Measuring health professional students' willingness to use AI chatbots in learning: A fuzzy-set qualitative comparative analysis.

Research in educational psychology and mathematics education has long distinguished between conceptual and procedural knowledge (for reviews, see Castro et al., ; Rittle‐Johnson, ; Rittle‐Johnson & Siegler, ). refers to the comprehension of mathematical ideas, principles and their interrelationships within a particular domain (e.g., Hiebert & Lefevre, ; Rittle‐Johnson et al., ). It is typically characterized as flexible, general and abstract—the kind of knowledge that enables a student to explain why a mathematical procedure works, to judge whether an answer is reasonable, to recognize connections between different representations of the same concept, or to transfer understanding to novel problem situations (e.g., Rittle‐Johnson, ). In contrast, a is a “step‐by‐step instruction that prescribes how to complete a task” (Hiebert & Lefevre, , p. 6). Procedural knowledge refers to knowledge of rules, procedures and algorithms used to solve problems (Byrnes & Wasik, ; Hiebert & Lefevre, ). It is usually assumed to be less flexible and more closely tied to specific problem types, contexts and practiced routines and is typically assessed through students' ability to execute procedures (e.g., Rittle‐Johnson, ). To understand relationships between conceptual and procedural knowledge, it is fundamental to have measures that assess both knowledge types with sufficient discriminant validity (e.g., Rittle‐Johnson, ; Schneider & Stern, ). is a psychometric concept rooted in construct validity theory (Campbell & Fiske, ). It refers to the extent to which measures of distinct theoretical constructs are also empirically distinguishable—that is, whether they capture unique variance rather than measuring essentially the same thing. Being able to measure conceptual and procedural knowledge with sufficient discriminant validity is important. For research, independent measurement is a prerequisite for studying how these knowledge types relate, develop over time, or respond to instructional interventions. For instance, if a teaching method targets conceptual understanding, its impact can only be assessed if conceptual knowledge can be measured with sufficient discriminant validity; otherwise, effects may be confounded with changes in procedural knowledge. For educational practice, separate measures allow educators to identify which type of knowledge a student lacks and to tailor instruction accordingly (e.g., emphasizing sense‐making for students with weak conceptual knowledge, or guided practice for those lacking procedural knowledge). Despite this importance, creating measures with sufficient discriminant validity is difficult. One reason is that the two knowledge types tend to be highly correlated (e.g., Hallett et al., ; Hecht et al., ; Jordan et al., ; Schneider et al., ). This frequently observed high correlation may be a consequence of instruction—the two knowledge types are often taught and practiced in close temporal proximity—and their developmental relationship. According to the , conceptual and procedural knowledge grow in tandem through mutually reinforcing cycles (e.g., Rittle‐Johnson et al., ). For example, a student who initially learns to solve equations by mechanically performing the same operation on both sides may, through repeated practice, come to understand why this procedure preserves equality. This conceptual insight, in turn, enables the student to flexibly adapt the procedure to unfamiliar equation types, such as equations with variables on both sides. Over time, this cycle increasingly entangles the two knowledge types, which is desirable from a learning perspective but creates a psychometric challenge. Despite this challenge, researchers have worked to develop paper‐and‐pencil measures that distinguish between the two knowledge types (e.g., Lenz et al., ). Paper‐and‐pencil tests are attractive because they can be administered to large samples, unlike more resource‐intensive alternatives, such as think‐aloud protocols, clinical interviews, or process‐tracing methods, that are less practical for large samples.