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| Preface | p. ix |
| Introduction | p. 1 |
| Defining Algebraic Thinking and an Algebra Curriculum | p. 3 |
| Defining Algebraic Thinking | p. 5 |
| "Doing Algebra in Grades K-4" | p. 5 |
| "Conceptions of School Algebra and Uses of Variables" | p. 7 |
| "Communicating the Importance of Algebra to Students" | p. 14 |
| Analyzing Algebra Curriculum | p. 22 |
| "Why Is Algebra Important to Learn?" | p. 22 |
| "Algebra: What Should We Teach and How Should We Teach It?" | p. 31 |
| "Why Elementary Algebra Can, Should, and Must be an Eighth-Grade Course for Average Students" | p. 40 |
| "Does Everybody Need to Study Algebra?" | p. 49 |
| "The Transition from Arithmetic to Algebra" | p. 52 |
| "Prealgebra: The Transition from Arithmetic to Algebra" | p. 59 |
| "Procedures for, and Experiences in, Introducing Algebra in New South Wales" | p. 71 |
| "What Should Not Be in the Algebra Curriculum of Average College-Bound Students" | p. 76 |
| "A Technology-Intensive Approach to Algebra" | p. 82 |
| "Revitalizing First-Year Algebra through Problem Solving with HALP" | p. 90 |
| Classroom Activities | p. 97 |
| Central Concepts | |
| Patterns | |
| "Literature and Algebraic Reasoning" | p. 99 |
| "What Comes Nex_?" | p. 106 |
| "Experiences with Patterning" | p. 112 |
| "Perimeter Patterns" | p. 120 |
| "Patterns as Tools for Algebraic Reasoning" | p. 123 |
| "Liz's Pattern" | p. 129 |
| "Teaching Patterns, Relationships, and Multiplication as Worthwhile Mathematical Tasks" | p. 133 |
| "Marcy's Dot Pattern" | p. 137 |
| "Introducing the Variable through Pattern Exploration" | p. 140 |
| "(Naturally) Numbers Are Fun" | p. 146 |
| Variables, Expressions, and Equations | |
| "On the Meaning of Variable" | p. 150 |
| "The Many Uses of Algebraic Variables" | p. 157 |
| "Teaching Informal Algebra" | p. 163 |
| "Teaching Algebraic Expressions in a Meaningful Way" | p. 168 |
| "Building Algebraic Expressions: A Physical Model" | p. 175 |
| "Constructing Meaning for the Concept of Equation" | p. 181 |
| "Algebra Can Be Elementary ... When It's Concrete" | p. 189 |
| "Building Equations Using MandM's" | p. 194 |
| Functions | |
| "Functions from Kindergarten through Sixth Grade" | p. 197 |
| "Algebra: Real-Life Investigations in a Lab Setting" | p. 202 |
| "Building the Concept of Function from Students' Everyday Activities" | p. 206 |
| "A Function Is a Mail Carrier" | p. 213 |
| Multiple Representations | |
| "Equivalent Representations in the Learning of Algebra" | p. 215 |
| "When Does a Dog Become Older Than Its Owner?" | p. 220 |
| "Multiple Representations and Connections Using Technology" | p. 225 |
| Technology | |
| "Spreadsheets, Patterns, and Algebraic Thinking" | p. 232 |
| "Using Spreadsheets to Promote Algebraic Thinking" | p. 238 |
| "Flower Beds and Landscape Consultants: Making Connections in Middle School Mathematics" | p. 247 |
| "An EXCELlent Bridge to Algebra" | p. 252 |
| "Technology, Linear Equations, and Buying A Car" | p. 255 |
| "Computers Support Algebraic Thinking" | p. 261 |
| "Solving Equations in a Technological Environment" | p. 268 |
| "Uses of Technology in Prealgebra and Beginning Algebra" | p. 275 |
| Assessment, Misconceptions, and Research Results | p. 281 |
| Assessment | |
| "Journals: Pathways to Thinking in Second-Year Algebra" | p. 282 |
| "The Write Way: A Look at Journal Writing in First-Year Algebra" | p. 286 |
| "Writing to Learn Algebra" | p. 291 |
| Misconceptions | |
| "Children's Difficulties in Beginning Algebra" | p. 299 |
| "Ideas about Symbolism That Students Bring to Algebra" | p. 308 |
| "Some Misconceptions concerning the Concept of Variable" | p. 313 |
| "What Are These Things Called Variables?" | p. 316 |
| "From Words to Algebra: Mending Misconceptions" | p. 321 |
| Research Issues | |
| "Advancing Algebra" | p. 328 |
| "The Learning and Teaching of School Algebra" | p. 341 |
| "An Agenda for Research on the Learning and Teaching of Algebra" | p. 362 |
| Professional Development | p. 373 |
| "Algebraic Thinking: A Theme for Professional Development" | p. 374 |
| "Algebra for Everyone: In-Service Training for Teachers" | p. 380 |
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