Error Patterns in Computation : Using Error Patterns to Improve Instruction

This book is the only one of its kind that instructs teachers to identify typical error patterns, to receive feedback on their diagnosis, and to gain insight regarding why a child may have adopted an incorrect procedure. Revised to link content to the new NCTM Standards, this new edition emphasizes the meaning of operations and using the appropriate method of computation. As in previous editions, it retains its focus on placing paper-and pencil instructional activities within the context of problem solving. Chapter topics cover diagnosing misconceptions and error patterns in computation, providing needed instruction in computation, and helping students who have learned error patterns. For mathematics teachers of special education classes or at the middle school level.

We want to help oar students learn to think mathematically. Mere skill in computing is not our primary concern. Even so, computation in its many forms--using estimation, mental computation, calculators and computers, and paper-and-pencil procedures--continues to have a significant role in both the learning of mathematics and in solving problems within the world around us. This is made clear inPrinciples and Standards for School Mathematics,published by the National Council of Teachers of Mathematics in 2000. We hope all of our students will understand what they study. We want them to succeed in mathematics and to enjoy solving problems--but students sometimes learn misconceptions. As they learn about operations and methods of computation, they sometimes adopt erroneous procedures in spite of our best efforts. This book was written for those who are willing to listen carefully to what each student says and to make thoughtful analyses of student papers--teachers who want to help each student by discovering error patterns they may be using, and to be enabled, thereby, to focus instruction more effectively. This book was written to help teachers, whatever the level, to look at all student work diagnostically. Error Patterns in Computationhas changed greatly through the years. The first 96 pages of this edition are devoted to instructional issues. These pages provide help with diagnosing misconceptions and error patterns in computation, and they present many ideas for teaching varied methods of computation. Much of the book focuses on detecting the systematic errors many students make when computing with paper and pencil. Reasons students may have learned erroneous procedures are considered, and strategies for helping those students are presented. Of course, many of the instructional strategies described are useful when teaching any student--whether that student has experienced difficulty under previous instruction or not. The erroneous patterns displayed by students are not due to carelessness alone, nor are they due to insufficient practice. Students observe patterns and make inferences during instruction. In the case of an error pattern, that which has been learned does not always produce correct answers. Interestingly, some incorrect procedures produce correct answers part of the time. When this happens, students are reinforced in their belief that they have learned the desired concepts and skills. You will find looking for error patterns to be a very worthwhile assessment activity. You will gain more specific knowledge of each student's strengths upon which to base future instruction. Whenever you observe error patterns in your own classroom, be sure to refrain from assigning practice activities that reinforce incorrect concepts and procedures. THE EIGHTH EDITION This edition reflects many of the concerns of NCTM'sPrinciples and Standards for School Mathematics,including emphasis on concepts as well as skills. In this edition: Understanding the meanings of operations is emphasized, as is knowing when to use each operation. Computation, by whatever method, is distinguished from the operation itself. Different methods of computation are presented with an emphasis on using each method when appropriate. Paper-and-pencil procedures are considered in the context of other methods of computation. Many error patterns are presented within problem-solving contexts. Varied means of assessment are described and illustrated; self-assessment is emphasized. Extensive material on interviewing is included. Instruction in computation is addressed extensively through topics such as: - Concepts and principles - Understanding operations - Computational fluency - Mental computation, estimation, using calculators - Paper-and-pencil