Collaborative Research: Understanding and Cultivating the Transition from Arithmetic to Algebraic Reasoning

这是三所大学之间的合作研究项目。该项目是一个全面、系统的研究和发展计划，涉及三个相互关联的研究层次：学生的学习和发展；教师的信念、知识和实践；以及专业发展。该项目既基于学生如何发展代数推理和获取领域知识和技能的合理理论，也基于教师的信念和现有做法。在学生层面，围绕算术向代数推理的过渡，构建了学生进化代数推理和技能习得的详细发展模型。在教学阶段，将测试一种很有前途的教学方法--衔接教学。在专业发展阶段，将实施教师专业发展原型。PrototypeT扩展了现有的基于技术的方法。它使可扩展的教师专业发展模式的评估成为可能。技术是这个项目的核心方面。这项研究的结果将被实施到一个连贯的教育计划中，利用代数认知导师和STEP网络教师专业发展环境为学生和教师提供支持。

This is a collaborative research project between three universities. The project is a comprehensive, systemic research and development program addressing three inter-related tiers of study: student learning and development; teacher beliefs, knowledge, and practice; and professional development. The project is grounded in both sound theory of how students develop algebraic reasoning and acquire domain knowledge and skills and in the beliefs and existing practices of teachers. In the student tier a detailed developmental model of students' evolving algebraic reasoning and skill acquisition will be constructed concentrating on the transition from arithmetic to algebraic reasoning. In the teaching tier a promising pedagogical approach, Bridging Instruction, will be tested. In the professional development tier a teacher professional development prototype will be implemented. The prototypeT extends an existing technology based approach. It enables the evaluation of a scalable model of teacher professional development. Technology is a central aspect of this project. The findings of this research will be implemented into a coherent educational program for students and teachers using Algebra Cognitive Tutors and the STEP web teacher professional development environments.