1. Basic Facts Understanding and Automaticity John SanGiovanni http://jsangiovanni.hcpss.wikispaces.net

2. Let’s Take a Test…

3. Traditionally, how have we taught (or learned) basic facts?

4. They don’t know their facts.

6. Drill on arithmetic facts does not necessarily lead to recall……. Drill must be preceded by sound instruction. 1935 - Brownell and Chazal, 1935

7. Has our approach to teaching basic facts met the needs of all of our students?

8. Has our approach met the needs of ANY of our students? Understanding Number sense Has it aligned with our ideas of good teaching?

9. Why hasn’t memorization worked?

10. Turn to a “shoulder buddy” and identify all of the skills needed for this everyday task.

12. In math… ½ + ¾ 2y + 4y 2 + 4 0.2 + 0.4 62 + 34

13. Have we confused memorization with AUTOMATICITY?

14. Automaticity reduces the load of working memory by as much as 90% (Schneider, 2003) Processing of new information makes heavy use of working memory. As skills are repeated, the brain recognizes the information and can process it more quickly and with less effort.

15. With this in mind… Computation in the “real world” is done mentally 84.6% of the time. - Northcote and McIntosh 1999

16. Solve the next in problem mentally.

17. 49 + 27

21. Does memorization contribute to understanding?

22. Does knowing your facts mean you understand?

23. If our approach that uses memorization doesn’t help kids develop number sense and/or computational fluency? When do they develop it?

24. If we memorize 6 + 8… Will it help with 56 + 38?

25. If I understand… Multiplying by 5 is the same as Multiplying by ½ of 10 4 x 5 is the same as ½ of 4 x 10 I know 68 x 5

26. If I understand… Multiplying by 9 is the same as Multiplying by 1 group less than 10 8 x 9 is the same as (8 x 10) – (8 x 1) I know 37 x 9

27. New Tricks for an Old Dog orOld Tricks for a New Dog Foundational Understanding Instruction in Context Intentional Practice Independent Practice Assessment

28. What +/-/x/÷ means.. • Commutative property • Associative property * Foundational Understanding Picture Removed

30. Picture Removed Foundational Understanding Picture Removed

31. Pictures Removed

33. Patterns andThe Beauty of Mathematics

34. +1/+2 (counting on) Develop Understanding 38 + 1 74 + 2

35. +1/+2 (counting on) +0 Develop Understanding 198 + 0 0 + 56

36. +1/+2 (counting on) +0 +10 Develop Understanding 10 + 23 45 + 10

37. +1/+2 (counting on) +0 +10 Doubles Develop Understanding 33 + 33 45 + 45

38. +1/+2 (counting on) +0 +10 Doubles Make ten Develop Understanding 4 + 66 53 + 7

39. +1/+2 (counting on) +0 +10 Doubles Make ten +8/+9 (Using Ten) Develop Understanding 38 + 7 59 + 4

40. +1/+2 (counting on) +0 +10 Doubles Make ten +8/+9 (Using Ten) Using Doubles Develop Understanding 33 + 34 45 + 46

41. +1/+2 (counting on) +0 +10 Doubles Make ten +8/+9 (Using Ten) Using Doubles Using Knowns Develop Understanding

42. x 2 (doubles) Develop Understanding 12 x 2 210 x 2

43. x 2 (doubles) x 10 Develop Understanding 12 x 10

44. x 2 (doubles) x 10 x 5 (1/2 of x10) Develop Understanding 33 x 5 (33 x 10) ÷ 2

45. x 2 (doubles) x 10 (double x5) x 5 x 1 Develop Understanding 14 x 1

46. x 2 (doubles) x 10 (double x5) x 5 x 1 x 0 Develop Understanding

47. x 2 (doubles) x 10 (double x5) x 5 x 1 x 0 x 3 (x2 + x1) Develop Understanding 6 x 3 (12 + 6) 14 x 3 (28 + 14)

48. x 2 (doubles) x 10 (double x5) x 5 x 1 x 0 x 3 (x2 + x1) x 4 (x2)(x2) Develop Understanding 7 x 4 (7 x 2) x 2 23 x 4 (23 x 2) x 2

49. x 2 (doubles) x 10 (double x5) x 5 x 1 x 0 x 3 (x2 + x1) x 4 (x2)(x2) x 6 (x3)(x2) Develop Understanding 7 x 6 (7 x 3) x 2 42 x 6 (42 x 3) x 2

50. x 2 (doubles) x 10 (double x5) x 5 x 1 x 0 x 3 (x2 + x1) x 4 (x2)(x2) x 6 (x3)(x2) x 8 (x2)(x2)(x2) Develop Understanding 8 x 5 (5 x 2) x 2 x 2 31 x 8 (31 x 2) x 2 x 2