Math in Motion: Investigating the relationship between formal mathematics and body action

这项建议的目的是探索新的方法来培养和培养所有学生的数学想象力。数学作为一门可以想象的科学，与记忆乘法表、数字事实或分数运算捷径并不矛盾，但它改变了这些记忆的组成部分。它是关于想象空间和时间：形状、模式或轨迹；它是关于设想事情可能是怎样的；它是关于区分有限与无限，离散与连续，可能与不可能。这一提议的主要猜想是，培养数学想象力与丰富身体动作/感知密切相关。本研究拟以高中学生和职前教师为对象，进行一系列的研究。

The aim of this proposal is to investigate new approaches to nurture and cultivate the mathematical imagination of all students. Mathematics as a science to imagine-with is not incompatible with memorizing the multiplication tables, number facts, or shortcuts to operate fractions, but it changes what these memories are part of. It is about imagiining space and time: shapes, patterns, or trajectories; it is about envisioning houw things could be; it is about discriminating the finite and infinite, the discrete from the continuous, and dthe possible from the impossible. The main conjecture of this proposal is that cultivating mathematical imagination is deeply related to enriching bodily action/perception. The research we propose intends to investigate this thesis through a series of studies with high school students and pre-service teachers.