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
Tweeting today? #ccss

2. Reasoning & Explaining in the Practices
EdWeb Webinar
7 March 2012
Sara Delano Moore, Ph.D.

3. 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.

4. 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

5. 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

6. 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

7. 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?

8. …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

9. 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?