Using Routines as an Instructional Tool for Developing Students' Conceptions of Proof

TERC、教育发展中心和芒特霍利奥克学院的开发人员和研究人员正在参与一个教学模式的开发和系统调查，以帮助教师在2-5年级发展关于证明的想法。这种教学模式既为小学教师提供了一种学习的工具，也为他们提供了一种在实施过程中可以学习的实践模式。该项目是一个教学实验，在这个实验中，模型被迭代地实施和改进，首先是有经验的教师将关于证明的想法融入他们的课堂教学(阶段1)，然后是相对缺乏经验的教师，无论是他们自己对证明的理解，还是他们对学生如何学习证明的知识(阶段2)。研究问题侧重于发展模式的组成部分，教师在实施模式时的学习，以及学生在模式指导下进行教学时的学习，特别关注在年级水平上有不同成绩的学生在数字和运算方面的成就。预期的结果是一个可以在更大范围内测试的教学模式，以及用于评估学生学习和教师对证据的理解的工具。该模式包括印刷材料，包括对例程和教学顺序的描述、实施每个组件的指导方针、教学框架以及书面和视频案例示例。

Developers and researchers at TERC, the Education Development Center, and Mount Holyoke College are participating in the development and systematic investigation of a teaching model to assist teachers in developing ideas about proof in grades 2-5. The teaching model provides both a tool for learning on the part of elementary teachers and a model of practice from which they can learn as they implement it. The project is a teaching experiment in which the model is iteratively implemented and refined, first with teachers experienced in incorporating ideas about proof into their classroom instruction (Phase 1), then with teachers who are relatively inexperienced, both in their own understanding of proof and in their knowledge of how their students can learn about proof (Phase 2). Research questions focus on developing the components of the model, the learning of teachers as they implement the model, and the learning of students as they engage in the instruction that is guided by the model, with particular attention to students with varied histories of achievement in grade-level work on number and operations. The expected outcome is a teaching model that can be tested on a larger scale as well as instruments for assessing student learning and teacher understanding of proof. The model includes printed material with descriptions of the routines and instructional sequences, guidelines for implementing each component, and a teaching framework as well as written and video case examples.