Pre-Service Teachers’ conceptual understanding of the arithmetic mean: A SOLO taxonomy analysis.

Despite the fact that the arithmetic mean is a basic statistical concept introduced at the Ghanaian junior and senior high schools, studies have found that students often see it more as an algorithmic procedure than as a conceptual entity used for analysing and interpreting data. This study explored pre-service teachers’ (PST) conceptual understanding of the arithmetic mean and assessed their levels of conceptual understanding of the arithmetic mean using the Structure of the Observed Learning Outcome (SOLO) taxonomy. The exploratory case study design was used to select 370 pre-service teachers (PSTs) through purposive and simple random sampling techniques. The Statistical Understanding Test of Arithmetic Mean (SUTAM) was primarily used as the instrument for data collection. Findings indicate that the majority of PSTs primarily perceive the arithmetic mean as a computational procedure – with the “add and divide algorithm” – rather than an entity with properties such as representativeness, balance, or fair share, thereby revealing substantial gaps in their conceptual understanding. Additionally, the majority (55.1%) of PSTs were found to operate at the lower levels (pre-structural and uni-structural) of the SOLO Taxonomy in their understanding of the arithmetic mean, with very few (14.6%) at the relational level. It was found that PSTs were deficient in the development of higher-order statistical reasoning. These highlight the need for pedagogical interventions that emphasise the conceptual properties of the arithmetic mean. It was therefore recommended that senior high school mathematics teachers prioritise teaching students the concept of the arithmetic mean and its properties before teaching its computation.