Preservice primary teachers’ definitions of the area of 2d figures

Background: Defining mathematical concepts is a critical component of preservice teacher training, as it reflects their foundational mathematical knowledge and instructional capacity. However, research shows that preservice primary teachers often encounter challenges when formulating robust definitions of geometric concepts. Objectives: This study aims to characterize how preservice primary teachers define the concept of area, focusing on identifying the objects and processes that underpin their definitions. Tools from the Onto-semiotic Approach to Mathematical Knowledge and Instruction are employed for this purpose. Design: A qualitative approach was adopted, utilizing content analysis to explore the definitions provided by preservice teachers. Setting and Participants: Data were gathered from 70 preservice primary teachers enrolled in a teacher education program at a Spanish university during the 2020-2021 academic year. All participants were in their third year of study and had completed coursework on geometry and measurement in prior semesters. Data collection and analysis: Definitions were collected via a semi-structured questionnaire that tasked participants with defining the concept of area for fifth-grade students. Content analysis was conducted to identify the primary objects, processes, and partial meanings mobilized by participants, as well as to evaluate the alignment between their personal and institutional meanings of area. Results: The findings indicate that most definitions are based on a single partial meaning (e.g., area as space bounded by a closed line). Few participants integrated multiple partial meanings (e.g., additive measurement or multiplicative structures). Definitions that combined all three partial meanings of area tended to align more closely with institutional meanings but often lacked abstraction or generalizability. Conclusions: This study underscores the need to strengthen preservice teachers' ability to formulate robust definitions through targeted formative activities that enhance their global personal meaning of area. Future research should explore how these definitions develop in real classroom settings to better support the creation of effective pedagogical practices.