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

加强中学职前数学教师的准备：数学推理和证明作为教学的镜头

基本信息

批准号：
1711163
负责人：
Orly Buchbinder
金额：
$ 28.32万
依托单位：
University of New Hampshire
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-06-01 至 2022-05-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1711163&HistoricalAwards=false
关键词：
Enhancing Preparation Secondary Preservice Mathematics

项目摘要

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.

该项目将有助于实现美国国家科学基金会改善本科 STEM 教育以扩大和加强美国 STEM 劳动力队伍的目标。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、知识渊博的教师，他们激励学生并为他们追求 STEM 学科做好准备。因此，培养能够在课堂上进行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、实施和研究一门新的、技术丰富的顶点课程“中学教师数学推理和证明”来解决教师的知识库问题。该课程将提高未来中学数学教师的教学内容和教学知识，以促进深入的概念理解、问题解决、推理和证明技能。这一重点与全国数学教师委员会提出的愿景和共同核心数学国家标准一致。这一愿景的成功实施依赖于高素质、知识渊博的教师队伍。该项目将产生基于证据的方法、教学模块和辅导员指南，以改善全国中学数学教师的准备，并通过扩展该项目将加强数千名中学生的数学教育。中学教师数学推理和证明的顶点课程的创新方面将包括虚拟学习环境支持的基于大学的经验、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。该项目将开发顶点课程的概念模型、四个教学模块以及随附的辅导员指南。每个教学模块将讨论与证明相关的关键主题，例如量化、条件陈述、直接证明和反证证明。该项目将利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了解学习环境及其设计组成部分对提高未来教师知识的影响。具体来说，该项目将有助于撰写有关数学推理和证明的文献，以及将其纳入教师准备并最终纳入数学课堂的方法。该项目产生的理论和经验知识将得到广泛传播，以帮助提高全国中学数学教师的准备。罗伯特·诺伊斯教师奖学金计划将为该项目提供共同资助，以表彰其与诺伊斯努力的更广泛的教师培训目标的一致性。