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

促进学生在看门人、大学代数等入门级本科数学课程中取得成功的机会，对于学生从大学毕业，特别是对STEM专业的坚持来说，是至关重要的。为了应对这一挑战，该项目将开发、实施和研究技术活动：将视频动画与动态、交互式图表联系起来的免费、基于网络的学习体验。这些引人入胜的活动将侧重于学生的协变推理，包括形成和解释数量变化之间的关系。协变推理对于学生在大学数学的关键领域（如函数、速率和图形）的成功以及作为一个受过教育的公民的批判性思维来说是一项重要的能力。通过嵌入专业发展干预，该项目将促进大学代数教师与学生一起使用技术。更广泛地说，这些技术将在Desmos中提供，Desmos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大学预科教育的利益相关者。该项目将实现三个目标：(1)开发和验证测量学生协变推理的工具；(2)通过提高学生参与度和协变推理能力，提高大学生代数成绩；(3)通过在学生对自己作为数学实干家的看法、他们在大学代数上的成功（通过他们在普通期末考试中的表现和期末课程成绩来衡量）和他们在协变推理工具上的表现之间建立联系，促进有目的的、投入的学生。此外，该项目将解决三个与项目目标直接相关的研究问题：(1)如何测量学生的协变推理？(2) techactivities PD干预后学生成绩提高到什么程度？(3)学生如何看待自己作为数学实干家？混合方法研究将包括对学生水平数据的分析，这些数据来自本科生的临床访谈、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，对教师对协变推理的看法的李克特量表测量，以及对教师的前后调查，以评估他们对Techtivities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.