Battista (mathematics education, Ohio State U.) explains cognition-based assessment (CBA), a framework to support teaching and enable all students to understand, make sense of, and become proficient in math. The approach focuses on deep understanding and reasoning within the context of continual assessment and understanding students' mathematical thinking, then building on that thinking with instruction, instead of teaching fixed content, with a focus on maximizing individual progress. It emphasizes research-based descriptions of students' development of meaning for core ideas and reasoning processes in elementary math, including understanding cognitive obstacles and basic mental processes; assessments of students' reasoning; and differentiated instruction activities. The book is one of six volumes on CBA and focuses on place value; it can be used with response to intervention tiers. Student work samples and assessment tasks are included. There is no index. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com)