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

促进学生有机会成功地守门，介绍本科数学课程，如大学代数，是学生从大学毕业的一般和坚持在STEM专业特别重要。为了应对这一挑战，该项目将开发，实施和研究Techtivities：免费的，基于网络的学习体验，将视频动画与动态，交互式图形联系起来。这些引人入胜的活动将集中在学生的协变推理，其中涉及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取得成功的重要能力（例如，函数、比率和图表）以及作为受过教育的公民的批判性思维。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活动。更广泛地说，技术活动将在Desmos中提供，Desmos是一个免费的数字数学工具，它将促进与广泛的利益相关者分享项目产品，包括那些投资于本科和大学预科教育的人。（2）通过提高学生的参与度和增强学生的协变推理能力来提高学生在大学代数中的成绩;以及（3）通过将学生将自己视为数学实践者的观点，他们在大学代数中的成功（通过他们在共同期末考试和最终课程成绩的表现来衡量），以及他们在协变推理工具上的表现。此外，该项目将解决三个研究问题，这是直接与项目的目标：（1）如何测量学生的协变推理？(2)在什么程度上做学生的成果增加后，Techtivities PD干预？(3)学生如何看待自己是数学的实践者？混合方法的研究将包括分析学生水平的数据来源，如临床采访本科生，学生的表现在一个共同的期末考试，和学生的表现上的协变推理工具。教师层面的数据将包括与参与教师的访谈，教师的认知协变推理的Likert量表测量，和前/后调查与教师，以衡量他们使用的Techtivities。

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.