How students can use coherence to reconstruct (partially) forgotten equations.

Introductory physics instruction emphasizes fluency with routine problem-solving procedures; however, even when applying these procedures, students frequently encounter challenges. This project investigates how students navigate such moments while answering qualitative E&M problems during interviews. Students frequently noted they had partially forgotten a key equation on a problem involving RC circuits. We present focal cases to show how coherence-seeking approaches were used to overcome this problem-solving challenge. We found that attempts to reconstruct these equations were guided by identifying and chaining qualitative dependencies and seeking coherence between their 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 attempts to expand students' use of mathematical sensemaking via explicit prompts, our cases illustrate students' spontaneous use of mathematical sensemaking strategies. We reflect on these cases to consider how such adaptive reasoning can be a target for instruction and assessment.