أثر المقاربة البنائيّة - النمائيّة - المعرفيّة في معالجة جوانب القصور لدى المتعلّمين في مقاربة حقل الكسور المفاهيمي في الصف الخامس من التعليم الأساسي في لبنان : مجموعة مدارس خاصة نموذجا
This study investigated the impact of a constructivist–developmental–cognitive approach on addressing learning deficiencies among grade five students in Lebanon in the conceptual field of fractions. A learning unit entitled “fractions around us” was developed to integrate conceptual knowledge and procedural knowledge, and to bridge real-life situations with abstract mathematical contexts through multiple representations (concrete, pictorial, and symbolic). Pedagogical content knowledge (PCK) was employed to design a training and follow-up program for teachers, enabling them to implement the unit within constructivist teaching practices. A mixed-methods methodology was adopted within a quasi-experimental design, involving two groups (experimental and control) across ten private schools distributed over five Lebanese governorates, with a total of 211 students. Data were collected through a pre- and post-test measuring the five fraction subconstructs (part–whole, measurement, ratio, quotient, and operator), both conceptual and procedural knowledge, and the ability to shift between real-life and abstract mathematical contexts. Additional tools included an attitude questionnaire, semi-structured interviews, focus groups, and classroom observations to capture the perceptions and practices of teachers and coordinators. Findings revealed statistically significant differences in favor of the experimental group across all post-test dimensions. Students demonstrated improved integration of conceptual and procedural knowledge, greater flexibility in shifting between real-life and abstract contexts, and enhanced attitudes toward mathematics. In particular, they reported greater enjoyment in learning fractions, increased recognition of the value and utility of mathematics, and stronger self-confidence in solving mathematical problems. This study demonstrates that adopting a constructivist–developmental–cognitive approach to teaching the conceptual field of fractions is an effective pathway for addressing learners’ deficiencies. It also provides a practical model to inform curriculum development efforts in Lebanon and opens avenues for further research in other mathematical domains. (Author's abstract)