Secondary Students’ Implicit Conceptual Knowledge of Algebraic Symbolism. An Exploratory Study through Problem Posing

Through the task of problem posing, we inquire into students’ conceptual knowledge of algebraic symbolism developed in compulsory secondary education. We focus on identifying the characteristics of equations and systems of equations that made the problem posing task difficult for the students and analyzing the meanings that they gave to the operations contained in the expressions. To collect the data we used two questionnaires in which students were asked to pose problems that could be solved by using given equations or system of equations. In the second questionnaire a specific meaning for the unknowns in the given expression was suggested. The results complement those of a previous study. Students evidence a good conceptual knowledge of algebraic symbolism when meanings for the unknowns are suggested. Decimal numbers and an equation including parenthesis and multiplication of unknowns are the main elements that made some weaknesses in students’ knowledge to surface. The results are more promising. They suggest the potential for compulsory algebra instruction to develop students’ conceptual knowledge, although greater attention should be paid to the semantic aspects of algebra if students are to access such knowledge unaided.