Mapping Skills and Knowledge in the Connected Mathematics Project 2 Curriculum

• In Event: Bridging Research and Practice: Findings From the National Center on Cognition and Mathematics Instruction

Abstract

This poster describes an analysis of the distribution of mathematical knowledge and skill within a widely implemented middle school mathematics program, Connected Mathematics Project 2 (CMP2). The goal was to map out in detail the concepts and skills targeted in the CMP curriculum to determine how knowledge and skills are distributed within units, across units, and across grades. Knowledge components consisted of four elements: skills, context, procedures, and responses. This mapping was applied to all Connected Mathematics Project (CMP) homework and assessment problems in the entire sixth and seventh grade and selected eighth grade units. Through this analysis we were able to ascertain where certain mathematical content is introduced, the practice frequency of specific skills, and the relationship between practice and test items. This analysis was important for the redesigned curriculum materials as well as in determining the types of mathematical problem sets to include in empirical studies. For example, from the curriculum mapping information, we modified teacher materials to include more elaborated information about the skills expected to already be mastered before the start of the particular unit, including all homework items in the upcoming unit where those previously mastered skills appear, in what prior unit the skill was expected to be mastered (according to CMP), a prototypical example of how each skill appeared in the mastered unit, and practice problems for each skill from the Additional Practice and Skills Workbook. Additionally, a tool for assessment of these prior skills, drawn from selected problems in the Additional Practice and Skills Workbook, was included.

The curriculum analysis supports the need for empirical studies to determine optimal patterns of the practice and assessment of specific skills, including whether skills varying in complexity and difficulty require differential practice and assessment plans to maximize student mastery and retention. However, implementing spaced practice over time for a variety of skills across a large number of students and providing an appropriate level of formative assessment is a complex task. In order to redesign the learning environment to better incorporate spaced practice and formative assessment, we utilized a web-based technology capable of tracing individual student performance across skills and time. ASSISTments (Feng, Heffernan, Koedinger, 2009). is a domain-general web-based system that allowed us to create individual practice and assessment assignments, composed of questions with associated hints and solutions. The combination of ASSISTments with our mapping of skills across the CMP curriculum enables individualized practice on specific skills based on student performance and allows improvement of students’ mathematical performance using the principles of spacing and formative assessment. Practical and theoretical implications, such as how such analyses can be applied to other curricula, will be discussed.

Authors

• Deena Soffer Goldstein, University of Illinois at Chicago

• Cristina Heffernan, Worcester Polytechnic Institute

• Neil T. Heffernan, Worcester Polytechnic Institute

• James W. Pellegrino, University of Illinois at Chicago

• Susan R. Goldman, University of Illinois at Chicago

• Timothy Matthew Stoelinga, University of Illinois at Chicago