PROCEEDINGS OF THE 16TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2013
Denver, Colorado
Commonly Identified Students’ Misconceptions About Vectors and Vector Operations
Page: 2-8
In this report we present the commonly identified error patterns and students’ misconceptions about vectors, vector operations, orthogonality, and linear combinations. Twenty three freshmen students participated in this study. The participants were non-mathematics majors pursuing liberal arts degrees. The main research question was: What misconceptions about vector algebra were still prevalent after the students completed a freshmen-level linear algebra course? We used qualitative data in the form of artifacts and students’ work samples to identify, classify, and describe students’ mathematical errors. Seventy four percent of students in this study were unable to correctly solve a task involving vectors and vector operations. Two types of errors were commonly identified across the sample: a lack of students’ understanding about vector operations and projections, and a lack of understanding (or distinction) between vectors and scalars. Final results and conclusions include research suggestions and practitioner-based implications for teaching linear algebra in high school and college.