Aritmética modular na formação continuada de professores: desenvolvendo o pensamento aritmético e algébrico

Abstract

This work describes a qualitative research on how the study of modular arithmetic,

through simulated problem situations proposed in a continuing education course, can

contribute to the development of the arithmetic and algebraic thinking of math teachers. Two

continuing education courses for teachers, approved by the Grande Rio University, were

conducted with ten math teachers working in basic education at the city of Duque de Caxias,

Rio de Janeiro, Brazil. Data were collected by the means of participant observation,

questionnaires and from the documents generated during the courses. The results of this

investigation show that through the adequate choice of subjects and teaching methods, the

study of subjects inherent to number theory, namely, modular arithmetic, contribute to the

promotion of arithmetic and algebraic thinking. This happens as this kind of activity favors

the development of competences and skills, such as formulating and validating conjectures;

representing and analyzing mathematical situations and structures using algebraic symbols;

producing models for representing and expressing a simulated problem situation; developing

some sort of generalization; demonstrating regularities or invariances; and developing a more

concise and syncopated language when speaking mathematically. However, the performance

of the teachers was not equally expressive in all stages of the courses. Some teachers

presented conceptual deficiencies regarding the study of properties and of operations with

integer numbers. There was also a certain resistance to solving problems that required proofs

or demonstrations. The final product of this research is presented in a Workbook, comprising

ten activities and four challenges based on the concept of modular arithmetic. There is also a

handout with the theoretical subject matters needed for approaching this mathematical subject

with basic education students.