Sources of Mathematical Thinking

为了理解和提高数学认知，人们必须了解构建数学认知的积木，以及组装这些积木以产生新概念和技能的过程。 过去的发现揭示了初等数学基础上的四种表示系统：表示精确小数的系统，表示精确小数的系统，表示近似大数的系统，基于集合的量化系统，如自然语言量词复数，以及表示距离，角度和意义的几何关系的系统。 拟议的实验建立在这些发现和探索的过程中，儿童掌握新的数字和几何概念，通过短期的，实验室为基础的培训。

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.