Date on Master's Thesis/Doctoral Dissertation


Document Type

Doctoral Dissertation

Degree Name

Ph. D.

Department (Legacy)

Department of Teaching and Learning

Committee Chair

Karp, Karen, 1951-

Author's Keywords

Algebra; Middle grades; Misconceptions; Mathematics; Errors


Algebra--Study and teaching (Middle school)


The purpose of this study was to examine common algebra-related misconceptions and errors of middle school students. In recent years, success in Algebra I is often considered the mathematics gateway to graduation from high school and success beyond. Therefore, preparation for algebra in the middle grades is essential to student success in Algebra I and high school. This study examines the following research question: What common algebra-related misconceptions and errors exist among students in grades six and eight as identified on student responses on an annual statewide standardized assessment? In this study, qualitative document analysis of existing data was used in order to analyze sixth- and eighth-grade student responses on a statewide standardized assessment. Secondary data sources consisted of Algebra I student responses which were also analyzed qualitatively using document analysis and follow-up interviews with key informants. The primary analysis indicated that (l) numerous misconceptions and errors identified in the review of literature were present on both the sixth- and eighth-grade open-responses; (2) basic computational errors with whole numbers (a secondary skill), were found consistently throughout the sixth- and eighth-grade open-responses; (3) a greater number of misconceptions and errors identified in the review of the literature were present on the eighth-grade items than were found on the sixth-grade items; (4) students often lost points for reasons other than mathematical misconceptions or errors; and (5) some refinement and reorganization of Welder's (2007) framework could prove beneficial when using the framework for data analytic purposes. The results of this study provided information about the common misconceptions and errors students possess on prerequisite algebra skills. The findings revealed common algebra misconceptions and trends that can help guide instruction for middle school mathematics teachers. The findings have direct implications for classroom practice and further confirm the need for strong and knowledgeable teachers of mathematics at the elementary and middle grades. The researcher suggests that schools, both in the state whose standardized assessment was examined as well as other states, use this information to help build awareness of common prerequisite algebra-related misconceptions and errors in elementary and middle grades mathematics teachers.