中文摘要：

新疆民俗数学是新疆各少数民族在长期的发展过程中,通过其独特的生产和生活方式创造、积累和传承下来的,具有鲜明民族特色和宗教内涵的数学文化以及独特的数学思想和思维方式。对于民俗数学的研究,一方面是通过对这些集数学知识与传统文化于一体的＂文化载体＂的搜集、整理和分析,以实现保护和传承之目的;另一方面则关注民俗数学研究成果的教育学转化,在充分考虑新疆少数民族儿童数学认知思维特征以及数学双语教学原则、方法等的基础上,通过实现民俗数学的＂课程化＂,以弥补当前新疆少数民地区以＂主流文化＂为主导的数学课程对少数民族传统文化的＂缺失＂,进而推进本地区基础教育课程改革和数学教育质量的提升。文章以新疆清真寺砖饰中的几何纹饰为例,就上述两方面的问题进行了论证。

英文摘要：

The Xinjiang ethno-mathematics is the unique mathematical thought and thinking mode and the mathematics culture has bright national characteristics and religious connotation. It creates, accumulates and inherits in the long-term development process of Xinjiang ethnic minorities through the unique mode of production and life.On the one hand, the research on Xinjiang ethno-mathematics is to protect and inherit Xinjiang ethno-mathematics through collecting, sorting and analyzing the ＂cultural carrier＂ which is a mixture of mathematical knowledge and traditional culture; On the other hand, based on the full account of Xinjiang ethnic minorities children＇s mathematical cognitive thinking characteristics, principles, methods and so on, we should concentrate on educational transformation of Xinjiang ethno-mathematics research, in order to make up the Xinjiang minority traditional cultures deficiency of the ＂mainstream culture＂ mathematics curriculum in Xinjiang national minority area, promoting mathematical educational quality and basic education curriculum reform through realizing the coursing of Xinjiang ethno-mathematics. This paper demonstrates the above two aspects based on the geometrical pattern of brick decoration of the Xinjiang mosque.