This qualitative study aimed to identify the changes in a prospective’ conceptions about the nature of mathematical tasks and pedagogy in video cases and to investigate the characteristics of the prospective’ professional knowledge and views during task design/modification. The study used the mathematical task demand engagement process, which includes task-sorting activity, selecting tasks, reflecting on illustrative cases, and teaching and reflecting on tasks as enacted. The findings regarding one prospective, Kar, were reported. Focus group interviews, individual interviews, and two recorded lessons were used as data sources. The content analysis method was employed for the in-depth analysis of the data. The findings suggested a change in Kar’s ideas about the nature of mathematical tasks, particularly about what characteristics low and high-level tasks possess and the efficiency of the Task Analysis Guide. Kar also generated detailed ideas on the pedagogy of high and low tasks and realized the role of teachers as facilitators while enacting high-level tasks. Another finding is that Kar’s decisions regarding task adaptation and her reasons catalyze both situated and global knowledge and views. Our findings suggest that providing an opportunity for prospective to reflect on and discuss the nature of mathematical tasks as planned, implemented, and revisited in a professional context is beneficial.

这项定性研究旨在确定潜在客户对视频案例中数学任务和教学法性质的概念的变化，并调查潜在客户在任务设计/修改过程中的专业知识和观点的特征。该研究使用了数学任务需求参与过程，包括任务分类活动、选择任务、反思说明性案例以及教学和反思已制定的任务。报告了关于一位潜在客户 Kar 的调查结果。焦点小组访谈、个人访谈和两个录制的课程被用作数据源。采用内容分析法对数据进行深入分析。这些发现表明 Kar 对数学任务的性质的看法发生了变化，特别是关于低级和高级任务具有哪些特征以及任务分析指南的效率。Kar 还对高低任务的教学法产生了详细的想法，并意识到教师在执行高级别任务时作为促进者的作用。另一个发现是 Kar 关于任务适应的决定和她的理由促进了情境和全球知识和观点。我们的研究结果表明，为准学生提供一个机会来反思和讨论在专业背景下计划、实施和重新审视的数学任务的性质是有益的。另一个发现是 Kar 关于任务适应的决定和她的理由促进了情境和全球知识和观点。我们的研究结果表明，为准学生提供一个机会来反思和讨论在专业背景下计划、实施和重新审视的数学任务的性质是有益的。另一个发现是 Kar 关于任务适应的决定和她的理由促进了情境和全球知识和观点。我们的研究结果表明，为准学生提供一个机会来反思和讨论在专业背景下计划、实施和重新审视的数学任务的性质是有益的。