Algebra Textbooks and Teachers Methods:

Abstract

The purpose of this paper is to examine the methods used in algebra textbooks and by secondary school algebra teachers to illustrate simplifying rational expressions, since teachers report that many students fail to develop accurate facility with this topic. A sample of 10 algebra textbooks was examined, 33 teachers were surveyed, and 6 teachers were interviewed. The results reveal that the vast majority of textbooks and teachers in the sample used a procedurally focused method rather than a conceptually focused method. Teachers gravitated toward the quick coverage offered by a procedural method showing students exactly what to do. Moreover, they even knew the possible disadvantages of using such a procedural method and the advantages offered by a conceptual method which offered a clearer explanation of the reasons behind the process. Despite the fact that teachers reported that rational expression simplification was a significant challenge for students to learn, the advantages offered by a conceptual method with the prospect of improved student knowledge was unheeded by most. Interviews with experienced algebra teachers revealed low expectations for student learning which may have a negative impact on student performance. A teaching strategy is suggested, based on the results of this paper and prior research, to include both procedural and conceptual methods for the simplification of rational expressions to enhance student success.