular cases by activity-effect reflection which, in some cases, lead to a change of focus enabling secondary-school pupils to achieve a reorganization of their knowledge. We argue that (a) the capacity of perceiving regularities in sets of particular cases is a characteristic of activity-effect reflection in the abstraction of mathematical conceptions in secondary school, and (b) the coordination of information by pupils provides opportunities for changing the attention-focus from the particular results to the structure of properties. Key words: Mathematical Abstraction. Activity-effect Reflection. Reflective Abstraction. Formation of Mathematical Objects. Participatory and Anticipatory Stages.
