“The more connections we make between an object and other objects, the more concrete it becomes for us. The richer the set of representations of the object, the more ways we have of interacting with it, the more concrete it is for us…It is only through use and acquaintance in multiple contexts, through coming into relationship with other words/concepts/experiences, that the word has meaning for the learner and in our sense becomes concrete for him or her.”
– From Abstract Meditations on the Concrete and Concrete Implications for Mathematics Education by Uri Wilensky.
“Every experience is a moving force. It’s value can be judged by only on the ground of what it moves toward and into…Experiences may be so disconnected from one another that, while each is agreeable or even exciting in itself, they are not linked cumulatively to each other.” -John Dewey 1938
“Spatial thinking is integral to everyday life. People, natural objects, human-made objects, and human-made structures exist somewhere in space, and the interactions of people and things must be understood in terms of locations, distances, directions, shapes, and patterns.”
-National Research Council
Math in Unexpected Spaces 