Abstract Teaching mathematical and geometric concepts through art forms that are a part of indigenous knowledge systems (IKSs) has become a key aspect of pedagogical transformation in many national arts and sciences curricula. This article delves into the nuances of artistic innovation, marketing, and mathematical process in contemporary Zulu, South Sotho, and Venda ceramic practices in both individual studio and workshop settings. The work of Azolina MaMncube Ngema, Lenky Nhlapo, and the Mukondeni Pottery Village are discussed in relation to expanding fields of ceramic consumption. Ceramic artists’ first-hand engagement in classroom workshops, portrayal in pedagogical writings, and strategic engagement with touristic venues are framed in the context of geometric reasoning, visual innovation, and potential classroom innovation.

中文翻译：

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拱门与线交汇：创新与传播的几何学

摘要 通过作为土著知识系统 (IKS) 一部分的艺术形式教授数学和几何概念已成为许多国家艺术和科学课程教学改革的一个关键方面。本文深入探讨了当代祖鲁、南索托和文达陶瓷实践在个人工作室和工作室环境中的艺术创新、营销和数学过程的细微差别。讨论了 Azolina MaMncube Ngema、Lenky Nhlapo 和 Mukondeni Pottery Village 与扩大陶瓷消费领域相关的工作。陶瓷艺术家在课堂工作坊中的第一手参与、教学著作中的描绘以及与旅游场所的战略参与都在几何推理、视觉创新和潜在的课堂创新的背景下被框定。