2026 ASEE Annual Conference & Exposition

A panel of experts rated a conceptual understanding of Induction as being the most important topic in discrete mathematics that computer science students should know. Yet, research has found signs that, even after instruction, students’ reasoning about inductive proofs illustrates conceptual difficulties. Students can misunderstand the function of key steps, including viewing the base case as non-essential and the inductive step as being circular reasoning, among other incorrect conceptions. Moreover, students are not convinced if the proof they have written is correct and are not sure when and why to use a proof by Induction.

Prior work has shown that students can shift their understanding of Induction and improve their articulation when provided with interventions such as Quasi-Induction on account of it moving students towards a transformational proof scheme. However, there is still a cognitive gap between Induction and Quasi Induction, and bridging it does not easily lend itself to worksheet style coursework. This limits their use and delivery to reach a broad population of students. Building on this prior work we aim to design interventions that can be used in a variety of classroom settings and, through moving students to a transformational proof scheme in a formal Induction context, will improve students' conception of Induction.

In this paper we have two goals. First, we replicate and extend prior work to study student conception of induction in a coursework context. We also develop material that can sharpen their understanding. Towards these goals, we are conducting think aloud interviews with 15 computer science students that have taken a proof based course in an R1 midwestern university. In our interviews we present students with a list of questions in a worksheet. Our approach in designing the worksheet leverages socratic-style questioning and compare and contrast prompts. Additionally, we have designed our questions to look at how multiple relevant coursework contexts change the activation of student resources. One question type asks students to evaluate and explain correct and incorrect formal proofs given to them. A deliberate design principle for these given proofs is to avoid standard inductive proof conventions – such as having the base case not be 0 or 1, not having an explicit inductive variable n, and having the inductive implication say k implies k+i for some i. By breaking from learned patterns,we can examine student understanding in cases where their procedural knowledge alone may be insufficient, and students will be unable to just appeal to authority or syntactic structure. A second problem type looks for whether students recognize and exploit the efficiency of induction in cases with a tedious but finite calculation. Other questions examine student understanding of particular elements of inductive proofs, such as the necessity of a base case or the use of a strong inductive step.

We are in the process of conducting interviews and will analyze the data once they are complete. We will code the interviews using qualitative methods. We will analyze and share themes that emerge in what students do or do not know about the purpose and function of the concepts that go into a proof by induction, for different and instructionally relevant contexts. We will also show how worksheet-style questions help them sharpen and articulate their ideas. We will also highlight whether our worksheets and instructional approach allow students’ concepts to change from beginning to end.