Enhancing Preparation of Secondary Preservice Mathematics Teachers: Mathematical Reasoning and Proving as a Lens for Teaching

该项目将有助于美国国家科学基金会改善本科STEM教育的目标，以扩大和加强美国的STEM劳动力。数学素养和stem导向专业的准备工作在学生进入大学之前就开始了。它始于高素质和知识渊博的教师，他们激励和培养学生追求STEM学科。因此，培养能够在课堂上实施有效教学实践的优秀数学教师势在必行。该项目将通过设计、实施和研究一门名为《中学教师数学推理与证明》的新技术丰富的顶点课程来解决教师知识库的问题。本课程将提高未来中学数学教师的教学内容和教学知识，以促进深刻的概念理解，解决问题，推理和证明技能。这种强调与国家数学教师委员会和国家数学共同核心标准所提出的愿景是一致的。这一愿景的成功实施依赖于一支高素质、知识渊博的教师队伍。该项目将制定循证方法、教学模块和辅助指南，以改善全国各地中学数学教师的准备工作，并进一步加强成千上万中学生的数学教育。顶点课程《中学教师数学推理与证明》的创新方面将包括虚拟学习环境支持的大学经验、当地学校的结构化实践经验，以及强调推理、论证和证明作为数学教学的总体方法。该项目将开发一个顶点课程的概念模型，四个教学模块，以及相应的辅助指南。每个教学模块都将讨论一个与证明相关的关键主题，如量化、条件陈述、直接证明和反命题证明。该项目将采用基于设计的研究方法来研究未来教师在数学推理和证明教学中的内容和教学知识如何在整个课程中发展。研究结果将有助于更好地理解学习环境及其设计要素对提高未来教师知识的影响。具体而言，该项目将有助于数学推理和证明的文献，以及将其纳入教师准备和数学课堂的方法。该项目产生的理论和实证知识将广泛传播，以帮助改善全国中学数学教师的准备工作。罗伯特·诺伊斯教师奖学金计划将为该项目提供共同资金，以表彰该项目与诺伊斯努力的更广泛的教师培养目标相一致。

This project will contribute to the National Science Foundation's goal of improving undergraduate STEM education to broaden and strengthen the U.S. STEM workforce. Preparation of mathematically literate and STEM-oriented majors begins prior to students reaching college. It begins with highly qualified and knowledgeable teachers, who inspire and prepare students to pursue STEM disciplines. Thus, it is imperative to prepare excellent mathematics teachers capable of enacting effective teaching practices in their classrooms. This project will address this teacher knowledge base through design, implementation, and study of a new, technologically rich capstone course called Mathematical Reasoning and Proving for Secondary Teachers. The course will enhance prospective secondary mathematics teachers' content and pedagogical knowledge to promote deep conceptual understanding, problem solving, reasoning, and proving skills. This emphasis concurs with the vision put forward by the National Council of Teachers of Mathematics and the Common Core State Standards for Mathematics. The successful implementation of this vision relies on a well-qualified and knowledgeable teacher workforce. The project will generate evidence-based approaches, instructional modules and facilitator guides to improve preparation of secondary mathematics teachers throughout the country, and by extension the project will enhance the mathematics education of thousands of middle school and secondary school students.The innovative aspects of the capstone course Mathematical Reasoning and Proving for Secondary Teachers will include university-based experiences supported by virtual learning environments, a structured practical experience in local schools, and an emphasis on reasoning, justification, and proving as an overarching approach for teaching mathematics. The project will develop a concept model of the capstone course, four instructional modules, and the accompanying facilitator guides. The instructional modules will each address a critical topic related to proving, such as quantification, conditional statements, direct proof and proof by contrapositive. The project will utilize design-based research methodology to study how prospective teachers' content and pedagogical knowledge for teaching mathematical reasoning and proving develop throughout the course. The results will help to better understand the impact of the learning environment and its design components on enhancing prospective teachers' knowledge. Specifically, the project will contribute to the literature on mathematical reasoning and proving and the ways to incorporate them in teacher preparation and, consequently, in the mathematics classroom. The theoretical and the empirical knowledge generated by the project will be broadly disseminated to help to improve preparation of secondary mathematics teachers nationwide. The Robert Noyce Teacher Scholarship program will provide co-funding for this project in recognition of its alignment with the broader teacher preparation goals of the Noyce effort.