The Affordances and Constraints of Diagrams on Students' Reasoning about State Machines

While the concept of state is foundational to computing, students possess a myriad of misconceptions about it and the role it plays within computing systems. Research on students' misconceptions reveals that their ability to use conceptually appropriate information varies based on the task they are performing and the representational tools they are provided. Critically, the tacit information in these representations influences this process, hindering or helping students. In this paper, we present a qualitative research study, in which we interviewed 24 students as they transformed finite state machines into synchronous, sequential logic circuits. We found that students generally had profound skill with procedures. However, their ability to reason about the four components of state, next-state, inputs, and outputs, were constrained by the representations that they were given or created themselves. Conversely, the order in which students produced their drawings provided complementary insights into students conceptual understanding. These findings revealed that students possess conceptions of computers as input-output systems rather than state-based systems. We suggest potential interventions and future research based on these findings.