Alan H. Schoenfeld University of California Berkeley, CA, USA Alans@Berkeley.Edu

1. Thoughts about Mathematical Sense-Making:Where we’re heading with the Common Core Standards and Smarter Balanced Assessments and How to Get Ready for It Alan H. Schoenfeld University of California Berkeley, CA, USA Alans@Berkeley.Edu

2. Today’s Activities • Playing with some mathematics • What’s coming down the pipe – Common Core Standards, Smarter Balanced Assessments • Thoughts about what to look for in productive mathematics classrooms • Q&A at any time • Lunch

3. 1. Let’s Play!

4. If you draw in the two diagonals of a quadrilateral, you divide the quadrilateral into four equal areas. David says, The question: Is David’s claim Always right? Sometimes right? Never right?

5. Always, Sometimes, or Never True?

6. Always, Sometimes, or Never True?

7. Always, Sometimes, or Never True?

8. Always, Sometimes, or Never True?

9. Always, Sometimes, or Never True?

10. Always, Sometimes, or Never True?

11. If you draw in the two diagonals of a quadrilateral, you divide the quadrilateral into four equal areas. David says, The question: Is David’s claim Always right? Sometimes right? Never right?

12. Student Work 1 If you draw in the two diagonals of a quadrilateral, you divide the quadrilateral into four equal areas.

13. Student Work 2 If you draw in the two diagonals of a quadrilateral, you divide the quadrilateral into four equal areas.

14. Some Questions. Did You Have To • Make sense of problems and persevere in solving them? • Reason abstractly and quantitatively? • Construct and critique viable arguments? • 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?

15. More Questions. • Was there honest-to-goodness math in what we did? • Did you engage in “productive struggle,” or did I dumb it down to where you didn’t? • Who had the opportunity to engage? A select few, or everyone? • Who had a voice? Did people get to say things, develop ownership? • Did instruction find out what you know, build on it?

16. 2. Thoughts about Mathematical Sense-Making:Where we’re heading with the Common Core Standards and Smarter Balanced Assessments and How to Get Ready for It

17. Not Sense-Making: How many two-foot boards can be cut from two five-foot boards?

18. National Assessment ofEducational Progress, 1983: An army bus holds 36 soldiers. If 1128 soldiers are being bussed to their training site, how many buses are needed? 29% 31R12 18% 31 23% 32 30% other

19. Kurt Reusser asks 97 1st and 2nd graders: There are 26 sheep and 10 goats on a ship. How old is the captain? 76 students "solve" it, using the numbers.

20. H. Radatz gives non-problems such as: Alan drove the 12 miles from his house in Berkeley to the Tilden Early Childhood Center at 3 PM. On the way he picked up 2 friends.

21. Sense-Making What happens when you add two odd numbers?

22. 7 + 9

23. 7 + 9

24. 7 + 9

25. The Challenge: To make sense of: - The (Common Core) Standards - High Stakes Assessment and what it’s likely to mean in California - Formative Assessment as a mechanism for making good stuff happen in our classrooms.

26. Let’s start with context. The Common Core State Standards in Mathematics (CCSSM) now exist.

28. But what do they mean? Huh? What do you mean, what do they mean? The words are there on the page…

29. Remember Alice and Humpty Dumpty?

30. Here’s WC Fields as Humpty Dumpty in the 1933 film “Alice in Wonderland”

31. “When I use a word,” Humpty Dumpty said in rather a scornful tone, “it means just what I choose it to mean – neither more nor less.” And so it is with Standards (Common Core or otherwise)

32. What defines the Standards? In today’s high stakes context, it’s the assessments. And in California, that’s meant the CST.

36. Why is this such a problem? W Y T I W Y G

37. But, the CST is going away… So things will change. How, and what might we do? That’s the rest of the conversation.

38. First, the Standards: Content and Practices

39. (Alan’s Biased Predictions) Content: Getting Richer Practices: A BIG Opportunity

40. The Practices in CCSS-M: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct and critique viable arguments 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.

41. Remember the “processes” in the ‘89 NCTM Standards: Mathematics as Problem Solving Mathematics as Communicating Mathematics as Reasoning Mathematics as Connections

42. Remember the goals of the 1992 CA Mathematics Framework: Mathematical Power Mathematical Performance Large Assignments Complete Work

43. Remember NCTM’s (2000) Principles and Standards: Five Content Standards: Number & Operations Algebra Geometry Measurement Data Analysis and Probability

44. And Five Process Standards: Problem Solving Reasoning and Proof Communication Connections Representation Remember NCTM’s (2000) Principles and Standards:

45. It’s no exaggeration to say that all of these things “count” in the Common Core Standards. But will they count in California?

46. It’s looking like the answer is YES And the reason is … Assessment

47. Specifically, the Smarter Balanced Assessment Consortium (SBAC) http://www.k12.wa.us/smarter/ (Just google SBAC)