Dianna Spence James Badger North Georgia College & State University January 28, 2010 AMTE

1. Evaluating Countywide Adoption and Implementation of K-5 Singapore Math A 2-Year Study in 21 Elementary Schools Dianna Spence James Badger North Georgia College & State University January 28, 2010 AMTE

2. What Is Singapore Math? • Curriculum based on elementary mathematics teaching techniques used in Singapore • Initial curriculum: “Primary Mathematics” • Created in 1981 • Developed by CDIS (Curriculum Development Institute of Singapore) • Revisions • 1992: stronger problem-solving focus (2nd Ed.) • 1999: reduced content (3rd Ed.) • 2001 & forward: adapted for U.S.

3. Why Singapore Math?Trends in International Math/Science Study • Singapore 4th graders consistently outperforming 4th graders in other countries TIMSS: Mean Score, 4th Grade Math COUNTRY 1995 2003 Singapore 590 594 Hong Kong 557 575 Japan 567 565 Netherlands 549 540 Latvia 499 533 England 484 531 Hungary 521 529 U.S. 518 518 Cyprus 475 510 Australia 495 499 New Zealand 469 496 Scotland 493 490 Slovenia 462 479 Norway 476 451 Source: http://nces.ed.gov/timss

4. Characteristics of Singapore Math • Concrete  pictorial  abstract approach for each concept • Strong emphasis on place value • Repetitive drill minimized: topics are sequenced to reinforce/apply skills • Problem solving based on conceptual approach rather than memorization of rules, “clue words”

5. 9 2 7 6,325 + 400 = 6,725 “12 of Jack’s marbles are red, which is 2/9 of his collection…” Hallmark Strategies of Singapore Math • Number bonds • operations and part-whole relationships • Mental math • leverages and reinforces place value • Bar models • helps conceptualize arithmetic operations, fractions, ratios, algebraic thinking

6. 10 10 10 10 10 10 10 10 10 10 10 10 100 100 100 100 100 100 100 1 1 1 1 1 1 1 1 1 1 1 Example: Place Value Disks 537 + 184 Thousands Hundreds Tens Ones . 7 1 2

7. Examples:Bar Modeling “12 of Jake’s marbles are red, and these make up 2/9 of his collection. How many marbles in Jake’s collection are not red?” 12 6 x 7 = 42 ? 6 6 6 6 6 6 6 6 6 Whole collection Answer: 42 marbles in Jake’s collection are not red.

8. 8 11 1 1 1 Algebraic Ideas – Before Algebra • Three more than twice a number is eleven. What is the number? 4 The number is 4

9. 3 Parts 4 Parts Ratios • The ratio of Clinton’s baseball cards to Jesse’s baseball cards was 3:4. After Clinton bought another 40 baseball cards, he had twice as many baseball cards as Jesse. How many baseball cards did Clinton have at first? Clinton Jesse

10. 40 Cards 2 Parts 1 Part Ratios • Ratio of cards was 3:4 • Clinton bought 40 more cards and then had twice as many as Jesse. • How many did Clinton have at first? Before 8 8 8 Clinton 8 x 3 = 24 3 Parts Clinton had 24 cards to begin with Jesse 4 Parts After 8 Clinton 40/5 = 8 Jesse

11. Ratios, Proportions, and Percents • If you mix 1 gal of 40% acid solution with 2 gal of 60% acid solution, what is the resulting acid concentration? 1 gal 2 gal 3 gal ? % 40 % + 60 % = 16/30 = 53 1/3 % The final concentration is 53 1/3 % acid.

12. Classroom Best Practices • Concrete  Pictorial  Abstract • Emphasis on place value, mental math • Conceptual approach, not rule-based • Spiral approach to topics 3 + 4 3 4

13. Research Questions • Has the implementation of Singapore Math resulted in higher student math scores? • Has the implementation of Singapore Math had a positive impact on student interest and/or confidence in mathematics? • Has the implementation of Singapore Math resulted in measurable changes in the teachers’ attitudes toward mathematics? • Is there fidelity in the implementation of the Singapore Math curriculum? • How do elementary teachers implement the Singapore Math curriculum?

14. Research Design County-wide implementation in a school district in the Southeastern U.S. Research Setting 21 experimental elementary schools Every elementary school in the county All K-4 teachers used Singapore Math (first year) 3 control schools From another county with similar demographics State-approved curriculum (no Singapore Math) Participants One teacher in each grade (K-4) from each of the 24 schools volunteered to participate

15. Qualitative and Quantitative Data • Teacher surveys – fall/spring • Student surveys – fall/spring • Interviews with teachers • Participating teachers’ journals • Classroom observations • Video-taping of mathematics lesson (4 per year) • Analysis: TPR (Teaching Performance Record) • Standardized test scores

16. Our Data: Things to Keep in Mind • Data collection occurred during most teachers’ first year using new curriculum • Most students in higher grades (e.g., 3rd and 4th) had not previously been taught using Singapore Math curriculum • We are more interested in data that will not be available for 3-4 more years.

17. 1. Teacher Survey Items (strongly disagree / disagree / agree / strongly agree) • I like mathematics. • I like teaching mathematics. Trend: Slight increase in teachers’ affinity for mathematics and for teaching mathematics from fall 2008 to spring 2009– especially among Kindergarten teachers.

