It is often assumed that a year twelve level of mathematics is sufficient background for primary student teachers to effectively develop their pedagogical skills to teach primary mathematics. However, for a cohort of primary student teachers at a regional Australian university, results from two mathematics diagnostic tests administered at the beginning of semester one and semester two in their first year of university studies showed that there were persistent misconceptions and critical skills that required explicit redressing to further enhance their content knowledge of primary mathematics. Student responses from the two Mathematics Diagnostic Tests were analysed using the Dichotomous Rasch Measurement Model to determine a hierarchical, cognitive development scale of mathematical competence of the content of the primary mathematics syllabus. Analyses of cognitive demands of the items and students' errors enabled the identification of persistent misconceptions. Main findings suggest that student teachers find solving word problems the most difficult followed by items on reasoning and operating with fractions, proportions and probability while the basic geometric, algebraic and numeric computation items were the easiest. These have implications for teaching primary mathematics competently and flexibly in ways that can motivate future primary students to engage meaningfully with mathematics learning.