Collaborative Research: Justification and Argumentation: Growing Understanding of Algebraic Reasoning (JAGUAR)

该项目的主要目标是了解教师如何1)发展特定的数学知识(代数证明)，2)将这些知识转化为课堂实践，以及3)改进他们的教学方法以促进学生的学习。该项目将通过数学家、教师和数学教育者之间的合作，阐明学校代数的正当性的含义。该项目侧重于教师在专业发展环境中的数学学习与随后的a)教学实践的变化和b)在实践中继续深化其教学知识之间的重要和未被充分挖掘的联系。此外，通过与选定的模范教师小组合作，该项目探索了高级探究式教学的发展，即通过辩护活动支持学生数学学习的教学。该项目设计的特点是协调双管齐下，在数学课程和教师自己的教室的背景下审查教师的学习。数据收集活动旨在促进协调分析，以调查这两种情况下的联系。教师暑期课程是以一门课程为蓝本的，该课程已作为NSF资助的专业发展项目的一部分成功实施。同样，在学年期间与教师开展的活动将为教师提供发展先进教学实践的机会，并为项目小组提供调查发展过程的机会。该项目将利用和扩展现有的工具来评估学生和教师对辩护的理解。代数和代数推理是数学学科的核心，对培养合格的STEM劳动力具有国家重要性。

The main goal of the project is to understand how teachers 1) develop specific mathematical knowledge (algebraic justification), 2) transform this knowledge to classroom practice, and 3) advance in their pedagogy to promote students' learning. The project will clarify the meaning of justification for school algebra through collaborations among mathematicians, teachers, and mathematics educators. The project focuses on the important and under-explored connection between teachers' mathematical learning in a professional development environment and the subsequent a) changes in their teaching practice and b) continued deepening of their content knowledge in practice. Additionally, by working with a select group of exemplary teachers, the project explores the development of advanced inquiry teaching, namely teaching that supports students' mathematics learning via justification activities. The project design features a coordinated two-pronged approach in which teacher learning is examined in the context of a mathematics content course and the teachers' own classrooms. Data collection activities are designed to facilitate coordinated analyses to investigate connections across these two contexts. The summer course for teachers is modeled on a course that has been implemented successfully as part of an NSF-funded professional development project. Similarly, activities conducted with teachers during the academic year will provide opportunities for the teachers to develop advanced teaching practices and opportunities for the project team to investigate the development process. The project will utilize and extend existing instruments for assessing students' and teachers' understanding of justification. Algebra and algebraic reasoning are core to the discipline of mathematics and have national importance for the development of qualified STEM workforce.