Hadas Levi

The interplay of mathematics within physics—termed here as —presents unique cognitive challenges for students, requiring coordination between mathematical reasoning and physical sensemaking. While previous studies have documented common physmatic difficulties, capturing these challenges as they emerge in classroom instruction is rare. This study analyzed 273 teacher–student interactions from 23 video-recorded physics lessons taught across a diverse range of classrooms, aiming to identify and categorize physmatic difficulties as they naturally arose during instruction. Twenty-four codes of difficulties were identified through content analysis and grouped into five overarching clusters: (i) , (ii) , (iii) , (iv) , and (v) . A key finding of this study was the identification of systematic associations between the modeling skills teachers aimed to develop (i.e., mathematization, manipulation, interpretation, and validation) and the corresponding student difficulties. These findings underscore the centrality of modeling as a pedagogical framework for physics instruction and suggest that teachers who are aware of the links between skills and difficulties may be better prepared to anticipate student struggles, respond to them in real time, and even leverage them as part of their instructional practice.

Students often face significant challenges related to the interplay between physics and mathematics, referred to as “physmatics.” This invited diagnosing the possible sources of students’ difficulties in this respect. The current study aims to identify and interpret students’ difficulties in three specific physmatic areas required for physics learning: arithmetic operations, overgeneralization of the mathematical zero-product property, and the region of applicability of a formula, distinguishing these from independent difficulties in mathematics or physics. The research is designed to investigate whether these difficulties originate from pure mathematics limited skills, from applying mathematical thinking to real-world problems, or from applying it specifically to problems in physics. A questionnaire was administered to 199 high school students to examine the influence of the context–purely mathematical, physics, and economic–on their responses. Findings indicate that limited mathematical skills do not explain students’ difficulties in solving real-world problems. We infer that the students harness three different content dependent mathematical thinking approaches when addressing the challenges posed to them: context-oriented thinking, mathematical thinking, and unripe-mathematical thinking. Each of these approaches is characterized by varying attentiveness to context. Understanding these thinking approaches can help educators develop instructional strategies that address students’ cognitive challenges, potentially improving physics education outcomes.