Enhancing Math Education: Key Strategies for Deeper Understanding and Problem Solving
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This program focuses on advancing mathematics education through three core ideas—deeper conceptual understanding, stronger procedural fluency, and greater emphasis on problem-solving. By reducing topics and increasing depth, students gain proficiency and the ability to apply mathematics effectively. Key instructional strategies like the Concrete-Pictorial-Abstract (CPA) model, visualization, and questioning help solidify understanding. Resources like Think Central and Holt McDougal Online support the curriculum, ensuring students are equipped to tackle mathematical challenges confidently.
Enhancing Math Education: Key Strategies for Deeper Understanding and Problem Solving
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Presentation Transcript
ETSD Mathematics Program: Big Ideas • Deeper conceptual understanding (making sense of math), fewer topics, greater depth; • Stronger procedural fluency (doing math), proficiency with math skills, facts and procedures; and • Greater emphasis on problem solving (using math), know how, why and when it works. Concepts Problem Solving Computation
Standards for Mathematical Practice • Make sense of problems and persevere in solving them. • Reason abstractly and quantitatively. • Construct viable arguments and critique the reasoning of others. • Model with mathematics. • Use appropriate tools strategically. • Attend to precision. • Look for and make use of structure. • Look for and express regularity in repeated reasoning.
Key Instructional Strategies • Concrete-Pictorial-Abstract Model (CPA) • Visualization • Making Connections • Questioning • Generalizing
Concrete->Pictorial->Abstract Tools • Ten Frames • Number Bonds • Base Ten Blocks • Place Value Disks • Number Balance
Integrating the CPA with Visualization x + 2x = 12
Bar Modeling A pictorial or diagram method of representing quantities and their relationships to solve both arithmetic and algebraic word problems. Student use rectangle blocks to represent the known and unknown: • Blocks are easily drawn and divided • Rectangles enable proportional representation and solving for the unit
Trajectory of Bar Modeling • Part/Whole • Comparison • Equal Parts • Before and After (change problems) Part Part
Technology Resources • Think Central (Grades K-5) • Holt McDougal Online (Grade 6 & 7) • Houghton Mifflin Harcourt: Singapore Math