Implementing Common Core Standards in Math

1. Implementing Common Core Standards in Math Wednesday, March 7th - 4pm Eastern Time Reasoning & Explaining in the Practices Presented by Sara Delano Moore, Ph.D. Sponsored by Join the Implementing Common Core Standards in Math community www.edweb.net/math Tweeting today? #ccss #mathchat @edwebnet

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4. Reasoning & Explaining in the Practices EdWeb Webinar 7 March 2012 Sara Delano Moore, Ph.D. smoore@etacuisenaire.com

5. Standards for Mathematical Practice • Make sense of problems & persevere in solving them. • Reason abstractly and quantitatively. • Construct viable arguments & critique the reasoning of others. • Model with mathematics. • Use appropriate tools strategically. • Attend to precision. • Look for & make use of structure. • Look for & express regularity in repeated reasoning.

6. Reason abstractly & quantitatively • Mathematics in and out of context • Working with symbols as abstractions • Quantitative reasoning requires number sense • Using properties of operations and objects • Considering the units involved • Attending to the meaning of quantities, not just computation

7. Construct viable arguments… • Understand and use assumptions, definitions, and prior results • Think about precision (MP6) • Make conjectures and build logical progressions to support those conjectures • Not just two column proofs in high school • Analyze situations by cases • Positive values of X and negative values of X • Two-digit numbers vs three-digit numbers • Recognize & use counter-examples • Maximum area problem

8. How do we help children learn this? • Provide rich problems where multiple pathways and solutions are possible • Look for the best answer and allow multiple interpretations of best • Recognize the difference between argument and opinion • Provide scaffolds for them

9. Scaffolding Argument • How can you show that your computation is correct? • Use a different tool or strategy • Compare your work with someone else • How can you explain why your answer is best? • What possibilities did you consider? • What criteria did you use? • Why did you reject some options? • What made you choose this option? • Embedding logic into your thinking • Does one part depend on another part? • Does changing one aspect of the problem change the result? • What are you sure about? What comes next?

10. …and critique the reasoning of others • Compare two plausible arguments • Distinguish correct from flawed reasoning • Explain/correct the flaw • Elementary student arguments might depend on concrete referents • Generalize the reasoning at later stage • Ask useful questions to clarify and improve arguments

11. Looking at Lessons • Should every lesson address every practice? • How is this practice addressed in this lesson? • What practices does this lesson highlight? • In what ways does this lesson highlight one or more practices?

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