Focusing on addition and subtraction in this volume of the series, Battista (mathematics education, Ohio State U.) details the cognition-based assessment (CBA) framework, which can be used with any curriculum and enables all elementary students to understand, make sense of, and become proficient in math. It focuses on deep understanding and reasoning within the context of continual assessment and understanding students' mathematical thinking, then building on that thinking instructionally (rather than teaching fixed content) and focusing on maximizing individual progress. He provides research-based descriptions of students' development of meaning for core ideas and reasoning processes in elementary math, including details on cognitive obstacles they face and fundamental mental processes; assessments that determine students' reasoning at various levels of sophistication; and descriptions of differentiated instructional activities. The book is one of six on the approach and can be used with the tiers of response to intervention. Student work samples and assessment tasks are integrated. There is no index. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com)