Enhancing Explorations in Functions for Preservice Secondary Mathematics Teachers

为了增加美国本科STEM专业的数量和多样性，在学生进入本科学习之前，提高他们对数学的兴趣和成功是至关重要的。中学年级对于为本科STEM专业的学生进行数学准备尤其重要，但严谨和吸引人的中学数学课堂需要一支准备充分的教师队伍来促进这些学习环境。改善本科生STEM教育参与学生学习探索和设计项目旨在改变职前数学教师在本科学习早期对数学的理解，从而促进他们本科生STEM教育的转变。更具体地说，该项目将为中学预科数学教师编写用于数学课程的课程材料，并开发指导材料，帮助数学家和其他教师在积极的学习环境中使用这些材料。这些材料将以研究为基础，重点放在有针对性的、基于探究的体验上，这些体验将加深对函数的理解，因为它们对应于高中课程和大学课程的头两年。最初的试行材料将在一个研究密集的拉美裔服务机构进行，该机构50%以上的教师培训候选人来自代表性不足的群体。此外，该项目将直接涉及使用广受好评的UTeach STEM教师培训模式的强大教师培训计划网络的参与。它还将通过UTeach网络和其他数学教师培训计划的协调传播，加强全国数千名职前中学数学教师在内容和教学方法方面的经验。因此，该项目将影响全国数十万社会经济困难学生的数学学习体验，因为66%的UTeach项目毕业生在大多数学生属于低收入家庭的学校任教。也就是说，不同的职前教师群体和他们所教的高度多样化的学生将受益于该项目对职前中学数学教师本科教育的改造。根据研究文献中有关中学数学教师在理解有关函数的关键概念和思想方面的陷阱的研究结果，该项目将加强和补充中学数学教师在大学数学学习的头两年广泛使用的资源。该项目将开发基于研究的任务和探索，解决关于函数的关键概念和想法，这些关键概念和想法通常是中学数学教师有问题的，包括函数与方程、函数模式的图形连接以及其他重要的函数概念。UTeach计划中广泛使用的课程将增加教师指南，为数学家和其他教授该课程的教师搭建课程和探索的脚手架。作为循环设计过程的一部分，该项目将收集证据，说明这些材料是否以及如何充分弥合研究文献中确定的关键问题概念的理解差距，从而有助于为中学数学教师职前教师设计和实施探究性材料的具体领域的知识库作出贡献。该项目将产生有关这类数学任务的主要特点的知识，以及数学家为中学数学教师实施探究性教材所需的教学和教学支持。该项目还将提供证据，说明课程材料和这些材料的实施如何解决教师在履行职能时遇到的概念困难。因此，该项目将为课程和教学提供证据，这些课程和教学可能会改变中学数学教师的教育。该项目的一个特点是，有目的地将关于在职和在职数学教师的关键数学陷阱或误解的数学教育研究文献整合到中学数学教师在数学学习的头两年的数学经验和探索的设计和重新设计中。

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.