Conceptual understanding is one of the main concerns of mathematics education. Numerous research have discussed student understanding of algebraic concepts, linear equations in particular. This research was drawn upon in order to develop a new approach for teaching and learning linear equations based on the equivalence concept, one that aims to improve students' algebraic thinking. The purpose of this paper is to evaluate the effectiveness of the equivalence approach teaching method over the traditional teaching method in improving students' flexibility and minimizing their errors in solving equations. The sample consisted of 61 junior-high-school Moroccan students that were assigned randomly to two groups: the control group and the experimental group. Within the posttest-only control group experimental design, the Mann-Whitney U test was used to compare differences in posttest scores between the two independent groups. Findings indicate that the equivalence approach teaching method was effective in enhancing students' flexibility and in minimizing two categories of errors: conceptual and transformations errors.