This book was written to give teachers the tools they need to help students go from believing they "can't do math" to achieving real success and gaining confidence in their math skills. This can be accomplished if parents and teachers, instead of trying the same thing over and over again, focus on how their students learn best. To do this, the authors present a systematic, three-step approach on how to assess student's strengths and weaknesses and then plan instruction accordingly. The three-step plan involves: 1. Creating a Data Analysis Sheet (DAS) 2. Considering the learners' strengths and areas of concern 3. Completing a Mathematics Improvement Plan (MIP) Each chapter deals with a different mathematical topic-place value, problem solving, fractions, addition, subtraction, division, decimals, time and money, etc. A number of errors by a variety of students are described using a case study of a "typical" struggling student. The text then explains how teachers can systematically assess the student's work and appropriately diagnose their problems.
By analyzing and understanding why and how their students make errors, teachers can design appropriate ways to correct their mistakes and then promote long-term learning through repetition and practice that is meaningful to them. This book addresses mathematics education in a manner that encourages positive content growth and attitude for both teachers and students.
Table of Contents
1. The Dissimilar Learner and Mathematics Instruction A Problem and a Solution The Learner-Centered Approach Why Do Students Struggle with Mathematics? How Is Mathematics Taught Effectively for All Students? 2. Place Value The Impact of Place Value on Mathematics Why Do Students Struggle with Place Value? Error Patterns: Diagnosis, Prescription, Remediation 3. Addition of Whole Numbers What Is Addition? What Should Students Understand About Addition? About the Student: Ian Error Patterns: Diagnosis, Prescription, Remediation 4. Subtraction of Whole Numbers What Is Subtraction? What Should Students Understand About Subtraction? About the Student: Caitlin Error Patterns: Diagnosis, Prescription, Remediation 5. Multiplication What Is Multiplication? What Should Students Understand About Multiplication? About the Student: Alberto Error Patterns: Diagnosis, Prescription, Remediation 6. Division What Is Division? What Should Students Understand About Division? About the Student: Marie Error Patterns: Diagnosis, Prescription, Remediation 7. Rational Numbers What Are Rational Numbers? Why Do Students Struggle with Rational Numbers? About the Student: Tawana Error Patterns: Diagnosis, Prescription, Remediation 8. Decimal Fractions What Are Decimals? Why Do Students Struggle with Decimals? About the Student: Jose' Error Patterns: Diagnosis, Prescription, Remediation 9. Problem Solving What Is Problem Solving? Why Do Students Struggle with Solving Problems? Improving Students' Problem-Solving Ability Learning to Solve Problems Suggested Lesson Plan Structure 10. Time and Money Time and Money as Measurement Topics Why Do Students Struggle with Learning About Time and Money? About the Student: Sarah Error Patterns: Diagnosis, Prescription, Remediation Appendix A Sample DAS and MIP Tables Appendix B Suggestions for Planning Academic Content Lessons Index