Although much creativity research has suggested that creativity is influenced by cultural and social factors, these have been minimally explored in the context of mathematics and mathematics learning. This problematically limits who is seen as mathematically creative and who can enter the discipline of mathematics. This paper proposes a framework of creativity that is based in what it means to know or do mathematics and accepts that creativity is something that can be nurtured in all students. Prominent mathematical epistemologies held since the beginning of the twentieth century in the Western mathematics tradition have different implications for promoting creativity in the mathematics classroom, with fallibilist and social constructivist perspectives arguably being most conducive for conceiving of creativity as a type of action for all students. Thus, this paper proposes a framework of creative mathematical action that is based in these epistemologies and explains key aspects of the framework by drawing connections between it and research in the field of creativity.

中文翻译：

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承认数学学生具有创造力：基于社区和可能性扩展的数学创造力

尽管许多创造力研究表明创造力受文化和社会因素的影响，但在数学和数学学习的背景下，对这些因素的研究很少。这在问题上限制了被认为具有数学创造力的人和可以进入数学学科的人。本文提出了一个创造力的框架，该框架基于对知识或数学的理解，并认为创造力是可以在所有学生中培养的东西。自20世纪初开始，西方数学传统中就一直存在着杰出的数学认识论，对于在数学课堂中促进创造力具有不同的含义，其中易犯错误和社会建构主义的观点可以说最有利于将创造力视为所有学生的一种行动。