Enhancing Explorations in Functions for Preservice Secondary Mathematics Teachers

加强职前中学数学教师职能探索

• 批准号: 1612380
• 负责人: James Alvarez
• 金额: $ 30万
• 依托单位: University of Texas at Arlington
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-07-01 至 2019-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1612380&HistoricalAwards=false
• 关键词: Enhancing; Explorations; Functions; Preservice; Secondary

In order to increase the number and diversity of undergraduate STEM majors in the United States, it is essential to improve students' interest and success in mathematics before they enter their undergraduate studies. The secondary grades are especially important for mathematically preparing students for undergraduate STEM majors, but rigorous and engaging secondary mathematics classrooms require a well-prepared teacher workforce to facilitate these learning environments. This Improving Undergraduate STEM Education Engaged Student Learning Exploration and Design project seeks to transform preservice mathematics teachers' understanding of mathematics early in their undergraduate studies, thus contributing to the transformation of their undergraduate STEM education. More specifically, this project will develop curriculum materials for use in mathematics courses for preservice secondary mathematics teachers as well as develop instructor materials that assist mathematicians and other instructors in using these materials in an active learning environment. The materials will be research-based and focus on targeted, inquiry-based experiences that will develop a deep understanding of functions as they correspond to the high school curriculum and the first two years of the university curriculum. The initial piloting of materials will take place at a research-intensive Hispanic Serving Institution with over 50% of its teacher preparation candidates coming from underrepresented groups. In addition, the project will directly involve the participation of a strong network of teacher preparation programs that use the highly-acclaimed UTeach STEM teacher preparation model. It will also enhance the experiences, both in content and pedagogy, for thousands of preservice secondary mathematics teachers across the country via coordinated dissemination across the UTeach network and other mathematics teacher preparation programs. As a result, the project will impact the mathematical learning experiences of hundreds of thousands of socio-economically disadvantaged students across the country, as 66% of graduates from UTeach programs teach in schools where the majority of students are low-income. That is, diverse groups of preservice teachers and the highly diverse students they teach will benefit from the project's transformation of undergraduate education for preservice secondary mathematics teachers. Guided by findings from the research literature regarding secondary mathematics teachers' pitfalls in understanding key concepts and ideas about functions, the project will enhance and supplement widely-used resources for preservice secondary mathematics teachers in the first two years of their university mathematics studies. The project will develop research-based tasks and explorations that will address key concepts and ideas about functions that are typically problematic for secondary mathematics teachers, to include functions versus equations, graphical connections to function patterns, and other important function concepts. Curriculum widely-used in the UTeach program will be augmented with an instructor's guide to scaffold the lessons and explorations for mathematicians and other instructors teaching the course. As part of the cyclic design process, the project will collect evidence on whether and how these materials adequately close gaps in understanding of critical problematic concepts identified in the research literature and therefore, will contribute to the knowledge base in the specific areas of design and implementation of inquiry-based materials for preservice secondary mathematics teachers. The project will generate knowledge about the key characteristics of such mathematical tasks and about what instructional and pedagogical supports mathematicians need to implement inquiry-based materials for preservice secondary mathematics teachers. The project will also provide evidence on how the curriculum materials and implementation of these materials address conceptual difficulties that teachers encounter with functions. Thus, the project will generate evidence for curriculum and instruction that could transform the education of preservice secondary mathematics teachers. A distinguishing feature of this project will be the purposeful integration of the mathematics education research literature on the key mathematical pitfalls or misconceptions held by preservice and inservice mathematics teachers into the design and redesign of mathematical experiences and explorations for secondary mathematics teachers in the first two years of their mathematics studies.

为了增加美国本科STEM专业的数量和多样性，在他们进入本科学习之前，必须提高学生对数学的兴趣和成功至关重要。二级年级对于数学上的学生为本科生的学生做好准备尤其重要，但是严格而引人入胜的中学数学教室需要准备好的教师劳动力来促进这些学习环境。这项改善的本科STEM教育与学生学习探索和设计项目旨在改变学前数学教师对数学的了解，从而在其本科学习中对数学的理解，从而有助于其本科STEM教育的转变。更具体地说，该项目将开发课程材料，以用于数学课程，以供二级数学老师，并开发教师材料，以帮助数学家和其他教师在主动学习环境中使用这些材料。这些材料将基于研究，并专注于基于询问的经验，这些经验将对功能进行深入了解，因为它们与高中课程相对应和大学课程的前两年。最初的材料试验将在研究密集的西班牙裔服务机构举行，其教师准备的50％来自代表性不足的团体。此外，该项目将直接涉及强大的教师准备计划网络的参与，该计划使用备受赞誉的UTEACH STEM教师准备模型。 它还将通过在UTEACH网络和其他数学教师准备计划中协调的传播计划来增强全国成千上万的二级数学教师的内容和教学法的体验。结果，该项目将影响全国数十万个社会经济处于弱势学生的数学学习经历，因为来自UTEARCE课程的66％的毕业生在大多数学生都是低收入的学校中教书。也就是说，各种各样的职前教师和他们所教的高度多样化的学生将受益于该项目的本科教育的转型，用于二级数学教师。在研究文献中有关二级数学教师在理解有关功能的关键概念和思想方面的陷阱的发现的指导下，该项目将在其大学数学研究的头两年中增强和补充广泛使用的资源，以供二级数学教师提供广泛使用的资源。 该项目将开发基于研究的任务和探索，这些任务和探索将解决有关次级数学教师通常有问题的功能的关键概念和想法，以包括功能与方程，图形连接到功能模式以及其他重要功能概念。 在UTEACH计划中广泛使用的课程将通过教师指南进行扩展，以踩踏数学家和其他教师教课程的课程和探索。作为循环设计过程的一部分，该项目将收集有关这些材料是否以及如何充分缩小研究文献中确定的关键问题概念的差距的证据，因此，将在设计和实施基于查询的材料的特定领域的知识基础上为前者二级数学教师的特定领域。该项目将产生有关此类数学任务的关键特征的知识，以及有关数学家需要哪些教学和教学支持，以实施基于查询的材料，以用于前二级数学教师。该项目还将提供有关课程材料和实施这些材料如何解决教师遇到功能的概念困难的证据。因此，该项目将为课程和教学提供证据，这些证据可以改变前二级数学教师的教育。该项目的一个显着特征将是关于数学教育研究文献的有目的性整合，内容涉及在其数学研究的前两年中，在数学和内存数学教师的设计和重新设计的二级数学教师的设计和重新设计。