Abstract
Background: In recent years, many states and municipalities have adopted official teaching materials to guide teacher practice. However, the relationship between the use of these materials and the continuing education of in-service teachers has been little investigated. Objective: To analyse how the development of the theoretical thinking of teachers about the multiplication of fractions impacts the choice, use, or adequacy of teaching materials. Design: The theoretical and methodological foundation is based on the historical-cultural perspective seeking, in the investigation of human activity, to understand the development of theoretical thinking. Setting and participants: Continuing education with a group of 11 mathematics teachers from the state public network of São Paulo. Learning triggering situations have been proposed to overcome discretisation in the approach to fractions. Data collection and analysis: Data were collected through video recordings, written material produced by teachers and registers in a field diary. Two isolated were organised for analysis “Movement of theoretical thinking about fractions” and “Didactic material as a mediator of the teacher's action.” Results: As they theoretically understand the meaning of multiplication between fractions, teachers overcome the mechanisation of rules and begin to reveal an understanding of the interrelationship of arithmetic, algebraic, and geometric elements in teaching. Conclusion: The development of aspects of theoretical thinking about the multiplication of fractions allowed teachers to organise teaching in order to make explicit the essential and theoretical relationships of the concept. Didactic material is understood as mediation in the teaching process and its use is no longer seen as an end in itself.
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