Using Research to Shape Instruction and Placement in Algebra and Precalculus

该项目正在开发一种新的基于研究的工具，用于安排学生学习代数和微积分预科课程，并传播这种新工具的书面描述和样本项目。这项工作基于早期的研究和测试，这些研究和测试产生了微积分概念准备测试(CCR)和配套的微积分概念前评估(PCA)。特别是，研究人员考虑了学生对关键概念的概念性理解，这些概念是在随后的数学课程中取得成功所必需的，在未来的职业生涯中，也是见多识广的公民。这项后续的发展和传播工作的目的有两个：一)影响和改进大学数学分级考试；二)指导和塑造代数和微积分预科课程的教学实践。这个项目的智力价值在于它认识到，虽然有足够的研究基础来指导更有效的教学实践，但各级教师缺乏随时可用的评估工具，以加强教学，提高学生的深刻概念理解。事实上，目前使用的大多数分级考试都侧重于程序流利性，从而强化了传统的教学方法。新的分级考试成为了一套连贯的工具的一部分，这些工具有助于在整个代数-微积分-预科-微积分的过程中改善教和学。该项目正在几个方面产生更广泛的影响。首先，新工具的推理和概念分类以及说明概念推理覆盖范围的样本项目正在公开提供，并在整个项目传播阶段使用，不仅为教授低级数学课程的学院和大学教师提供信息，也为K-12教师提供信息。其次，该项目由美国数学协会(MAA)领导，该协会是世界上最大的专注于本科生数学的专业组织。该组织的在线和印刷出版物以及在国家和区域会议上举行的会议提供了多样化和影响深远的传播渠道。此外，与寻求提高数学教学质量的其他国家组织的现有关系为MAA提供了一个独特的机会来开发、试点和严格记录分级考试的可靠性和有效性。最后，该项目的成果有助于改善中学和中学后数学之间的衔接，并为职前和在职教师的数学教育提供信息。

This project is developing a new research-based instrument for placement of students in algebra and precalculus and disseminating documented descriptions and sample items of this new instrument. The work is based on earlier research and testing that produced a Calculus Concepts Readiness test (CCR) and a companion Precalculus Concepts Assessment (PCA). In particular, researchers considered students' conceptual understanding of key concepts required for success in subsequent mathematics courses, in future careers, and as informed citizens. The purpose of this follow-on development and dissemination effort is twofold: i) to influence and improve college mathematics placement tests and ii) to inform and shape instructional practice in algebra and precalculus courses. The intellectual merit of this project rests in its recognition that while there is an adequate research base to inform more effective instructional practice, teachers at all levels lack ready access to assessment tools that reinforce teaching for improving students' deep conceptual understanding. Indeed, most placement tests currently in use focus on procedural fluency, thus reinforcing traditional instructional approaches. The new placement test becomes part of a coherent suite of instruments that serve to improve teaching and learning throughout the entire algebra-precalculus-calculus pathway. The project is exerting its broader impacts in several ways. Firstly, the reasoning and conceptual taxonomies of the new instrument, as well as sample items to illustrate the conceptual reasoning coverage, are being made publicly available and used throughout the dissemination phase of the project to inform professional development efforts not only for college and university faculty teaching lower-division mathematics courses, but also for K-12 teachers. Secondly, the project is being led by the Mathematical Association of America (MAA), the largest professional organization in the world with a focus on undergraduate mathematics. The organization's online and print publications, and sessions at national and regional meetings provide diverse and far-reaching channels for dissemination. In addition, existing relationships with other national organizations seeking to raise the quality of mathematics instruction gives the MAA a unique opportunity to develop, pilot, and rigorously document the reliability and validity of placement tests. Finally, the results of this project are contributing to improved articulation between secondary and post-secondary mathematics and informing pre-service and in-service teacher education in mathematics.