RUME 28
2026
Alexandria, Virginia
Analyzing a Student’s Observations and Conjectures About Markov Chains: Identifying Scheme Elements and Their Instrumentation of Digital Figures
Page: 608
This study investigates how a first-year undergraduate mathematics student engaged with a set of digital interactive figures to explore properties of stochastic matrices and Markov chains. Using the frameworks of instrumental genesis and Vergnaud’s theory of conceptual fields, we analyzed the student’s interaction in terms of their observations and conjectures, two key stages in our Observation, Conjecture, Proof, Theorem (OCPT) pedagogical model. Through task- based interview data, we identified elements of the student’s emerging conjecturing scheme, including rules-of-action and theorems-in-action that illustrate their process of sensemaking and experimentation. We argue that this scheme development evidences the student’s instrumentation of the figures into a functional instrument for mathematical reasoning.