Error Patterns in Computation: Using Error Patterns to Help Each Student Learn (10th Edition)

Product Description

“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.

Features

• Emphasizes assessment and the role of diagnosis within formative assessment.
• Provides guidance and resources for assessing and interviewing students.
• Incorporates students’ papers in which readers identify patterns of responses and compare their instructional recommendations with those of the author.
• Readers also practice identifying misconceptions and error patterns.
• Focuses on concepts and principles.
• Allows an instructor to teach computation in accordance with the NCTM Standards.
• Gives students an understanding of the meanings of operations and not just methods of computation.
• Enables students to know when particular operations are needed for solving a problem.
• Retains its emphasis on computational fluency.
• Stresses estimation and the best computing choice (mental computation, paper-and-pencil, calculator) in specific scenarios.
• Stresses estimation.
• Encourages readers to ask their students, “Is it reasonable?”
• Provides current strategies.
• Examines models and concrete materials, graphic organizers, self-assessment, portfolios, peer tutoring, and cooperative groups used when teaching computation.
• Incorporates reader recommendations that increase the text’s user-friendly and pragmatic appeal.
• NEW! Gives new emphasis to diagnosis as a part of formative assessment--Teachers can use varied approaches to diagnosis before instruction and also as they intervene during instruction.
• Open-ended assessment and problem writing are examples of procedures illustrated.
• NEW! Supplies more coverage of making connections among facts, procedures, and concepts–Will help teachers and students make connections by applying big ideas.
• Compensation principles, relations between operations, and “There are many names for a number” are examples.
• NEW! Furnishes a distinction between misconceptions and error patterns in computation–Encourages teachers to focus on concept development when appropriate rather than merely reviewing procedures.
• NEW! Offers an increased understanding of our system of numeration–Provides additional material that enables teachers to diagnose understanding of multi-digit numerals at a deeper level.
• NEW! Helps teachers and students to better understand the meanings of operations--additional material is provided to help teachers and students understand the operations of arithmetic so they will know when to use each operation when solving problems.
• NEW! Provides greater emphasis on representations--Teachers are instructed to represent concepts and procedures in a variety of ways.
• NEW! Includes a new section on using classroom discourse--Teachers listen carefully to classroom discourse and then ask questions that probe and guide thinking.
• NEW! Features a new focus on dispositions–Helps teachers to assess disposition.
• NEW! Incorporates a new section illustrating a thematic unit in mathematics--Enables teachers to plan varied instruction that involves connections with other mathematics and numerous applications.

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