This article sets out design principles to consider when student mathematics teachers are expected to learn mathematical modelling during their formal education. Blum and Leiß’s modelling cycle provided the theoretical framework to explain the modelling process. Learning to teach mathematical modelling, and learning to solve modelling tasks, while simultaneously fostering positive attitudes, is not easy to achieve. The inclusion of real-life examples and applications is regarded as an essential component in mathematics curricula worldwide, but it largely depends on mathematics teachers who are well prepared to teach modelling. The cyclic process of design-based research was implemented to identify key elements that ought to be considered when mathematical modelling is incorporated in formal education. Fifty-five third-year student teachers from a public university in South Africa participated in the study. Three phases were implemented, focusing firstly on relevance (guided by a needs analysis), secondly on consistency and practicality via the design and implementation of two iterations, and lastly on effectiveness by means of reflective analysis and evaluation. Mixed data were collected via a selection of qualitative instruments, and the Attitudes Towards Mathematical Modelling Inventory. Through content analyses students’ progress was monitored. Results analysed through SPSS showed significant positive changes in their enjoyment and motivation towards mathematical modelling. Student teachers require sufficient resources and opportunities through their formal education to participate regularly in mathematical modelling activities, to develop competence in solving modelling tasks, and to augment positive attitudes. This study adds value to the global discussion related to teachers’ professional development regarding mathematical modelling.

中文翻译：

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学生教师学习数学建模时要考虑的设计原则

本文列出了学生数学教师在正规教育期间学习数学建模时要考虑的设计原则。Blum 和 Leiß 的建模周期为解释建模过程提供了理论框架。学习教授数学建模，学习解决建模任务，同时培养积极的态度，并不容易实现。包含现实生活中的例子和应用程序被认为是全球数学课程的重要组成部分，但这在很大程度上取决于准备好教授建模的数学教师。实施了基于设计的研究的循环过程，以确定在将数学建模纳入正规教育时应考虑的关键要素。来自南非一所公立大学的 55 名三年级学生教师参加了这项研究。实施了三个阶段，首先关注相关性（以需求分析为指导），其次通过两次迭代的设计和实施来关注一致性和实用性，最后通过反思分析和评估来关注有效性。通过选择定性工具和对数学建模清单的态度收集混合数据。通过内容分析，监测学生的进步。通过 SPSS 分析的结果显示，他们对数学建模的享受和动机发生了显着的积极变化。学生教师需要足够的资源和机会通过正规教育定期参与数学建模活动，培养解决建模任务的能力，并增强积极的态度。本研究为与数学建模教师专业发展相关的全球讨论增添了价值。