"Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge." From the Principles for School Mathematics of NCTM standards, copyright NCTM 2000-2004. Yet sometimes when students are learning mathematics, they learn misconceptions and adopt erroneous procedures despite the best efforts of their teacher. This book was written to help teachers to detect the systematic errors many students make-whether using paper and pencil, or calculators or computers. Emphasizing concepts and skills, in accordance with the NCTM standards, this readable and engaging supplementary text will help all teachers of math methods to become more proficient at diagnosing and correcting computational procedures. Teachers will gain skills by actually looking for error patterns, making decisions, and planning instruction. The book is organized into two parts with appendices. The first part is mainly devoted to instructional issues and considers the place of computation in today's world of technology and then focuses on various aspects of assessment and instruction for both concepts and skills. Part Two presents sample student papers within topical chapters. These papers provide opportunities to identify patterns of error and to reflect on the best course of corrective instruction. Readers can then compare their responses with those of the author. The appendices provide additional papers for even more practice in identifying error patterns. New To This Edition: * NEW! Gives greater emphasis on diagnosis as a part of formative assessment.* NEW! Includes more material on understanding the meanings of operations to help teachers and students understand the operations of arithmetic so they will know when to use each operation when solving problems. * NEW! Enables teachers to plan varied instruction that involves connections with other mathematics and varied applications.