Evidence from physics education research suggests that the introduction of mathematical formalism in quantum physics instruction can support the development of students’ conceptual understanding, particularly by promoting functional ways of reasoning about quantum phenomena. However, empirical findings on the effectiveness of such approaches at the secondary school level remain inconclusive, and little is known about the extent to which learning outcomes are shaped by instructional design as opposed to learners’ affective and cognitive characteristics. This study addresses this gap by investigating the relative influence of instructional approach on students’ understanding of single-photon states, while controlling for prior knowledge, cognitive load, situational interest, and physics self-concept. A quasi-experimental pre-post design was implemented with N=172 upper secondary students, comparing a qualitative instructional condition with an approach supplemented by a reduced Dirac formalism. Learning outcomes were assessed using the framework of Functional Fidelity and Fidelity of Gestalt. A multivariate analysis of covariance (MANCOVA), followed by univariate analyses (ANCOVAs), was conducted to examine the contributions of instructional and learner-related variables. The findings indicate that affective variables emerge as strong predictors of functional understanding and suggest that learning in quantum physics is driven less by instructional format than by learners’ affective and cognitive prerequisites. In particular, fostering interest appears to be a key mechanism for supporting the development of functional understanding. The results highlight the importance of integrating affective dimensions into instructional design and provide a basis for future research on the interaction between instructional approaches and learner characteristics in quantum physics education.