Project-Based Learning and Mathematical Competencies in Primary Education: A Neutrosophic Cognitive Map Reading of a Critical Integrative Review

Developing mathematical competencies in primary school is essential for interacting with the environment. Faced with the limitations of traditional direct instruction, project-based learning (PBL) has emerged as an active alternative. This study analyzes, through a critical integrative review of ten reference studies (2016-2026), whether PBL determines the development of basic mathematical competencies in primary school students, and formalizes the resulting conceptual system as a neutrosophic cognitive map (NCM) with eight concepts and nine causal connections classified as positive, negative, or indeterminate. The static analysis of the map identifies PBL as the most central concept, with total centrality 6 + I, and makes the core epistemic finding of the review explicit: the mediated path through real-context problem solving and motivation is consistently positive, while the direct edge from PBL to mathematical competencies remains indeterminate (I) given the scarcity of pure experimental and longitudinal evidence. Documented gaps in early primary grades and in rural contexts with digital divides complete the indeterminacy inventory. We conclude that PBL acts as a catalyst whose effect is conditional on authentic problem situations, curricular flexibility, and teacher training, and that the neutrosophic representation preserves this conditionality instead of collapsing it into a binary verdict.