Beyond Beliefs: Using Scheme Theory to Understand Implementation in Mathematics Education

Abstract Implementation studies in mathematics education often cite teachers’ beliefs as a decisive factor in success or failure. While this perspective has yielded valuable insights, the construct of beliefs is frequently defined too broadly to offer precise guidance for implementation design. This paper explores an alternative approach by applying scheme theory to a re-analysis of Handal and Bobis’ (2004) study on thematic teaching. We demonstrate how findings attributed to beliefs can be understood as elements of teachers’ schemes, that is, organized structures of action comprising goals, rules of action, operational invariants, and inferences. This reframing highlights factors of influence beyond beliefs and offers a more operationalizable lens for analyzing implementation outcomes. We conclude that scheme theory, alongside other fine-grained perspectives, can generate actionable insights into factors that influence the outcomes of implementation projects, thereby strengthening the planning, support, and sustainability of innovation projects in mathematics education. The impact sheet to this article can be accessed at https://doi.org/10.1163/26670127-bja10031 under Supplementary Materials.