Are you having trouble in finding Tier II intervention materials for elementary students who are struggling in math? Are you hungry for effective instructional strategies that will address students' conceptual gap in additive and multiplicative math problem solving? Are you searching for a powerful and generalizable problem solving approach that will help those who are left behind in meeting the Common Core State Standards for Mathematics (CCSSM)? If so, this book is the answer for you. . The conceptual model-based problem solving (COMPS) program emphasizes mathematical modeling and algebraic representation of mathematical relations in equations, which are in line with the new Common Core. . "Through building most fundamental concepts pertinent to additive and multiplicative reasoning and making the connection between concrete and abstract modeling, students were prepared to go above and beyond concrete level of operation and be able to use mathematical models to solve more complex real-world problems. As the connection is made between the concrete model (or students' existing knowledge scheme) and the symbolic mathematical algorithm, the abstract mathematical models are no longer "alien" to the students." As Ms. Karen Combs, Director of Elementary Education of Lafayette School Corporation in Indiana, testified: "It really worked with our kids!" . "One hallmark of mathematical understanding is the ability to justify,... why a particular mathematical statement is true or where a mathematical rule comes from" (http://illustrativemathematics.org/standards). Through making connections between mathematical ideas, the COMPS program makes explicit the reasoning behind math, which has the potential to promote a powerful transfer of knowledge by applying the learned conception to solve other problems in new contexts. . Dr. Yan Ping Xin's book contains essential tools for teachers to help students with learning disabilities or difficulties close the gap in mathematics word problem solving. I have witnessed many struggling students use these strategies to solve word problems and gain confidence as learners of mathematics. This book is a valuable resource for general and special education teachers of mathematics. - Casey Hord, PhD, University of Cincinnati
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Acknowledgements; About the Author; 1. Conceptual Model-based Problem Solving: Teach Students with Learning Diffi culties to Solve Math Problems Introduction; Algebra Thinking in Problem Solving; Mathematical Modeling; Theoretical Framework: Conceptual Model-based Problem Solving; SBI that Emphasizes Semantic Analyses and Representation of the Problem; COMPS that Emphasizes Algebraic Expression of Mathematical Relations; Summary; Program Components; The scope and sequence of the program; Target Audience and Users of the Program; 2. COMPS Program Introduction; Singapore Bar Models (SBM) to Facilitate the Transition to Mathematical Models; Word Problem [WP] Story Grammar (Xin et al., 2008); A Cognitive Heuristic DOTS Checklist (Xin et al., 2008); Additive and Multiplicative Word Problem Structure and its Variations; Instructional Phases; Part 1: Additive Problem Solving; Unit 1: Representing Part-Part-Whole (PPW) Problems; Lesson 1: Introduction; Lesson 2: Part-Part-Whole Problem Representation; Unit 2: Solving Part-Part Whole (PPW) Problems; Lesson 3: Solving PPW Problems; Unit 3: Representing Additive Compare (AC) Problems; Lesson 4: Representing AC-More Problems; Lesson 5: Representing AC-Less Problems; Unit 4: Solving Additive Compare (AC) Problems; Lesson 6: Solving Mixed AC Problems; Unit 5: Solving Mixed PPW and AC Problems; Lesson 7: Solving mixed PPW and AC Problems; Part 2: Multiplicative Problem Representation and Solving; Unit 6: Representing Equal Groups (EG) Problems; Unit 7: Solving Equal Groups (EG) Problems; Unit 8: Representing Multiplicative Compare (MC) Problems; Unit 9: Solving Multiplicative Compare (MC) Problems; Unit 10: Solving Mixed Equal Groups and Multiplicative Compare Problems; Part 3: Solving Complex Problems; Unit 11: Solving Complex Word Problems; Unit 12: Solving Mixed Multi-Step Problems; 3 Connection between Mathematical Ideas: Extend Multiplicative Reasoning to Geometry Learning; Appendix A: Student Worksheets; Appendix B: Reference Guide; References.