What Is a Solution of an Algebraic Equation?

This paper aims to broaden the scope of the construct concept image by addressing the mathematically oriented notion of "solution of an algebraic equation." The notion solution of an algebraic equation is not mathematical per se, but it is most prevalent in mathematical communications and in mathematics education. The paper describes five episodes of lesson segments that were collected in a secondary school mathematics teaching certificate program. The specific tasks, the episodes, and the related class discussions, involving the notion of solution of algebraic equation, are described. Several issues, arising from the various concept images of solution of equations, including miscommunication, ambiguity about correctness, ranking correctness, and minimizing errors, are discussed. Along an analysis of these data, 4 suggestions are offered for improving the communication around the notion solution of an algebraic equation: promote awareness, offer instructional guidelines, suggest a vocabulary, and be sensitive. [ABSTRACT FROM AUTHOR]