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准备和维持一支具有全球竞争力的STEM劳动力队伍的关键因素。然而，数学课程往往对学生在获得STEM领域学位方面的进步造成障碍。为了解决这一全国性的问题，本项目将集中于一项研究性研究，以探索本科数学教育中的两个关键问题：(1)未来的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准备教授数学，是决定本科数学教学质量和风格的一个因素。不幸的是，这种教学往往不会对本科生产生积极影响。数学研究生助教(MGTA)在从事数学教学的职业生涯中往往只接受最低限度的培训，因此，他们的教学实践仍然植根于以讲座为基础的教学。对于大多数学生来说，以讲授为基础的本科数学教学并不是最好的教学形式，这表明MGTA迫切需要基于研究的专业发展计划。然而，很少有研究调查MGTA在研究生课程不同阶段对专业发展的需求。这项研究将通过跟踪MGTA在他们的研究生课程中的进步来填补这一研究空白。这些发现将产生新的知识，为全国的STEM部门提供信息，如何更好地为研究生教学做好准备，这反过来将导致美国STEM工作队伍准备得更好。该项目的一个基本目标是创建MGTA教学发展阶段的模型，研究人员和实践者将能够利用该模型来设计有效的、长期的专业发展计划，从而导致数学教学提高学生在本科数学课程中的成绩。为了调查MGTA的教学发展阶段，将制定调查和访谈方案，以捕捉知识、信念、数学观和教学方面的任何变化。这些调查将有开放式的问题，探讨MGTA对数学教学的想法，以及是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。访谈过程将更深入地了解他们的教学实践、最近的教学经验、他们是否感到得到了足够的支持，以及他们认为需要哪些其他支持。MGTA将在他们的研究生课程期间接受调查和访谈，以确定他们的教学观是否有任何变化，以及他们对教学的支持需求。他们对调查和面试问题的回答将使用演绎主题分析阶段进行分析。这项研究的一个长期目标是利用这一新知识来设计一种基于研究的、脚手架式的培训计划模式，该模式将随着数学研究生的教学和教学思想的发展而经历的各个阶段。

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.