Expanding the CBAL™ Mathematics Assessments to Elementary Grades: The Development of a Competency Model and a Rational Number Learning Progression

Abstract

Prior work on the CBAL™ mathematics competency model resulted in an initial competency model for middle school grades with several learning progressions (LPs) that elaborate central ideas in the competency model and provide a basis for connecting summative and formative assessment. In the current project, we created a competency model for Grades 3–5 that is based on both the middle school competency model and the Common Core State Standards (CCSS). We also developed an LP for rational numbers based on an extensive literature review, consultations with members of the CBAL mathematics team and other related research staff at Educational Testing Service, input from an advisory panel of external experts in mathematics education and cognitive psychology, and the use of small-scale cognitive interviews with students and teachers. Elementary mathematical understanding, specifically that of rational numbers, is viewed as fundamental and critical to developing future knowledge and skill in middle and high school mathematics and therefore essential for success in the 21st century world. The competency model and the rational number LP serve as the conceptual basis for developing and connecting summative and formative assessment as well as professional support materials for Grades 3–5. We report here on the development process of these models and future implications for task development.