Pedagogical Content Knowledge of Ohm’s Law in Two Physics Teachers: A Descriptive Characterization from the Gess-Newsome Model and the Complexity Hypothesis

Abstract

Pedagogical Content Knowledge (PCK) constitutes a central construct for understanding how teachers transform disciplinary knowledge into meaningful teaching experiences. This case study, conducted with two secondary Physics teachers from a Scientific High School in Costa Rica, analyzes their PCK in teaching Ohm's Law, taking as a reference the Teacher Professional Knowledge Bases (TPKB) model proposed by Gess-Newsome (2015). Data collection was carried out through semi-structured interviews based on the Content Representations (CoRe) proposed by Loughran et al. (2004), validated by specialists in Science Education, and applied at a specific moment of both teachers' professional practice (cross-sectional design). A category system was developed from the participants' discourse, linking PCK with the technical, practical, and critical dimensions of the Complexity Hypothesis (Vázquez-Bernal et al., 2010), as well as with the strategies teachers employ to address obstacles in their pedagogical mediation. This analytical system allowed the identification of recurrent action patterns evidencing how each teacher articulates their Teacher Professional Knowledge Bases in a differentiated manner.

The results evidence a progression from the practical toward the critical dimension in both teachers, manifested in the promotion of inquiry processes among students, explicit attention to conceptual cores, and the construction of a personal PCK that positions teachers as learning facilitators, rather than as mechanical transmitters of content. Teacher A develops abstraction ability through variable analysis, promotes active participation through experiments and simulations, and fosters data interpretation through graphing. This teacher also designs worksheets that guide the experimental process, formulates open-ended questions centered on variable variation, and conceives knowledge as a construction favored through classroom inquiry. In addition, she incorporates technological resources regularly due to the nature of the course and integrates them with active methodologies such as problem-based learning and inquiry, promoting a deep understanding of the content. These decisions evidence an active integration among content knowledge, student knowledge, and pedagogical knowledge, configuring an articulated and situated knowledge consistent with Gess-Newsome's (2015) TPKB. Furthermore, the presence of elements associated with Technological Pedagogical Content Knowledge (TPCK) emerged recurrently, suggesting a conscious integration among disciplinary content, pedagogical strategies, and technological tools.

Teacher B, promotes abstraction through problem posing and concept comprehension, emphasizes teamwork, and proactively addresses students' specific difficulties. Regarding didactic resources, he is not limited to using a single textbook but draws on various university-level bibliographical sources, suggesting a marked centrality of disciplinary knowledge within his PCK. His epistemological distinction between model and scientific law stands out, evidencing disciplinary mastery and a concern for the nature of scientific knowledge. Additionally, he expresses the intention to incorporate experimental activities in the future to complement theoretical explanations, which reveals an awareness of the value of practical work in meaningful learning. In both cases, the absence of traits associated with the technical dimension is observed, as neither structures his or her teaching exclusively around mechanical repetition or closed-ended problem solving, suggesting a level of professional complexity that transcends a strictly procedural approach. Consequently, both configure a PCK oriented toward content problematization and epistemologically informed understanding of Ohm's Law, consistent with teaching that transcends the mechanical application of formulas.