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Evaluating the Implementation of Singapore Math:A Large-Scale Study of 21 Elementary Schools
James Badger
Dianna Spence
North Georgia College & State University
NCTM Regional Conference 2009Thursday, November 19
Agenda
Singapore Math Overview & Examples Dianna
Overview of Research & Methodology James
Quantitative Findings Student Performance (Test Scores) Dianna
Conceptual Framework & Qualitative Findings (Surveys, Observations, Interviews) James
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.
Why Singapore Math?Trends in International Math/Science Study
Singapore 4th graders consistently outperforming 4th graders in other countries
TIMSS: Mean Score, 4th Grade MathCOUNTRY 1995 2003Singapore 590 594Hong Kong 557 575Japan 567 565Netherlands 549 540Latvia 499 533England 484 531Hungary 521 529U.S. 518 518Cyprus 475 510Australia 495 499New Zealand 469 496Scotland 493 490Slovenia 462 479Norway 476 451Source: http://nces.ed.gov/timss
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”
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
9
2 7
6,325 + 400 = 6,725
“12 of Jack’s marbles are red,which is 2/9 ofhis collection…”
Example: Place Value Disks
Thousands Hundreds Tens Ones .
110100
11
1 1
11
111 1
537+ 184
1010
1010
10
10
10
1010
10
100
100
100100
100
10
100
27 1
Example: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?”
666666666
12 6 x 7 = 42
Whole collection
?
Answer: 42 marbles in Jake’s collection are not red.
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
Research Questions
1. Has the implementation of Singapore Math resulted in higher student math scores?
2. Has the implementation of Singapore Math had a positive impact on student interest and/or confidence in mathematics?
3. Has the implementation of Singapore Math resulted in measurable changes in the teachers’ attitudes toward mathematics?
4. Is there fidelity in the implementation of the Singapore Math curriculum?
5. How do elementary teachers implement the Singapore Math curriculum?
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
Qualitative and Quantitative Data
i. Interviews with teachers & students
ii. Participating teachers’ journals (4 times)
iii. Classroom observations
iv. Teacher and student survey – fall/spring
v. Video-taping of mathematics lesson (4 times) – analysis using TPR (Teaching Performance Record)
vi. Standardized test scores
Quantitative Findings: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)
What patterns did we look for? Degree of increase or decrease in mean score Increase or decrease in students meeting
minimum requirements Increase or decrease in percentile rankings
Student Test Performance: Things to Keep in Mind
Testing occurred during most teachers’ first year using new curriculum
Most students in higher grades (e.g., 3rd and 4th) had not previously been taught Singapore Math
Data we are really interested in will not be available for 3-4 more years.
Student Performance: CRCTSchool Mean Math Score by Grade
Change in CRCT Math Mean ScoreGrade 1
Increased80%
Decreased20%
Change in CRCT Math Mean ScoreGrade 2
Increased85%
Decreased15%
Student Performance: CRCTSchool Mean Math Score by Grade
Change in CRCT Math Mean ScoreGrade 3
Increased70%
Decreased30%
Change in CRCT Math Mean ScoreGrade 4
Increased85%
Decreased15%
Student Performance: CRCTPercent Change in Mean Math Score
Percent Change in Math CRCT Mean ScoreGrade 1 - Top 5 vs. Lowest 5
-0.62%
-0.16%
-0.15%
-0.13%
