Graphing formulas to give meaning to algebraic formulas

Abstract

Many students have difficulties giving meaning to algebra. In this study, we investigated how graphing formulas by hand can help grade 11 students to give meaning to algebraic formulas, defined as the ability to “read through” an algebraic formula: i.e., to recognize its structure and to link it to graphical features. During five 90-minute lessons, 21 students worked on graphing tasks focusing on recognition and heuristic search. To assess the effects of this intervention, a graphing task, and a cardsorting task were administered to the students. In addition, six students were asked to think aloud during the graphing task. The results of the card-sorting task showed that 14 students used categories similar to the ones experts use, but had trouble in consistently categorizing all formulas. The thinkingaloud protocols showed that the students improved their recognition of basic functions and graph features, and their qualitative reasoning, which allowed them to give meaning to algebraic formulas