A Didactic Model for Forming Mathematical Competence in Primary Education Through Geometric Concepts

Abstract

The competence-based transformation of primary mathematics education requires instructional models that connect conceptual understanding, procedural fluency, reasoning, and communication within meaningful learning situations. Geometry provides a particularly powerful pathway for competence formation because it naturally integrates visualisation, measurement, spatial reasoning, and argumentation, while also supporting the development of mathematical language. This article proposes and justifies a didactic model for forming mathematical competence in primary education through fundamental geometric concepts. The model is grounded in documentary analysis of international frameworks that emphasise mathematical reasoning and application, including the cognitive domain logic of TIMSS (knowing, applying, reasoning) and the mathematical literacy orientation of PISA, alongside research on developmental progressions in geometric thinking (notably the van Hiele theory). The model is described as a coherent system linking learning outcomes, content selection, instructional design, formative assessment, and feedback loops. It specifies how core geometric ideas—point, line, segment, ray, angle, plane figures, symmetry, perimeter, area, and spatial relationships—can function as “conceptual organisers” for broader mathematical competence. The proposed design foregrounds representational transitions (from concrete manipulation to schematic drawings and symbolic notation), discourse routines, and criterion-referenced assessment. The article argues that the model is feasible for teacher education and school practice because it offers operational design principles for lesson planning, task construction, and assessment. It also defines evaluation indicators for monitoring competence growth, including shifts in students’ reasoning quality, use of geometric language, and ability to model real situations with geometric representations.