“Because You’re Exploring this Huge Abstract Jungle…”: One Student’s Evolving Conceptions of Axiomatic Structure in Mathematics

For several decades, literature on the history and pedagogy of mathematics has described how history of mathematics is beneficial for the teaching and learning of mathematics. We investigated the influence of a history and philosophy of mathematics (HPhM) course on students’ progress through the lens of various competencies in mathematics (e.g., mathematical thinking and communicating) as a result of studying mathematical ideas from the perspective of their historical and philosophical development. We present outcomes for one student, whom we call Michael, resulting from his learning experiences in an HPhM course at university. We use the framework from the Competencies and Mathematical Learning project (the Danish KOM project) to analyze the evolution of Michael’s competencies related to axiomatic structure in mathematics. We outline three aspects of axiomatic structure to situate our analysis: Truth, Logic, and Structure. Although our analysis revealed that Michael’s views and knowledge of axiomatic structure demonstrate need for his further development, we assert what he experienced during the HPhM course regarding his mathematical thinking and communication about axiomatic structure is promising support for his future mathematical studies. Finally, we argue that a HPhM course has potential to support students’ progress in advanced mathematics at university.