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

PrefaceDeveloping Strategic Competence through Modeling Mathematical IdeasDEVELOPING STRATEGIC COMPETENCE THROUGH MODELING MATHEMATICAL IDEASPROMOTING MATHEMATICAL PROFICIENCY AND PRACTICESPROBLEM SOLVING AND MATHEMATICAL MODELING IN THE ELEMENTARY AND MIDDLE GRADESMULTIPLE REPRESENTATIONS AND STRATEGIES AS TOOLS TO CULTIVATE VISIBLE THINKING IN MATHEMATICSIMPORTANCE OF UNDERSTANDING THE VERTICAL LEARNING PRoGRESSIoN To Deepen STuDENTS' mathematical understanding of conceptual modelsTECHNOLOGY INTEGRATION IN PROBLEM SOLVINGMORE RELATED RICH PROBLEMS TO EXPLORESetting Math Norms to Promote Math Reasoning and ModelingDEVELOPING PERSISTENT PROBLEM SOLVERS WITH a productive disposition toward mathematicsUNPACKING THE MATHEMATICS FOR DEEPER CONCEPTUAL LEARNING-CONCEPT MAPPINGCHOOSING WORTHWHILE TASKS THROUGH COGNITIVE DEMAND ANALYSISPROMOTING EFFECTIVE TEACHING PRACTICES TO OPTIMIZE THE LEARNING ENVIRONMENTINTEGRATION TECHNOLOGY TO MOTIVATE AND DIFFERENTIATE LEARNINGASSESSING STUDENTS UNDERSTANDING THROUGH A PROBLEM-BASED TASKEngaging in Mathematical Modeling in the Elementary and Middle GradesMATHEMATICAL MODELING IN THE ELEMENTARY AND MIDDLE Grades: wHAT Are The BuILDING BLoCKS?MATHEMATICAL MODELING THROUGH UNSTRUCTURED REAL-WORLD PROBLEMSOrganizing a table tennis tournament (Unstructured problem from PRIMAS)LESSON STUDY FOCUSED ON MATHEMATICAL MODELING: TRAFFIC-JAM TASKPROMOTING THE TWENTY-FIRST-CENTURY SKILLSTECHNOLOGY INTEGRATION IN PROBLEM POSING AND PROBLEM SOLVINGA RELATED RICH PROBLEM TO EXPLOREUnderstanding Numbers and OperationsLESSON STUDY VIGNETTE: PRIME AND COMPOSITE NUMBERSVISIBLE THINKING IN MATH: USING MULTIPLE REPRESENTATIONS AS RECORDS of students' strategic thinkingZOOMING IN ON THE LEARNING PROGRESSION Of NUMBERS AND OPERATIONSTEACHING STRATEGIES: USING MATH HAPPENINGS TO SHOWCASE REAL-WORLD MATHEMATICS APPLICATIONSCONNECTING PROCEDURAL FLUENCY AND CONCEPTUAL UNDERSTANDINGTECHNOLOGY INTEGRATION IN PROBLEM SOLVINGMORE RELATED RICH PROBLEMS TO EXPLOREModeling Math Ideas with Patterns and Algebraic ReasoningLESSON STUDY VIGNETTE-GROWING STAIRCASE PROBLEMVISIBLE THINKING IN MATH: USING A MODELING MATH MATPATTERNS AND ALGEBRA: ZOOMING IN ON THE LEARNING PROGRESSIONSTEACHING STRATEGIES: PROMOTING THE ALGEBRAIC HABITS Of MINDLESSON VIGNETTE: WHAT WOULD YOU CHOOSE? ANALYZING CHANGE IN NUMBER PATTERNSTECHNOLOGY INTEGRATION IN PROBLEM SOLVINGMORE RELATED RICH PROBLEMS TO EXPLOREExtending the Mathematical Learning Progressions for Expressions and Equationslesson study vIGNETTE: SETTING A MATH learning agendaZOOMING IN ON THE LEARNING PROGRESSIONS FOR ALGEBRAVISIBLE THINKING IN MATH: NAMING, SEQUENCING, AND CONNECTING Math StrategiesTEACHING STRATEGIES: USING MISCONCEPTIONS TO REPAIR UNDERSTANDING AND LOOKING FOR EFFICIENCYTECHNOLOGY INTEGRATION IN PROBLEM SOLVINGMORE RELATED RICH PROBLEMS TO EXPLOREDeveloping Fraction SenseLESSON STUDY VIGNETTE: THE UNUSUAL BAKERVISIBLE THINKING IN MATH: ASSESSING STUDENT LEARNING THROUGH CLASSROOM ARTIFACTSZOOMING IN ON THE LEARNING PROGRESSIONS: FRACTIONSIMPLEMENTING MATHEMATICAL TASKS THAT PROMOTE REASONING AND PROBLEM SOLVINGTEACHING STRATEGIES, USING REPRESENTATIONS, AND OVERCOMING COMMON MISCONCEPTIONTECHNOLOGY INTEGRATION IN PROBLEM SOLVINGMORE RELATED RICH PROBLEMS TO EXPLOREModeling Operations with FractionsLESSON STUDY VIGNETTE: STUFFED WITH PIZZA-ADDING FRACTIONSVISIBLE LEARNING IN MATH-USING TOOLS TO PROVE THEIR THINKINGLEARNING PROGRESSION IN FRACTION OPERATIONS— ZOOMING IN ON MULTIPLYING AND DIVIDING FRACTIONSLESSON STUDY VIGNETTE: SHARE MY CANDYTEACHING STRATEGIES: STRATEGY MAPPING ON THE BOARD PLANUSE OF STUDENTS' DIVERSITY Of STRATEGIES AS PEDAGOGICAL CONTENT TOOLSTECHNOLOGY INTEGRATION IN PROBLEM SOLVINGMORE RELATED RICH PROBLEMS TO EXPLOREModeling Math Ideas with Ratio and Proportional ReasoningLESSON STUDY VIGNETTE: THE LEAKY BATHTUBZOOMING IN ON THE LEARNING PROGRESSIONS ON PROPORTIONAL REASONINGVISIBLE THINKING IN MATH: USING REPRESENTATIONAL MODELS For PRopoRTIoNAL REASoNINGLESSON STUDY VIGNETTE: THE CATHEDRAL PROBLEMDEEPENING TEACHER KNOWLEDGE AND THEIR STRATEGIC COMPETENCEPROMOTING REASONING TO RICH TASKSTECHNOLOGY INTEGRATION IN PROBLEM SOLVINGMORE RELATED RICH PROBLEMS TO EXPLOREPulling it All TogetherPRACTICE-BASED ACTIVITIES TO FOCUS ONMODELING MATH WITH TOOLS AND REPRESENTATIONS TO STRENGTHEN STRATEGIC COMPETENCEUNDERSTANDING CONCEPTUAL AND INTERPRETATIVE Models Of Math IDEAS TO STRENGTHEN STRATEGIC COMPETENCEMODELING MATH THROUGH PROBLEM SOLVING to strengthen strategic competenceposing tasks lor mathematical modeling through UNSTRUCTURED REAL-WoRLD PRoBLEMS to strengthen strategic competenceSTRENGTHENING STRATEGIC COMPETENCE FOR MODELING MATHEMATICAL IDEAS