Identification of students' errors made in the solution of linear equations
Carryl Diane Koe · cIRcle (University of British Columbia) · 2010
This study describes the development and validation of a diagnostic checklist intended to assess students' understandings of beginning algebraic concepts and identify the errors made on one-, two-, and multi-step linear equations in one variable with integral coefficients and solutions. The study occurred in five phases: (1) textbook analysis for scope of concepts and sequence of equations; (2) error-categorization scheme development based on previous research; (3) construction, testing, and selection of equations based on systematic variation of complexity, structural format and numerical sign and magnitude; (4) initial testing of the instrument for format and wording changes; (5) testing of the final instrument and investigation of the nature, frequency, and interrelationships among the concepts held and the errors which occurred. The checklist used a semi-structured interview technique in conjunction with error-analysis. The results indicated that the checklist was a useful diagnostic tool and provided many insights into the interrelationships among students' concepts, errors, and achievement levels. Implications for instruction in algebra were explored, and suggestions for future instrument development were made.