Modeling mathematical ideas: developing strategic competence in elementary and middle school - Modeling mathematical ideas: developing strategic competence in elementary and middle school -

Preface Developing Strategic Competence through Modeling Mathematical Ideas DEVELOPING STRATEGIC COMPETENCE THROUGH MODELING MATHEMATICAL IDEAS PROMOTING MATHEMATICAL PROFICIENCY AND PRACTICES PROBLEM SOLVING AND MATHEMATICAL MODELING IN THE ELEMENTARY AND MIDDLE GRADES MULTIPLE REPRESENTATIONS AND STRATEGIES AS TOOLS TO CULTIVATE VISIBLE THINKING IN MATHEMATICS IMPORTANCE OF UNDERSTANDING THE VERTICAL LEARNING PRoGRESSIoN To Deepen STuDENTS' mathematical understanding of conceptual models TECHNOLOGY INTEGRATION IN PROBLEM SOLVING MORE RELATED RICH PROBLEMS TO EXPLORE Setting Math Norms to Promote Math Reasoning and Modeling DEVELOPING PERSISTENT PROBLEM SOLVERS WITH a productive disposition toward mathematics UNPACKING THE MATHEMATICS FOR DEEPER CONCEPTUAL LEARNING-CONCEPT MAPPING CHOOSING WORTHWHILE TASKS THROUGH COGNITIVE DEMAND ANALYSIS PROMOTING EFFECTIVE TEACHING PRACTICES TO OPTIMIZE THE LEARNING ENVIRONMENT INTEGRATION TECHNOLOGY TO MOTIVATE AND DIFFERENTIATE LEARNING ASSESSING STUDENTS UNDERSTANDING THROUGH A PROBLEM-BASED TASK Engaging in Mathematical Modeling in the Elementary and Middle Grades MATHEMATICAL MODELING IN THE ELEMENTARY AND MIDDLE Grades: wHAT Are The BuILDING BLoCKS?MATHEMATICAL MODELING THROUGH UNSTRUCTURED REAL-WORLD PROBLEMS Organizing a table tennis tournament (Unstructured problem from PRIMAS)LESSON STUDY FOCUSED ON MATHEMATICAL MODELING: TRAFFIC-JAM TASK PROMOTING THE TWENTY-FIRST-CENTURY SKILLS TECHNOLOGY INTEGRATION IN PROBLEM POSING AND PROBLEM SOLVING A RELATED RICH PROBLEM TO EXPLORE Understanding Numbers and Operations LESSON STUDY VIGNETTE: PRIME AND COMPOSITE NUMBERS VISIBLE THINKING IN MATH: USING MULTIPLE REPRESENTATIONS AS RECORDS of students' strategic thinking ZOOMING IN ON THE LEARNING PROGRESSION Of NUMBERS AND OPERATIONS TEACHING STRATEGIES: USING MATH HAPPENINGS TO SHOWCASE REAL-WORLD MATHEMATICS APPLICATIONS CONNECTING PROCEDURAL FLUENCY AND CONCEPTUAL UNDERSTANDING TECHNOLOGY INTEGRATION IN PROBLEM SOLVING MORE RELATED RICH PROBLEMS TO EXPLORE Modeling Math Ideas with Patterns and Algebraic Reasoning LESSON STUDY VIGNETTE-GROWING STAIRCASE PROBLEM VISIBLE THINKING IN MATH: USING A MODELING MATH MAT PATTERNS AND ALGEBRA: ZOOMING IN ON THE LEARNING PROGRESSIONS TEACHING STRATEGIES: PROMOTING THE ALGEBRAIC HABITS Of MIND LESSON VIGNETTE: WHAT WOULD YOU CHOOSE? ANALYZING CHANGE IN NUMBER PATTERNS TECHNOLOGY INTEGRATION IN PROBLEM SOLVING MORE RELATED RICH PROBLEMS TO EXPLORE Extending the Mathematical Learning Progressions for Expressions and Equations lesson study vIGNETTE: SETTING A MATH learning agenda ZOOMING IN ON THE LEARNING PROGRESSIONS FOR ALGEBRA VISIBLE THINKING IN MATH: NAMING, SEQUENCING, AND CONNECTING Math Strategies TEACHING STRATEGIES: USING MISCONCEPTIONS TO REPAIR UNDERSTANDING AND LOOKING FOR EFFICIENCY TECHNOLOGY INTEGRATION IN PROBLEM SOLVING MORE RELATED RICH PROBLEMS TO EXPLORE Developing Fraction Sense LESSON STUDY VIGNETTE: THE UNUSUAL BAKER VISIBLE THINKING IN MATH: ASSESSING STUDENT LEARNING THROUGH CLASSROOM ARTIFACTS ZOOMING IN ON THE LEARNING PROGRESSIONS: FRACTIONS IMPLEMENTING MATHEMATICAL TASKS THAT PROMOTE REASONING AND PROBLEM SOLVING TEACHING STRATEGIES, USING REPRESENTATIONS, AND OVERCOMING COMMON MISCONCEPTION TECHNOLOGY INTEGRATION IN PROBLEM SOLVING MORE RELATED RICH PROBLEMS TO EXPLORE Modeling Operations with Fractions LESSON STUDY VIGNETTE: STUFFED WITH PIZZA-ADDING FRACTIONS VISIBLE LEARNING IN MATH-USING TOOLS TO PROVE THEIR THINKING LEARNING PROGRESSION IN FRACTION OPERATIONS— ZOOMING IN ON MULTIPLYING AND DIVIDING FRACTIONS LESSON STUDY VIGNETTE: SHARE MY CANDY TEACHING STRATEGIES: STRATEGY MAPPING ON THE BOARD PLAN USE OF STUDENTS' DIVERSITY Of STRATEGIES AS PEDAGOGICAL CONTENT TOOLS TECHNOLOGY INTEGRATION IN PROBLEM SOLVING MORE RELATED RICH PROBLEMS TO EXPLORE Modeling Math Ideas with Ratio and Proportional Reasoning LESSON STUDY VIGNETTE: THE LEAKY BATHTUB ZOOMING IN ON THE LEARNING PROGRESSIONS ON PROPORTIONAL REASONING VISIBLE THINKING IN MATH: USING REPRESENTATIONAL MODELS For PRopoRTIoNAL REASoNING LESSON STUDY VIGNETTE: THE CATHEDRAL PROBLEM DEEPENING TEACHER KNOWLEDGE AND THEIR STRATEGIC COMPETENCE PROMOTING REASONING TO RICH TASKS TECHNOLOGY INTEGRATION IN PROBLEM SOLVING MORE RELATED RICH PROBLEMS TO EXPLORE Pulling it All Together PRACTICE-BASED ACTIVITIES TO FOCUS ON MODELING MATH WITH TOOLS AND REPRESENTATIONS TO STRENGTHEN STRATEGIC COMPETENCE UNDERSTANDING CONCEPTUAL AND INTERPRETATIVE Models Of Math IDEAS TO STRENGTHEN STRATEGIC COMPETENCE MODELING MATH THROUGH PROBLEM SOLVING to strengthen strategic competence posing tasks lor mathematical modeling through UNSTRUCTURED REAL-WoRLD PRoBLEMS to strengthen strategic competence STRENGTHENING STRATEGIC COMPETENCE FOR MODELING MATHEMATICAL IDEAS