18. 1. Teacher Survey Items (strongly disagree / disagree / agree / strongly agree) • I believe I have the training and resources to effectively teach mathematics. Major shift toward teachers feeling that they had necessary training and resources

19. 1. Teacher Survey Items (strongly disagree / disagree / agree / strongly agree) • I believe mathematics is an important part of everyday life. • I believe a person is either good at math or not; some people just have mathematical minds. • I believe that in math class, students can learn to be creative and discover concepts independently. Responses to these items were relatively unchanged from fall 2008 to spring 2009.

20. 1. Teacher Survey Items (strongly disagree / disagree / agree / strongly agree) • I believe that ordinarily, elementary studentscannot be expected to understand mathematical concepts; instead they should memorize mathematical facts and processes and use them as instructed. • I believe developing problem-solving skills is an important component for success in learning mathematics. Responses to these items were relatively unchanged from fall 2008 to spring 2009.

21. 1. Teacher Survey Items • I am confident that I understand mathematics concepts covered at the level of…& • I am confident that I can effectively teach mathematics concepts covered at the level of… • K-2 only • K-5 only • K-8 only • K-10 only • K-12 only • College

22. 1. Teacher Survey Items (K-2 only / K-5 only / K-8 only / K-10 only / K-12 only / college) • Confident I can effectively teach mathematics concepts covered at the level of… Trend: Slight increase in teachers’ self-reported ability levels in mathematics and mathematics teaching, especially among grade 3-5 teachers.

23. 2. Student Survey Items, Grades 1 – 4 (strongly disagree / disagree / agree / strongly agree) • I like math. • I am good in math. • Math is easy. • Math is important, even outside of school. Fall ’08 to spring ’09: No significant differences • I like to work math problems by drawing pictures No significant differences, but interesting trend: • slight decline in most schools • slight increase in schools that had piloted Singapore Math in 2007-2008

24. 2. Student Survey Items, Grades 3 – 4 (strongly disagree / disagree / agree / strongly agree) • I like word problems. • I like to figure out math problems in my head. • I am good at organizing the information in a word problem. • I like to work math problems by using counters or things I can move around. • If I cannot work a math problem the first time, I will keep trying until I get it. Fall ’08 to spring ’09: No significant differences

25. 3. Teacher Interview Trends • Teachers appreciated training and support provided by school system • Teachers reported manipulatives frequently integrated in the classroom • value discs and number bonds cited as fostering learning • Teachers reported perceptible increase in formative test results

26. 3. Teacher Interview Trends Teachers reported students possessed a deeper understanding of mathematical concepts. Teachers claimed that they have higher expectations of students in Singapore Math. Parents’ reactions to Singapore Math ranged from enthusiasm to frustration.

27. 4. Teacher Journal Trends:Teachers’ Observations • Students liked using place value disks • Helpful in assisting students grasp the concept of place value • Strong success with place value concepts • Questioning, strategies, exercises provided • Students enjoyed activities and games included in the curriculum • Differentiating instruction was more challenging

28. 4. Teacher Journal Trends:Teachers’ Attitudes & Beliefs • Teachers felt transition from concrete to abstract was too fast • Teachers felt that curriculum moved too quickly from simple exercises to more challenging and complicated ones • Believed students needed more practice with basics • Used many of their own supplemental materials • Resistance to extensions • One teacher stated that the curriculum materials “tend to ‘add’ questions containing problems that have never been taught.”

29. 5. Classroom Observation6. Video-taped Lessons • Use of place value disks prevalent • teacher demonstrating with magnetic disks on board • teacher drawing disks on board • students working individually with disks • Use of number bonds prevalent • Use of mental math strategies evident • Use of bar model strategies evident

30. 5. Classroom Observation6. Video-taped Lessons • Some teachers • tended to emphasize low-level cognitive processes in their instruction • rarely asked students to draw associations to real-world contexts • maintained teacher-centered instruction instead of providing more occasions for cooperative student learning • did not probe with deeper questioning

31. 7. Standardized Test Scores • What standardized test scores did we examine? • State criterion-reference test: Criterion-Reference Competency Test (CRCT) • Nationally norm-referenced test: Iowa Test of Basic Skills (ITBS)

32. 7. Standardized Test Scores • What patterns did we look for?By grade level for each school… • CRCT • Mean score – increase or decrease • Percentage of students meeting minimum requirements – increase or decrease • ITBS • Percentile rankings – increase or decrease

33. Student Performance: CRCTSchool Mean Math Score by Grade

34. Student Performance: CRCTSchool Mean Math Score by Grade

35. Student Performance: CRCTPercent Change in Mean Math Score

36. Student Performance: CRCTPercent Change in Mean Math Score

37. Student Performance: CRCTPercent Change in Mean Math Score

38. Student Performance: CRCTPercent Change in Mean Math Score

39. Student Performance: CRCTStudents Meeting Min. Requirements

40. Student Performance: CRCTStudents Meeting Min. Requirements

41. Students Meeting CRCT Math Req.’sChange in Percentage Points

42. Students Meeting CRCT Math Req.’sChange in Percentage Points

43. Students Meeting CRCT Math Req.’sChange in Percentage Points

44. Students Meeting CRCT Math Req.’sChange in Percentage Points

45. Student Performance: ITBSMean Percentile Ranking in Math

46. Student Performance: ITBSChange in Mean Percentile Ranking

47. Student Performance: ITBSChange in Mean Percentile Ranking

48. Student Performance: ITBSChange in Mean Percentile Ranking

49. Fidelity of Curriculum Implementation (O’Donnell, 2008) Theoretical Framework Curriculum potential Teaching Curriculum-in-use Adaptation

50. Fidelity of Curriculum Implementation (O’Donnell, 2008) Guiding Questions