Perceived Calculus Readiness and Markov-Informed Intervention Scenarios among Preservice Teachers in Colleges of Education

Abstract

Purpose: This study examined preservice teachers' perceived readiness for calculus and used observed readiness transitions to construct Markov-informed intervention scenarios for Ghanaian Colleges of Education. Methods: An explanatory sequential mixed-methods design was employed. The quantitative strand drew on achievement records for 363 third-year preservice teachers selected from an accessible population of 650 across five zonally distributed Colleges of Education. It also used 236 valid questionnaire responses, with the regression model estimated from 233 complete cases, while the qualitative strand involved interviews with seven mathematics tutors. Achievement scores were converted to a common 0-30 scale and classified into four readiness states. Raw questionnaire responses were reanalysed to estimate composite reliability, standardised regression coefficients, multicollinearity indices and residual diagnostics. Findings: Institutional support was the strongest correlate of perceived readiness (B = 0.456, β = 0.464, HC3 p < .001), followed by mathematical self-efficacy/motivation (B = 0.223, β = 0.244, HC3 p = .008). Tutors attributed weak readiness development to gaps in prerequisite knowledge, procedural learning histories, limited feedback, large class sizes, inadequate access to mathematics software and the absence of teaching assistants. The Markov scenarios are presented as illustrative sensitivity projections. Under the stated assumptions, a combined package of foundational bridging, concept-focused pedagogy, peer-assisted learning and institutional support shifted the projected steady-state distribution towards the Prepared and Highly Prepared categories. Conclusion: Calculus readiness is best understood as a developmental condition shaped by instruction, learner confidence and institutional support, rather than as a fixed attribute students bring into college.