Sources of Mathematical Thinking

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To understand and enhance mathematical cognition, one must understand the building blocks from which it is constructed and the processes by which those blocks are assembled to yield new concepts and skills. Past findings reveal four representational systems at the foundation of elementary mathematics: a system for representing exact small numbers, a system for representing exact small numbers, a system for representing approximate large numbers, a system of set-based quanitification as in the natural language quantifier plural, and a system for representing geometric relation of distance, angle and sense. The proposed experiments build on these findings and probe the processes by which children master new numerical and geometrical concepts through short-term, lab-based training.