The teaching of mathematics does not only require the teacher to have knowledge about the subject, but the teacher also needs mathematical knowledge that is useful for the teaching and explaining thereof, as the teacher’s knowledge effects the students’ knowledge. A teacher should use appropriate mathematical explanation to be understood well by her/his students. In the study reported on here we investigated how prospective mathematics teachers defined the concept of prime number and which strategies they employed to explain the concept. The study was a descriptive survey within qualitative research. Forty-eight participants took part in the study and all completed the abstract algebra courses where they learned about the concept in question. The data collection tool was a form comprising 3 open-ended questions challenging what the concept of prime number was and how this concept could be explained to secondary/high school students. The data were analysed and the results show that the preservice teachers experienced great difficulty in defining the concept of prime number and that they used rules to explain prime numbers. Keywords: explanatory strategies; prime number; prospective mathematics teachers

中文翻译：

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素数的概念和解释素数的策略

数学教学不仅要求教师具有学科知识，教师还需要对教学和解释有用的数学知识，因为教师的知识影响学生的知识。教师应使用适当的数学解释，以使其学生能很好地理解。在这里报告的研究中，我们调查了未来的数学教师如何定义素数的概念以及他们采用哪些策略来解释这个概念。该研究是定性研究中的描述性调查。四十八名参与者参加了这项研究，他们都完成了抽象代数课程，在那里他们了解了所讨论的概念。数据收集工具是一种包含 3 个开放式问题的表格，挑战质数的概念是什么以及如何向中/高中学生解释这个概念。对数据进行了分析，结果表明，职前教师在定义素数的概念时遇到了很大的困难，他们使用规则来解释素数。关键词：解释策略；素数；未来的数学教师