The overarching goal of this project is to develop innovative instructional resources and professional development to support middle grades teachers in meeting the challenges set by college- and career-ready standards for students' learning of algebra. This 4-year project includes three major components: (1) development and empirical testing of learning trajectories for linear functions and linear equations, (2) collaborations with teachers of Connected Mathematics Project 2 (CMP2) to create and test a set of instructional resources focused on formative assessment processes, and (3) iterative refinement of a professional development model for engaging teachers with the instructional resources in ways that optimize students' learning of algebra. The professional development activities provide opportunities for teachers to develop specialized content knowledge of learning trajectories for linear functions and equations in algebra, processes for interpreting students' performances with respect to those trajectories and providing feedback and additional instructional activities based on "where" the student is with respect to the overall learning trajectory. Such changes in teacher knowledge and practice are anticipated to produce improved student learning outcomes for key concepts and procedures in algebra. One of the major stumbling blocks to teachers' implementation of effective formative assessment practice is the sheer volume and management of the information needed to monitor and interpret student performance. The project addresses this impediment by employing the ASSISTments platform, a web-based online system for delivering mathematics problem sets and capable of adapting problem presentation to student performance in real time.
Research on learning trajectories in mathematics has mostly centered on concepts at the primary school level. While research at this level has been prolific and informative in multiple aspects of mathematics education, there are major knowledge gaps in our understanding of learning trajectories in several domains of mathematics, specifically in algebra. Indeed, there is a growing need for new research and development projects to fill these critical knowledge gaps.
This project focuses on two critical areas in mathematics: students' understanding of linear functions and linear equations, and students' ability to use them to solve problems. Empirically validated learning trajectories will support curriculum development in these areas. In addition, this project contributes to the research base to improve the curriculum standards by providing empirical evidence for hypothesized trajectories for selected content standards for middle school students. Finally, the use of CMP2 augmented by the online management system increases the probability of widespread impact of the professional development model targeted at teachers' formative assessment practices. Although we are using a specific curriculum program, the treatment of linear functions and equations topics in CMP is consistent with other functions-based curricula in the U.S. Thus, the work done in the context of this project will be useful in examining learning trajectories and formative assessment in other instructional programs.
