Algebraic Equations and Inequalities: Issues for Research and Teaching. Research Forum

The presentations address a variety of difficulties occurring in students' solutions of equations and inequalities, and suggest different reasons for these difficulties. When analyzing students' performances, [BB] and [TTT] mention students' tendencies to make irrelevant connections between equations and inequalities as a problematic phenomenon. It should be noted, however, that [K] presents connections made between equations and inequalities as an important step in solving algebraic problems by means of non-algebraic methods. [BB] mention traditional, algorithmic teaching approaches as a main reason for students' errors, Dreyfus and Hoch [DH] mention the need to enhance the internal structure of equations that students hold, while [S] carefully analyzes difficulties with reference to the various solving methods and indicates that even the functional approach and the use of graphic calculators do not automatically lead to errorless solutions. However, beyond their differences, the presentations share common goals. One such goal is to investigate ways to promote performance on algebraic equations and inequalities by seeking means for analyzing students' reactions to various representations of equations and inequalities in different contexts, while considering the way this topic was taught. Thus, this forum will also shed light on the more general issues concerning the interplay between theory, research and instruction. Papers in this forum include: (1) Inequalities in Mathematics Education: The Need for Complementary Perspectives (Paolo Boero and Luciana Bazzini); (2) The Equation/Inequality Connection in Constructing Meaning for Inequality Situations (Carolyn Kieran); (3) Problems Related to the Use of Graphs in Solving Inequalities (Catherine Sackur); (4) Equations--A Structural Approach (Tommy Dreyfus and Maureen Hoch); (5) "New Errors" and "Old Errors": The Case of Quadratic Inequalities (Pessia Tsamir, Dina Tirosh, and Sarit Tiano); (6) Reflections on Research and Teaching of Equations and Inequalities (David Tall); and (7) Syntax and Meaning (Luis Radford). (Individual papers contain references.) [For complete proceedings, see ED489178.]