Sources of Mathematical Thinking

要理解和提高数学认知，就必须了解构成数学认知的积木，以及组装这些积木以产生新概念和技能的过程。以往的研究结果揭示了小学数学基础上的四个表征系统：精确小数表示系统、精确小数表示系统、近似大数表示系统、自然语言量词复数中基于集合的量化系统以及距离、角度和感觉的几何关系表示系统。拟议的实验建立在这些发现的基础上，并探索儿童通过基于实验室的短期培训掌握新的数字和几何概念的过程。

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.