What are Basic Skills in Mathematics in 2008 (and Why Don't My Students Have Them)?

1. What are Basic Skills in Mathematics in 2008(and Why Don't My Students Have Them)? AMTNJ October 2008 Dr. Eric Milou Rowan University Department of Mathematics milou@rowan.edu 856-256-4500 x3876

2. Overview • National Math Panel Recommendations • Number Sense & Computation Proficiency • NJ State Assessments

3. National Math Panel (NMP) • A focused, coherent progression of mathematics learning, with an emphasis on proficiency with key topics, should become the norm in elementary and middle school mathematics curricula. Any approach that continually revisits topics year after year without closure is to be avoided.

4. NMP • Instructional practice should be informed by high-quality research, when available, and by the best professional judgment and experience of accomplished classroom teachers. High-quality research does not support the contention that instruction should be either entirely “student centered” or “teacher directed.”

5. NMP • A major goal for K–8 mathematics education should be proficiency with fractions (including decimals, percents, and negative fractions).

6. A NMP train…

7. Response by Peppermint Patty

8. Your Test! 4 x 9 x 25 How many ounces are in a gallon? 50 ÷ 1/2

9. What’s “Typical?” in US

10. Third International Math & Science Study (TIMSS) Proceduresvs. Concepts

11. STATED vs. DEVELOPED Teaching Gap, Stigler and Hiebert, 1999

12. We need a BALANCE • Balance • Direct Instruction • Constructivism • Balance • Conceptual Understanding • Algorithmic Proficiency • These are NOT Dichotomous

13. Conceptual Understanding • 24 ÷ 4 = 6 • 24 ÷ 3 = 8 • 24 ÷ 2 =12 • 24 ÷ 1 = 24 • 24 ÷ 1/2 = ??

14. Fractions - Conceptually The F word More than 1 or Less than 1 Explain your reasoning

15. Which is larger? • (2/3 + 3/4 + 4/5 + 5/6) OR 4 • 12.5 x 45 OR 4.5 x 125 • (1/3 + 2/4 + 2/4 + 5/11) OR 2

16. Conceptual Fraction task • Kim’s teacher asked her class to design a flag using four colors, dividing a square into parts, and to color the parts as follows: • 1/2 is colored red • 1/4 is colored blue • 1/8 is colored green • Any other part is to be left white

17. Flags

18. 1.49 1000 Decimals • 1000 ÷ 1.49 = 671.1409396 = Torture! • Big Macs Sell for $1.49, how many Big Macs can I buy for $10.00? • 1 is $1.50 • 2 are $3 • 4 are $6 • 6 are $9 Number Sense is a vital skill

19. Computation is Important • Engaging & Active • Less passive worksheets • More thinking & reasoning

20. Computation

21. Active Computation • Fifty (1, 2, 3, 4, 5, 6 and addition) • Buzz (3) • Wipe Out • Product Game • http://illuminations.nctm.org/ActivityDetail.aspx?id=29

22. Web Applets • NCTM Illuminations • http://illuminations.nctm.org • National Library of Virtual Manipulatives (NLVM) • http://www.nlvm.usu.edu/ • Shodor Interactivate • http://www.shodor.org/interactivate/activities/

23. Conceptual & Contextual • 8 + 7 = ? • How do we teach this? x x x x x x x x x x x x x x x x x

24. 8 + 7 = ? 8 + 7 = ? 5 2 10 + 5 = 15

25. 17 - 8 = 0 17 / / 1 7 - 8 2 7 8 --> --> 10 --> --> --> --> --> --> --> 17

26. How Many Circles? 50

27. 1000 - 279 = ? 279 +1 = 280 + 20 = 300 +700 = 1000

28. 1000 - 279 = ? 1000 - 1 = 999 999 -278 721

29. Multiplication • 13 x 17 = ? 10 7 2 10 3 1 3 x 1 7 1 0 0 7 0 ------- 3 0 2 1 9 1 1 3 0 ------- 2 2 1 221

30. Conceptual approach leads to ? • Algebra: (x + 3) (x + 7) = x 7 x 3 x2 7x 3x 21

31. NJ ASK 5, 6, 7, & 8

32. The Effect

33. Why? • “In 2008 we propose raising the standard for student achievement resulting in fewer students being deemed proficient. The impact of this decision will lead to identifying students for intervention and assistance earlier in their school careers, which has long been a goal of the State Board. Our hope is that this will better prepare all students for success in high school and beyond.” Lucille E. Davy, NJDOE Commissioner

34. NJ STEPS proposal • End of course Alg I assessment will replace HSPA math beginning with graduating class of 2012 (08-09) • End of course Geometry assessment will be required beginning with graduating class of 2014 (10-11) • End of course Alg II assessment will be required beginning with graduating class of 2016 (12-13)

35. Proposed Amendments to N.J.A.C. 6A:8, Standards and Assessment for Student Achievement (Sept 17, 2008) to State Board • The biology competency assessment has replaced the science portion of the HSPA. • For language arts literacy and mathematics, the intent is to implement the assessments first and then to review the results and consider the impact on students, schools, and districts of possibly phasing out the traditional HSPA. • These amendments do not include a proposed schedule for eliminating the HSPA in mathematics or language arts literacy.

36. Algebra II field test results • Total possible points (76) • 46 points from MC items • 30 points from Constructed response items • 88,344 students participated nationwide • Average number of points correct was 20 out of 76 or 26.9% • Average number of points correct on constructed response items was 3 out of 30 (10.2%)

37. NJ Algebra II results • 9,813 students were tested • Approximately 43,000 students are enrolled in Alg II in NJ • Average score was 21/76 or 27.5% • Average score on constructed response items was 3/30 or 10.7%

38. Fact #1 A

39. Fact #2 B

40. Fact #3 C

41. Fact #4 D

42. Fact #5 E

43. Fact #6 F

44. Fact #7 G

45. Fact #8 H

46. Fact #9 I

47. What is this?

48. What is this? F A C E

49. What If? C A B F D E I G H

50. Try Again