Modelling calculus readiness trajectories of pre-service teachers using a Markov chain approach

This study investigated the calculus-readiness trajectories of pre-service teachers in Ghana using a longitudinal quantitative design and a discrete-time Markov chain framework. The participants were 363 pre-service teachers selected from an accessible population of 650 across five purposively selected Colleges of Education, with one college drawn from each of the five zones in which the colleges had been grouped. Readiness was assessed at baseline, mid-semester, and end-of-semester, and scores were converted to a common 30-point scale before classification into four readiness states: Unprepared, Partially Prepared, Prepared, and Highly Prepared. Transition count matrices, transition probability matrices, selected confidence intervals, a homogeneity check and a pooled steady-state distribution were estimated. The baseline results showed substantial underpreparedness, with most students entering calculus below the desired readiness level and no student classified as Highly Prepared. Transitions in the first half of the semester showed strong upward movement from lower readiness states, whereas later transitions were more variable, with both improvement and regression observed. The homogeneity check indicated that the two observed transition periods were not identical; therefore, the pooled steady-state distribution was interpreted cautiously as a descriptive projection under the observed transition dynamics. The findings show that calculus readiness among pre-service teachers is not fixed but develops unevenly across instructional time. Continuous diagnostics, bridging support, conceptual instruction and sustained formative feedback are therefore necessary in Colleges of Education.