Related Data for: Orchestrating mathematics lessons: Beyond the use of a single rich task

Teachers have several challenges when designing and implementing mathematically-rich tasks, and hence, these tasks are not prevalent in many mathematics classrooms. Instead, teachers often use typical problems, such as standard textbook tasks and examination questions, to develop students’ procedural fluency. This begs the question of whether, and if so, how teachers can think about, and use these typical problems differently to develop conceptual understanding. In this paper, we report findings drawn from a two-year design-based research project and highlight two teaching vignettes to illustrate how typical problems were used to orchestrate instructional activities. Our findings suggest three important principles for teachers to consider when using typical problems.

教师在设计与实施蕴含丰富数学内涵的教学任务时面临诸多挑战，致使这类任务在多数数学课堂中难以普及。与之相反，教师通常会选用典型习题——如标准课本习题与考试考题——来培养学生的程序性技能熟练度(procedural fluency)。这便引出了一个值得深究的问题：教师能否，以及若能的话，该如何创新思路运用此类典型习题，以培养学生的概念性理解(conceptual understanding)？本论文基于一项为期两年的设计研究(design-based research)项目，汇报了相关研究发现，并呈现两个教学案例片段，用以展示教师如何借助典型习题统筹开展教学活动。本研究结果提出了教师在使用典型习题时可参考的三项重要原则。