Pedagogical Content Knowledge of Measurement through the Analysis of Associative Cognitive Networks

Measurement estimation is a fundamental mathematical skill, yet teaching it presents significant challenges, largely due to weaknesses in teachers' Pedagogical Content Knowledge (PCK). This study proposes a structural approach to analyze the knowledge organization of 31 pre-service elementary school teachers regarding measurement estimation. Based on an open-ended questionnaire, a qualitative analysis was conducted, resulting in 68 subcategories, which were modeled as nodes in an Associative Cognitive Network (ACN). The co-occurrences between subcategories in the pre-service teachers' responses generated 1,959 weighted edges. Quantitative graph analysis reveals a highly dense and efficient network (density = 0.860; ASPL = 1.087), featuring a hyper-connected core of practical and procedural ideas. The conceptual hubs, identified by their high Weighted Degree, correspond mainly to instructional actions and basic measurement concepts—such as extensive quantities and quantitative magnitudes—as well as measurement as a comparison process and the use of physical objects (all with weighted degree values close to 1000). In contrast, key formal mathematical concepts, such as proportionality (Weighted Degree = 146) and transitivity (Weighted Degree = 84), occupy peripheral positions and rarely serve as bridges. Modularity analysis (Q ≈ 0.042) identifies two large functional communities: a Didactic–Operational Core and a Peripheral Conceptual Belt, which are strongly interconnected. These results quantify the gap between concrete pedagogical knowledge and abstract mathematical foundations, underscoring the need for initial teacher education to focus not only on introducing new concepts but also on reinforcing the structural connections between practical knowledge and the formal mathematical principles that underpin it.