The process of algebraic generalization: the constant movement between the empirical and the theoretical

• Grant number: 11/23473-6
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: September 01, 2012
• End date: December 31, 2012
• Field of knowledge: Humanities - Education - Educational Teaching and Learning
• Principal Investigator: Manoel Oriosvaldo de Moura
• Grantee: Maria Lucia Panossian
• Supervisor: Joaquin Gimenez Rodriguez
• Host Institution: Faculdade de Educação (FE). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: Universitat de Barcelona (UB), Spain
• Associated to the scholarship: 10/15383-4 - Contributions of cultural-historical theory to organize the teaching of algebra, BP.DR

Abstract

The present abroad research project is an action of the whole research of the PhD project in development titled "Contributions of cultural-historical theory to organize the teaching of algebra". An initial analysis about the data obtained from a actualization course for teachers and from some curricula programs, indicate the predominance of the generalization process as fundamental to algebra teaching. However, what kind of generalization process is it? Is it the empirical generalization obtained by abstraction from what is common in particular cases (leading to a generalized arithmetic) or the theoretical generalization that extracts what is general and essential of different situations and constituted the essence of algebraic concepts? Since this issue was generated the objective of investigate the algebraic generalization process in its logical-historic movement emerged as a means of achieving the teaching organization for the formation of theoretical thinking. This research will be developed at University of Barcelona, under the supervision of Professor Joaquin Gimenez, renowned researcher of Math teaching, and with his research group during the second semester of 2012. (AU)