Concepções de alunos do 3º ano do ensino médio sobre o significado do símbolo "=" em contextos aritméticos e algébricos

Abstract

The goal of the present research was investigate the pupils ‘conceptions of the 3rd High School year about the symbol “=” in arithmetic and algebraic contexts. We have chosen to use the term conception establised in the analyzed studies in chapters1 and 2. The symbol “=” is used in all teaching Mathematics levels in versatile way, so that in some cases, the qualities of the symbol “=”, depending the context that it is inserted, neither always they are compatible to the equality notion. Literature has been investigating, mainly, the interpretation of the pupils about the meaning of the symbol “=” in expressions corresponding to the arithmetic operations, of arithmetic equalities and equations. We have elaborated two investigate ways produced, each one, from four items, that the symbol “=” was inserted, respectively, into expressions corresponding to the arithmetic operations contexts, of arithmetic equalities, of equations and functions. Way 1, the expressions presented the structure operation before “=”, while the way 2, the expressions presented operation structure after “=”. We jut out as well that only two pupils’ conceptions about the equality sign are generously recognized in Literature: the operational and relational. During our study, we got to define five conceptions a priory (operational, equality relational, equivalence in conditional equality,functional and name – symbol relational) and two a posterior(separator symbol and syntactic operational). The found results showed a discordance between the pupils conceptions and the meaning of “=” symbol in the context that it is inserted. Our results also indicated there was a major tendency of students showing the operational conception and the relational conception name-symbol. It is important to realize that the operational conception is associated to own characteristics of the “=” symbol in the arithmetic operations, while that the relational conception name-symbol isn’t associated to any context in particular, but it send to relation between the equality name and the “=” symbol. Finally, we jut out that the operational conceptions and equality relational were found in answers refer to the algebraic context of equations and function, while that equivalence conceptions in conditional equality, functional and syntactic operational, they weren’t found in answers refer to the arithmetic contexts of operations and equalities.