Battista (mathematics education, Ohio State U.) outlines a cognition-based, needs-sensitive framework to use with any curriculum to support teaching that allows all students to understand, make sense of, and become proficient in elementary-level math, with an emphasis on geometric shapes in this volume. The assessment method focuses on deep understanding and reasoning within the context of continually assessing and understanding students' mathematical thinking, and building on that thinking with instruction, instead of teaching predetermined, fixed content. He describes research on students' development of meaning for core ideas and reasoning processes in learning geometric shapes, assessments that determine how they are reasoning about these ideas, and differentiated instructional activities to help them at each level of reasoning. Student work examples are included. There is no index. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com)