Implementing Techtivities to Promote Students' Covariational Reasoning in College Algebra (ITSCoRe)

促进学生在把关、入门的本科数学课程中取得成功的机会，如大学代数，对一般学生从大学毕业，特别是对STEM专业的坚持不懈至关重要。为了应对这一挑战，该项目将开发、实施和研究技术：免费的、基于网络的学习体验，将视频动画与动态、互动的图形联系起来。这些引人入胜的活动将集中在学生的协变推理上，这涉及到形成和解释变化量之间的关系。协变推理是学生在大学数学关键领域(如函数、速率和图形)取得成功的重要能力，也是作为受过教育的公民进行批判性思维的重要能力。通过嵌入专业发展干预，该项目将培养大学代数教师与学生使用技术能力。更广泛地说，Desmos将提供这些技术，这是一个免费提供的数字数学工具，它将促进与广泛的利益相关者共享项目产品，包括那些投资于本科和预科教育的人。该项目将实现三个目标：(1)开发和验证一种测量学生协变推理的工具；(2)通过提高学生参与度和增强学生的协变推理，提高学生在大学代数方面的成绩；以及(3)通过将学生认为自己是数学实践者、他们在大学代数上的成功(通过他们在普通期末考试和期末课程成绩中的表现来衡量)和他们在协变推理工具上的表现联系起来，来促进有目的的、积极参与的学生。此外，该项目将解决与项目目标直接一致的三个研究问题：(1)如何衡量学生的协变推理能力？(2)在技术发展干预后，学生的结果增加到什么程度？(3)学生如何看待自己是数学实践者？这项混合方法的研究将包括对学生水平的数据进行分析，这些数据来自对本科生的临床访谈、学生在普通期末考试中的表现，以及学生在协变推理工具上的表现。教师层面的数据将包括对参与的教师的访谈，教师对协变推理感知的利克特量表，以及对教师进行的前后调查，以衡量他们对技术能力的使用。

Promoting students' opportunities to succeed in gatekeeping, introductory undergraduate mathematics courses, such as college algebra, is of utmost importance for students' graduation from college in general and for persistence in STEM majors specifically. To address this challenge, this project will develop, implement, and study Techtivities: free, web-based, learning experiences that link video animations with dynamic, interactive graphs. These engaging activities will focus on students' covariational reasoning, which involves forming and interpreting relationships between changing quantities. Covariational reasoning is a competency important for students' success in key areas of college mathematics (e.g., functions, rates, and graphs) as well as for critical thinking as an educated citizen. By embedding a professional development intervention, the project will foster college algebra instructors' use of Techtivities with their students. More broadly, the Techtivities will be available in Desmos, a freely available digital mathematics tool, which will promote sharing project products with a wide range of stakeholders, including those invested in both undergraduate and pre-college education.The project will accomplish a threefold goal: (1) develop and validate an instrument measuring students' covariational reasoning; (2) improve student outcomes in college algebra by increasing student engagement and enhancing students' covariational reasoning; and (3) promote purposeful, engaged students by drawing connections between students' views of themselves as doers of mathematics, their success in college algebra (as measured by their performance on a common final exam and their final course grade), and their performance on a covariational reasoning instrument. In addition, the project will address three research questions, which are directly aligned with the project's goals: (1) How can students' covariational reasoning be measured? (2) To what degree do student outcomes increase after Techtivities PD intervention? (3) How do students view themselves as doers of mathematics? The mixed-methods study will include analysis of student-level data from sources such as clinical interviews with undergraduates, student performance on a common final exam, and student performance on the covariational reasoning instrument. Instructor-level data will include interviews with participating instructors, a Likert-scale measure of instructors' perceptions of covariational reasoning, and pre-/post-surveys with instructors to gauge their use of Techtivities.