Using Research to Shape Instruction and Placement in Algebra and Precalculus

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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.