Contents
Foreword James W. Stigler?xi
Acknowledgments?xiii
Introduction?1
Part I: Understanding the Approach
1.?Thinking Differently About Teaching and Learning?9
What It Looks Like in a Real Classroom?9
Why This Book??12
2.?Engineering Design, Mathematics, Science, and Literacy?17
A Visual Model of Our Approach?18
The Design Process: Dynamic, Iterative Waves of Divergent and Convergent Thinking?19
Integrating Mathematical Modeling, Scientific Challenges, and Literacy Practices?24
3.?Affordances and Supports?29
Supporting Productive Struggle by Learners?30
Promoting Equity in the Classroom?32
Complex Instruction?33
Reflective Teaching Practice?36
Leveraging the Design Process for Reflective Teaching?38
4. Why Do We Think This Works??41
Evidence-Based Teaching Practices?41
Evidence Base for Core Components of Our Approach?46
Evidence Base for Bringing It All Together?49
5.?Personifying Best Practices?53
(Re)Designing Industrial Farming in Your State?53
Connecting Theory to Practice?55
Part II: Making It Real
6.?Design and Mathematical Modeling?From Artifacts to Processes?63
Affordances for Systems-Level Learning Across the Artifact-to-Process Continuum?65
Returning to the Grocery Store?70
7.?How Constraints and Criteria Affect Design and Mathematical Modeling?73
How Many Marbles Can You Fit in a Piece of Aluminum Foil Before It Sinks??74
Keeping a Cold Drink Cold for Longer (Co-Constructing Constraints)?74
8.?Scaffolding Student Learning in Design and Mathematical Modeling?79
Productive Struggle in Design-Based Learning?80
Scaffolding Productive Struggle?82
Strategically Using Formative Assessment Data?85
Giving Students Voice in Design Constraints, Criteria, and Methods of Assessment?87
9.?Design and Mathematical Modeling Across Content Areas and Grade Levels?91
Gingerbread-House Lesson (6th-Grade Mathematics Class)?91
Predator/Prey Lesson (8th-Grade Science Class)?95
Skater-Ramp Lesson (7th-Grade Mathematics and Science Class)?98
Adapting Design-Based Learning Activities to Your Students?101
10.?Design and Mathematical Modeling Across Instructional Modalities?105
Taking Design-Based Learning Online?106
Examples of Design-Based Learning at a Distance?108
Connecting Examples to Core Components, Affordances, and Supports?111
Part III: Making It Your Own
11.?Linking an Integrative Series of Design and Mathematical Modeling Activities?115
Problem-Based, Design-Based, and Project-Based Integration?115
Energy and the Environment Thematic Unit?117
Pulling It All Together?122
12.?Address Any Content Standard and ÒFixÓ Textbook Problems?123
Starting From Standards?123
Starting From Existing Activities or Problems?127
(Re)Designing Effective Teaching Practices?131
Conclusion: The Wicked Problem of Education for All?133
References?135
Index?143
About the Authors?147
