Vector Misconceptions in Finnish Matriculation Examination

Abstract

We used a large data set to discover what kind of misconceptions Finnish secondary school students have in elementary vector calculations. The study was based on a data set from the spring 2020 advanced mathematics exam in the Finnish matriculation examination. The data set consisted of answers from 13,284 students who participated in the exam. We focused on a question about vectors and compared the results to another question about equations and inequalities. We analyzed and classified the answers and explain common misconceptions the students had in the exam. Certain typical mistakes included not understanding that the result of a dot product is a scalar, and not a vector, or not understanding the notation for the norm of a vector.