AN INTEGRATED APPROACH THAT COMBINES TRIZ, HEURISTIC LEARNING, AND MATHEMATICAL MODELING TO DEVELOP PRESCHOOLERS' MATHEMATICAL THINKING—FROM SETS AND QUANTITIES TO NUMBERS AND RELATIONSHIPS

Modern preschool education enables teachers to design authorial programs for children’s mathematical development. However, sustainable innovation requires a strong methodological grounding in mathematical theory and in evidence-based approaches used in both preschool and early primary curricula. This article substantiates the pedagogical potential of integrating the Theory of Inventive Problem Solving (TRIZ), heuristic learning, and mathematical modeling in preschool mathematics. The paper outlines a functional definition of mathematical modeling with preschoolers, proposes a classification of modeling practices (by set-theoretic meaning and spatial orientation), and presents a developmental logic linking sensory, intellectual, and creative abilities across preschool ages.