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

TERC、教育发展中心和蒙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型的开发和系统调查，以帮助教师在2-5年级发展关于证明的想法。 该教学模式为小学教师提供了一个学习工具和一个实践模型，他们可以在实施过程中从中学习。该项目是一个教学实验，在该实验中，该模型被反复实施和完善，首先是有经验的教师将证明的想法纳入课堂教学（第一阶段），然后是相对缺乏经验的教师，无论是在他们自己的理解证明，并在他们的知识，他们的学生如何可以学习有关证明（阶段2）。研究问题的重点是开发模型的组成部分，教师的学习，因为他们实施的模型，和学生的学习，因为他们从事的教学，是由模型指导，特别注意学生的成绩在年级水平的工作上的数量和操作的不同历史。预期的结果是一个教学模式，可以在更大的规模上进行测试，以及评估学生学习和教师的理解证明的工具。 该模型包括印刷材料与例程和教学序列的描述，实施每个组件的指导方针，以及教学框架，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.