Bridges 2011 Workshop Paper

When Froebel, the inventor of the Kindergarten [1] designed the ``Gifts'' and ``Occupations'' given to the children, he deliberately selected materials that provided a haptic dimension to their explorations. This physicality in the interaction with the gifts can create a significant potential learning focus making full use of concepts of spatial reasoning (front-back, over-under, etc.). For adults playing with the materials for the first time, and incorporating a reflective component in their doing and their thinking, the Gifts can provide a novel perspective on other, deeper mathematical concepts. The following paper and its accompanying workshop present some activities possible with Gift #14, which involves the Occupation of paper weaving, and explore ideas in modular arithmetic, combinatorial geometry, ethnomathematics and more.