Abstract
Background: One of the great challenges for mathematics education in the 21st century is to alleviate the difficulties of students in the transition from arithmetic to algebra. There is already a consensus that there should not be a transition, as several experts have indicated algebraic approaches since the early years of schooling. Objectives: This study aims to describe and analyze the operative invariants of algebraic patterns present in the strategies of students of the 3rd grade of an elementary public school in the countryside of the state of Rio Grande do Sul. Design: The methodology used in this research was the clinical method of manipulation-formalization, created by Jean Piaget and applied in several of his studies. Setting and Participants: Students of the 3rd grade. Data collection and analysis: Clinical interviews. Results: We start from the assumptions of Gerard Vergnaud's theory of conceptual fields to analyze the strategies used by the research participants. Conclusions: We identified four operative invariants: the theorems-in-action "count the places each time a table is introduced" and "add two places each time a table is introduced", respectively linked with the concepts-in-action "putting the tables together" and "place at the ends of the tables".
Highlights
Algebra is one of the major areas of mathematics that comprises the study of equation solving methods and the more general properties of polynomials
We can think of a parallel concerning the children’s’ learning of Algebra, that is, at first, they express their algebraic ideas in their natural language, understanding and trying to generalize these ideas as they come in contact with gradually more formal problems throughout their schooling
According to data from NCTM (2000), one of the great challenges for mathematics education in the 21st century is to alleviate the difficulties of students in the transition from
Summary
Algebra is one of the major areas of mathematics that comprises the study of equation solving methods and the more general properties of polynomials. The difference between the methods of the ancient peoples to the methods introduced by the Arabs is in representation While the former were more dedicated to describing the resolution of practical problems, expressing the resolution through natural language, the Arabs created a specific language to communicate the most general ideas of their methods. Objectives: This study aims to describe and analyze the operative invariants of algebraic patterns present in the strategies of students of the 3rd grade of an elementary public school in the countryside of the state of Rio Grande do Sul. Design: The methodology used in this research was the clinical method of manipulation-formalization, created by Jean Piaget and applied in several of his studies.
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