ABSTRACT

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 The second part of this paper will inspect these influences drawing on Fröbel’s previously unpublished notes.

摘要

弗里德里希·弗洛贝尔 (Friedrich Fröbel) 被称为现代幼儿园的创始人，并因其开发了名为“天赋与职业”的新颖学习材料而闻名。弗洛贝尔计划的重点之一是数学教育，他通过各种活动来解决和教授数学原理，这些活动鼓励在很大程度上隐含地传播数学原理。基于对弗洛贝尔数学和晶体学背景的历史分析，并借鉴弗洛贝尔的笔记，本文的第一部分提出，弗洛贝尔幼儿园教授和使用的数学和各种天赋源于两个传统，这两个传统相交于弗洛贝尔的思想：首先，受水晶图影响的视觉传统；第二，一种受德国唯心主义影响的传统，包括几何方法和概念，以及源自用于分析晶体结构的晶体学的概念，主要由 Christian Samuel Weiß 开发。本文的第二部分将根据弗洛贝尔之前未发表的笔记来考察这些影响。