Friedrich Fröbel is known as the founder of the modern kindergarten and for his development of novel learning materials called Gifts and Occupations. One of the foci of Fröbel's programme was mathematical education, which he addressed and taught through various activities that encouraged the largely implicit transmission of mathematical principles. Based on a historical analysis of Fröbel's background in mathematics and crystallography and drawing on Fröbel's notes, the first part of this paper proposes that the mathematics and the various Gifts taught and used in Fröbelian kindergartens have their roots in two traditions, both of which intersected in Fröbel's thought: first, a visual tradition, influenced by drawings of crystals; second, a tradition influenced implicitly by German Idealism consisting of geometric methods and conceptions as well as notions derived from crystallography used to analyse the structure of crystals and mainly developed by Christian Samuel Weiß. The second part of this paper will inspect these influences drawing on Fröbel's previously unpublished notes.