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

TERC、教育发展中心和Mount Holyoke学院的开发人员和研究人员正在参与一种教学模式的开发和系统调查，以帮助教师发展关于2-5年级证明的想法。教学模式既为小学教师提供了学习的工具，又为他们提供了实践的模型，使他们在实施教学模式的过程中可以从中学习。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完善，首先是有经验的教师将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，他们对证明的理解和他们对学生如何学习证明的知识（阶段2）。研究问题的重点是发展模型的组成部分，教师在实施模型时的学习，以及学生在模型指导下参与教学时的学习，特别关注那些在年级水平的数字和运算工作中有不同成就历史的学生。预期的结果是一种可以在更大范围内进行测试的教学模式，以及评估学生学习和教师对证据理解的工具。该模型包括印刷材料的例程和教学顺序的描述，指导方针，实施每个组成部分，和教学框架，以及书面和视频案例。

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.