Students’ conceptual understanding of the arithmetic mean and the standard deviation a case study at the University of Education, Winneba

Abstract

This study investigated undergraduate mathematics students’ conceptual understanding of the arithmetic mean and the standard deviation after going through the Ghanaian Junior and Senior High School's core and elective mathematics curriculum. It also sought to determine the levels of conceptual knowledge of the arithmetic and standard deviation that these students have with respect to the Action, Process, Object and Schema (APOS) Theoretical Framework. The study employed the case study design. The purposive and convenience sampling techniques were used to select four hundred and thirty first year students from three different year batches admitted into the Department of Mathematics Education of the University of Education, Winneba. Two instruments were used to collect data on students’ conception of the arithmetic mean and the standard deviation: a test and an interview schedule. The test was given to students in their first semesters on admission before lectures for the introductory statistics course begun. Nine students were randomly selected from the 2014/15 year group and interviewed. Findings revealed that undergraduate mathematics students have conceptualized the arithmetic mean as an average, and as a computational act. They exhibited an incomplete Process conception of the arithmetic mean with respect to the APOS Framework. Participants demonstrated to have no conceptual understanding of the standard deviation, revealing not even an Action conception with respect to the APOS Framework. A recommendation was made for lecturers and tutors responsible for training teachers to ensure that they teach student teachers the concepts of the arithmetic mean and standard deviation before their computations.