Conceptual and procedural understanding of algebra concepts in the middle grades

Abstract

In this study, the balance between conceptual and procedural teaching and its effect on the development of algebraic reasoning was examined. Participants included two seventh grade mathematics teachers and their students in targeted classes (N = 33). One video taped lesson from each teacher was selected for in-depth analysis of the balance between conceptual teaching, procedural teaching, and classroom time that included neither. Student participants took pretest and posttest algebra tests. Distribution of student responses and scores were analyzed for the degree of conceptual understanding demonstrated by students and then related to observed instructional practices. It was concluded that the students of the teacher with a more explicit conceptual emphasis in her lessons performed better on the test and were better able to exhibit flexible reasoning in unfamiliar contexts. Students whose teacher focused more heavily on procedural instruction without conceptual connections were less flexible in their reasoning and unable to apply some of the procedures taught in class.