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

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

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.

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 In and out of context – inspire page Number sense – fractions vs whole numbers, positive vs negative, place value and scale Properties of operations – multiplication makes bigger vs multiplication as area Consider the units – money, measurement – school bus problem - meanings

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 Counter-examples – max area problems lead to squares – not when one side is the barn rather than fencing

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

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?

…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

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?