EAGER: Exploring Mathematics Graduate Teaching Assistants' Developmental Stages for Teaching

数学在科学、技术、工程和数学（STEM）学科中发挥着核心作用，学生在本科数学课程中的成功是满足国家培养和维持具有全球竞争力的STEM劳动力需求的关键因素。然而，数学课程往往会阻碍学生在STEM领域获得学位。为了解决这一全国性问题，本项目将重点研究本科数学教育中的两个关键问题：(1)未来数学教师如何为教学做准备；(2)本科课堂数学教学的形式。这两个问题是直接相关的。未来的数学教师如何做好数学教学的准备，是影响本科课堂数学教学质量和教学风格的一个决定性因素。不幸的是，这种教学往往对本科生没有积极的影响。数学研究生助教（mgta）通常只接受过很少的数学教学培训，因此，他们的教学实践仍然植根于以讲座为基础的教学。在本科数学教学中，以讲座为基础的数学教学已被证明不是大多数学生的最佳教学形式，这表明mgta迫切需要以研究为基础的专业发展计划。然而，很少有研究调查MGTA在研究生课程的不同阶段对专业发展的需求。本研究将通过跟踪mgta在研究生课程中的进展来填补这一研究空白。这些发现将产生新的知识，告知全国各地的STEM部门如何更好地为研究生教授本科生做好准备，这反过来又将使美国的STEM劳动力准备得更好。该项目的一个基本目标是创建一个mgta发展阶段的教学模型，研究人员和从业人员将能够利用该模型设计有效的、长期的专业发展计划，从而使数学教学提高学生在本科数学课程中的成绩。为了调查mgta在教学方面的发展阶段，将创建调查和访谈协议，以捕捉知识、信仰、数学观点和教学方面的任何变化。调查将有开放式的问题，询问mgta对教学和学习数学的想法，以及什么影响了他们对教学的看法。其他项目将涉及他们的认知信念和自我效能。面试过程将提供对他们的教学实践，他们最近的教学经验，他们是否觉得他们得到了足够的支持，以及他们认为他们需要什么其他支持的更深入的看法。mgta将在其研究生课程期间接受调查和访谈，以确定他们对教学的看法是否有变化，以及他们对教学支持的需求。他们对调查和访谈问题的回答将使用演绎主题分析的阶段进行分析。本研究的长期目标是利用这些新知识来设计一个以研究为基础的、脚手架式的培训计划模型，该模型将参与数学研究生在教学和教学思想发展过程中所经历的各个阶段。

Mathematics plays a central role in Science, Technology, Engineering, and Mathematics (STEM) disciplines, and student success in undergraduate mathematics courses is a crucial ingredient in meeting the Nation's need to prepare and sustain a globally competitive STEM workforce. However, mathematics courses often create barriers to student progress in obtaining degrees in STEM areas. To address this national problem, this project will focus on a research study to explore two critical issues in undergraduate mathematics education: (1) how future mathematics faculty members are prepared for teaching and (2) the format of mathematics teaching in undergraduate classrooms. These two issues are directly related to one another. How future mathematics faculty are prepared to teach mathematics is a determining factor in the quality and style of mathematics teaching in undergraduate classrooms. Unfortunately, all too often, this teaching does not have a positive impact on undergraduate students. Mathematics graduate teaching assistants (MGTAs) often receive minimal training for a career of teaching mathematics and, as a result, their teaching practices remain rooted in lecture-based instruction. Lecture-based mathematics teaching in undergraduate mathematics has been shown not to be the best form of instruction for the majority of students, indicating that there is critical need for research-based professional development programs for MGTAs. Yet, few studies have investigated MGTA needs for professional development at different points in their graduate programs. This study will fill this gap in the research by following MGTAs as they progress through their graduate programs. The findings will generate new knowledge to inform STEM departments across the country how to better prepare graduate students for teaching undergraduates, which, in turn, will lead to a better prepared United States STEM workforce.A fundamental goal of the project is to create a model of MGTAs' developmental stages for teaching that researchers and practitioners will be able to use to design effective, long-term professional development programs that will result in mathematics instruction that improves student outcomes in undergraduate mathematics courses. To investigate MGTAs' developmental stages for teaching, surveys and interview protocols will be created to capture any changes in knowledge, beliefs, views of mathematics, and teaching. The surveys will have open-ended questions that inquire into MGTAs' thoughts about teaching and learning mathematics and what influences the way they think about teaching. Other items will address their epistemic beliefs and self-efficacy. An interview process will provide a deeper view of their teaching practices, their most recent teaching experiences, whether they feel that they are receiving adequate support, and what other support they feel they need. MGTAs will be surveyed and interviewed for the duration of their graduate programs to determine any changes to their views of teaching and their need of support for teaching. Their responses to the survey and interview questions will be analyzed using the stages of deductive thematic analysis. A long-term goal of this study is to use this new knowledge to design a research-based, scaffolded training program model that will attend to the stages mathematics graduate students go through as their teaching and thoughts about teaching evolve.