Reasoning Language for Teaching Secondary Algebra

几十年的研究表明，更强的数学课堂话语，以及多种数学表征的使用和联系，与学生的学习成绩呈正相关。这种关系在代数中尤其突出，使学生可用的表示形式多样化可以为概念理解的发展提供重要的支持。第二代数教学的推理语言(Relate-SA)项目建议研究7-9年级的代数的教与学，特别关注课堂语言明确描述代数对象的性质和相互关系的方式。该项目旨在调查推理丰富的代数话语和学生对核心代数概念(如方程、方程求解过程和函数)的数学含义之间的双向关系。以教师为中心，Relate-SA将分析有关代数概念和程序的课堂叙事，并提供80小时的专业发展计划，旨在支持教师对代数对象、它们的性质和它们之间的关系进行更强有力的解释。Relate-SA项目将调查与代数相关的教师话语实践的三个方面。首先，这个项目将研究教师用来解释代数对象、它们的性质和它们之间的关系的语篇和语篇例程。这将通过开发和部署一项名为代数语言和推理调查的评估来实现，以确定教师在代数背景下的论述例行公事和叙述。该仪器要求教师通过描述学生的数学推理和潜在的数学理解来解释学生的作业和解释。其次，该项目将通过以代数话语为重点的80小时专业发展干预，支持教师代数话语实践的潜在增长。这种干预的影响将通过教师对代数语言和推理调查的反应模式的变化、对教师在专业发展中的工作的分析以及专业发展结束后的课堂观察分析来衡量。第三，该项目将寻求了解教师如何制定明确侧重于发展学生的代数推理和话语的课程。这一目标将通过对参与教师课堂上的数学课程的任务、计划和实施进行分析来实现。将为该项目招聘三组教师，每组12名。基于这一探索性项目的结果，该团队打算对专业发展及其对代数教学的影响进行更大范围的研究。探索研究预科-12项目(DRK-12)旨在通过研究和开发创新资源、模型和工具，显著提高预科-12学生和教师的科学、技术、工程和数学(STEM)的学习和教学。DRK-12计划中的项目建立在STEM教育的基础研究和先前的研究和开发工作的基础上，为拟议的项目提供了理论和经验上的证明。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Decades of research have demonstrated that stronger mathematics classroom discourse, along with the use and connection of multiple mathematical representations, correlates positively with gains in student learning. This relationship is particularly salient in algebra, where diversifying the representations available to students can provide important supports for the development of conceptual understanding. The Reasoning Language for Teaching Secondary Algebra (ReLaTe-SA) project proposes to study the teaching and learning of algebra in grades 7-9, with a specific focus on the ways in which classroom language explicitly describes properties of and relationships among algebraic objects. The project seeks to investigate the bi-directional relationship between reasoning-rich algebraic discourse and the mathematical meanings students hold for core algebraic concepts such as equations, the equation-solving process, and functions. With a focus on the teacher, ReLaTe-SA will analyze classroom narratives about algebraic concepts and procedures and provide an 80-hour professional development program designed to support teachers in developing stronger explanations of algebraic objects, their properties, and their relationships.The ReLaTe-SA project will investigate three aspects of teacher discourse practice related to algebra. First, the project will study the discourse and discourse routines that teachers use to explain algebraic objects, their properties, and their relationships. This will be accomplished through the development and deployment of an assessment called the Survey of Algebraic Language and Reasoning to identify teachers' discursive routines and narratives in the context of algebra. The instrument asks teachers to interpret student work and explanations by describing the student's mathematical reasoning and underlying mathematical understandings. Second, the project will support potential growth in teachers' algebraic discourse practices through an 80-hour professional development intervention focused on discourse in algebra. The impact of this intervention will be measured by changes to teachers' response patterns on the Survey of Algebraic Language and Reasoning, analyses of teachers' work within the professional development, and the analysis of classroom observations after the professional development has concluded. Third, the project will seek to understand the ways in which teachers develop lessons that explicitly focus on the development of students' algebraic reasoning and discourse. This goal will be realized through analyses of the tasks, plans, and implementations of mathematics lessons in participating teachers' classrooms. Three cohorts of 12 teachers each will be recruited for the project. Based on the results of this exploratory project, the team intends to follow up with a larger-scale study of the professional development and its impact on the teaching and learning of algebra.The Discovery Research preK-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models and tools. Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.