NCDPI Curriculum and Instruction Mathematics

1. “Teaching for Understanding” “To B or Not to b?” NCDPI Curriculum and Instruction Mathematics

2. “Teaching for Understanding” Phil Daro Math SCASS February 12, 2013

3. Dr. Phil Daro “In Person” (Almost)

4. Problem: Mile wide –inch deep curriculum Cause: Too little time per concept Cure: More time per topic “LESS TOPICS”

5. Why do students have to do math problems? • To get answers because Homeland Security needs them, pronto. • I had to, why shouldn’t they? • So they will listen in class. d. To learn mathematics.

6. What is learning? • Integrating new knowledge with prior knowledge; explicit work with prior knowledge • Prior knowledge varies across students in a class (like fingerprints); this variety is key to the solution, it is not the problem. • Thinking in a way you haven’t thought before and understanding what and how others are thinking.

7. To Learn Mathematics • Answers are part of the process, they are not the product. • The product is the student’s mathematical knowledge and know-how. • The ‘correctness’ of answers is also part of the process. Yes, an important part.

8. “Answer Getting vs. Learning Mathematics” United States: • “How can I teach my kids to get the answer to this problem?” Japan: • “How can I use this problem to teach the mathematics of this unit?”

9. “The Butterfly Method”

11. Discussion • How might these ideas challenge teachers in your district or school? • How can we move from “answer getting” to “learning mathematics”? • What evidence do you have that teachers might not know the difference?

12. “The Butterfly Method”

14. Commercial Break!! Blogstop.com

15. “Faster Isn’t Smarter”byCathy Seeley“Hard Arithmetic is not Deep Mathematics”p. 83

16. “Hard Arithmetic is not Deep Mathematics” • What issues or challenges does this message raise for you? • In what ways do you agree or disagree? • What barriers might keep students from reaching these standards, and how can you tackle these barriers?

17. Instructional Task I • What rectangles can be made with a perimeter of 30 units? Which rectangle gives you the greatest area? How do you know? • What do you notice about the relationship between area and perimeter?

18. Instructions • Discuss the following at your table • What thinking and learning occurred as you completed the task? • What mathematical practices were used? • What are the instructional implications?

19. Compared to…. 5 10 What is the area of this rectangle? What is the perimeter of this rectangle?

20. “Who’s doing the talking, and who’s doing the math?” Cathy Seeley, former president, NCTM

21. The Mathematical Practices develop character: the pluck and persistence needed to learn difficult content. We need a classroom culture that focuses on learning…a try, try again culture. We need a culture of patience while the children learn, not impatience for the right answer. Patience, not haste and hurry, is the character of mathematics and of learning.

22. How can we move from “answer getting” to “learning mathematics”?

23. “Modeling in Mathematics” by CCSSO and Math SCASS (Council of Chief State School Officers) (The State Collaborative of Assessment and Student Standards)

24. What is modeling? A word with different meanings 1. “Modeling a Task” - An instructional strategy where the teacher shows step by step actions of how to set up and solve the task Use step by step actions to “model” how to solve this task Mathematical Task: 2 + ___ = 8

25. What is modeling? A word with different meanings 2. “Model with Manipulatives” - Start with the math then use manipulativesto demonstrate and understand how to solve the problem. math Toothpicks as a model

26. What is modeling? A word with different meanings 3. “Model with Mathematics” - Start with the task and choose an appropriate mathematical model to solve the task Choose a grade appropriate mathematical model to solve the task: e.g. writing the number sentence 4 – 2 = 2 Four birds sat on a wire, 2 flew away. How many birds remain on the wire?

27. What is modeling? A word with different meanings 4. “A Model with Mathematics”

28. What is modeling? A word with different meanings • “Modeling a Task” • “Modeling with Manipulatives” • “Model with Mathematics” • “A Model with Mathematics”

29. What is modeling? A word with different meanings • “Modeling a Task” • “Modeling with Manipulatives” • “Model with Mathematics” • “A Model with Mathematics”

30. What makes something a modeling task? • Are there criteria for “modeling tasks”? • What are the skills involved?

31. Task 932: (Unpublished)

32. How well posed is well enough posed? • Should a student still have questions after they read the task? • Should students have to find their own information outside of what is given in the problem? • Should assumptions be stated, or reasoned differently by each individual student?

33. Five Problems to Ponder • Painting A Barn • The Ice Cream Van • Birthday Cakes • Graduation • Sugary Soft Drinks

34. The Barn

35. Task 85: Ice Cream Van N-Q.A.1

36. Birthday Cakes Would all the birthday cakes eaten by all the people in Arizona in one year fit inside the University of Phoenix football stadium? Cody Patterson Original

37. Graduation

38. Sugary Soft Drinks How many packets of sugar are in a 20 ounce bottle of soda? http://threeacts.mrmeyer.com/sugarpackets/

39. Collecting and Selecting Information 5. Determine what information is needed and find the information yourself 2. Brainstorm what you need and then are given it 1. All and only relevant information is given 3. Told what you need, you go and find it 4. Given information, but you decide what is useful Images: http://www.dbarn.net/, http://blog.pinkcakebox.com/25th-birthday-cake-2007-09-15.htm, www.NYC.gov, Dan Meyer, http://balfour.rbe.sk.ca/node?page=3, http://www.realmagick.com/ice-cream-vans/

40. Matching Activity • Match each task with a “Collecting and Selecting Information” description. • Place them in order as they should appear on a continuum based on; • What information is needed?

41. Collecting and Selecting Information 3. Told what you need, you go and find it 5. Determine what information is needed and find the information yourself 1. All and only relevant information is given 2. Brainstorm what you need and then are given it 4. Given information, but you decide what is useful Images: http://www.dbarn.net/, http://blog.pinkcakebox.com/25th-birthday-cake-2007-09-15.htm, www.NYC.gov, Dan Meyer, http://balfour.rbe.sk.ca/node?page=3, http://www.realmagick.com/ice-cream-vans/

42. Collecting and Selecting Information 1 1 What information is needed? 5 5 4 3 2 Find the information needed. 4 3 2

43. “All Around the School” A class was studying metric and customary measurement, comparing quantities of one unit of measure to quantities in the other. (2003) Question:If all the students in the school hold hands, will they create a chain long enough to circle the school?

44. Compared To…… Our school is 485 meters around. There are 535 students in the school, and the average arm span of a child is 2 meters. Can we circle the school if we hold hands and make a human chain?

45. Lunch

46. Commercial Break!! Blogstop.com

47. “Faster Isn’t Smarter”byCathy Seeley“Constructive Struggling”p. 88

48. What is learning? • Integrating new knowledge with prior knowledge; explicit work with prior knowledge • Prior knowledge varies across students in a class (like fingerprints); this variety is key to the solution, it is not the problem. • Thinking in a way you haven’t thought before and understanding what and how others are thinking.

49. 16 3 =  • What concept is addressed in this situation? • What strategies could be used to develop conceptual understanding?

50. Show 15  3 =  • As a multiplication problem • Equal groups of things • An array (rows and columns of dots) • Area model • In the multiplication table • Make up a word problem