"I forgot the formula:" How students can use coherence to reconstruct a (partially) forgotten equation

TL;DR

This paper explores how students use coherence-seeking strategies to reconstruct forgotten equations in physics, highlighting spontaneous mathematical sensemaking as a key learning process.

Contribution

It demonstrates how students employ coherence and qualitative understanding to reconstruct equations without explicit prompts, informing instructional approaches.

Findings

Students spontaneously use coherence to reconstruct equations.

Qualitative dependencies guide equation reconstruction.

This approach reveals adaptive reasoning in physics learning.

Abstract

Introductory physics instruction emphasizes fluency with routine problem-solving procedures. However, even when applying these procedures, students frequently encounter challenges. This paper investigates how students navigate such moments when answering qualitative E&M problems in interviews. Students frequently noted they had partially forgotten a key equation on a problem involving RC circuits. We present focal cases that show how coherence-seeking approaches were employed to overcome this problem-solving challenge. In attempts to reconstruct these equations, participants were guided by identifying and chaining qualitative dependencies and seeking coherence between qualitative and mathematical understanding of the physical system. These moments of forgetting and reconstructing equations are a useful site for studying broader physics learning goals. While prior work investigates the use of mathematical sensemaking by examining how students respond to explicit prompts, our cases illustrate how students can spontaneously use mathematical sensemaking strategies. We reflect on these cases to consider how such adaptive reasoning can be a target for instruction and assessment.