0.03%
1.01%
1.04%
1.32%
1.35%
1.54%
-5.00% -4.00% -3.00% -2.00% -1.00% 0.00% 1.00% 2.00% 3.00% 4.00% 5.00%
Mean Score Change
Student Performance: CRCTPercent Change in Mean Math Score
Percent Change in Math CRCT Mean ScoreGrade 2 - Top 5 vs. Lowest 5
-0.28%
-0.13%
-0.01%
0.02%
0.11%
0.83%
0.96%
1.22%
1.40%
2.34%
-5.00% -4.00% -3.00% -2.00% -1.00% 0.00% 1.00% 2.00% 3.00% 4.00% 5.00%
Mean Score Change
Percent Change in Math CRCT Mean ScoreGrade 3 - Top 5 vs. Lowest 5
-2.64%
-0.93%
-0.51%
-0.49%
-0.24%
1.77%
1.86%
1.92%
2.33%
4.32%
-5.00% -4.00% -3.00% -2.00% -1.00% 0.00% 1.00% 2.00% 3.00% 4.00% 5.00%
Mean Score Change
Student Performance: CRCTPercent Change in Mean Math Score
Percent Change in Math CRCT Mean ScoreGrade 4 - Top 5 vs. Lowest 5
-0.86%
-0.83%
-0.30%
0.01%
0.17%
1.37%
1.50%
2.10%
2.52%
3.72%
-5.00% -4.00% -3.00% -2.00% -1.00% 0.00% 1.00% 2.00% 3.00% 4.00% 5.00%
Mean Score Change
Student Performance: CRCTPercent Change in Mean Math Score
Student Performance: CRCTStudents Meeting Min. Requirements
Change in Percentage of Students Meeting CRCT Math Minimum Requirement
Grade 1
Increased85%
Decreased15%
Change in Percentage of Students Meeting CRCT Math Minimum Requirement
Grade 2
Increased95%
Decreased5%
Student Performance: CRCTStudents Meeting Min. Requirements
Change in Percentage of Students Meeting CRCT Math Minimum Requirement
Grade 3
Increased75%
Decreased25%
Change in Percentage of Students Meeting CRCT Math Minimum Requirement
Grade 4
Increased60%
Decreased40%
Change in Percentage of Students Meeting Minimum Math CRCT Requirements
Grade 1: Top 5 and Lowest 5
-3.1
-2.5
-1.9
0.1
2.3
8.2
9.4
12.3
13.9
15.4
-40.0 -30.0 -20.0 -10.0 0.0 10.0 20.0 30.0 40.0
Change in Percentage
Students Meeting CRCT Math Req.’sChange in Percentage Points
Change in Percentage of Students Meeting Minimum Math CRCT Requirements
Grade 2: Top 5 and Lowest 5
-1.4
0.1
0.2
0.2
0.3
8.9
9.1
9.6
9.8
24.5
-40.0 -30.0 -20.0 -10.0 0.0 10.0 20.0 30.0 40.0
Change in Percentage
Students Meeting CRCT Math Req.’sChange in Percentage Points
Change in Percentage of Students Meeting Minimum Math CRCT Requirements
Grade 3: Top 5 and Lowest 5
-24.0
-8.0
-6.7
-3.5
-2.8
12.8
13.7
13.9
28.4
34.0
-40.0 -30.0 -20.0 -10.0 0.0 10.0 20.0 30.0 40.0
Change in Percentage
Students Meeting CRCT Math Req.’sChange in Percentage Points
Change in Percentage of Students Meeting Minimum Math CRCT Requirements
Grade 4: Top 5 and Lowest 5
-7.9
-7.0
-6.4
-5.6
-5.4
7.7
11.5
19.2
27.7
27.8
-40.0 -30.0 -20.0 -10.0 0.0 10.0 20.0 30.0 40.0
Change in Percentage
Students Meeting CRCT Math Req.’sChange in Percentage Points
Student Performance: ITBSMean Percentile Ranking in Math
Change in ITBS Mean Percentile Ranking in Math
Grade 2
Increased70%
Decreased30%
Change in ITBS Mean Percentile Ranking in Math
Grade 3
Increased100%
Decreased0%
Change in ITBS Mean Percentile Ranking in Math
Grade 4
Increased100%
Decreased0%
Student Performance: ITBSChange in Mean Percentile Ranking
Change in Mean Percentile Ranking on ITBS Math Scores
Grade 2: Top 5 and Lowest 5
-6.35
-6.00
-2.23
-1.79
-0.86
8.20
8.41
9.11
10.32
11.39
-30.00 -20.00 -10.00 0.00 10.00 20.00 30.00
Change in Mean Percentile Ranking
Change in Mean Percentile Ranking on ITBS Math Scores
Grade 3: Top 5 and Lowest 5
0.98
1.08
2.43
4.65
5.70
11.91
12.11
12.44
15.83
17.29
-30.00 -20.00 -10.00 0.00 10.00 20.00 30.00
Change in Mean Percentile Ranking
Student Performance: ITBSChange in Mean Percentile Ranking
Change in Mean Percentile Ranking on ITBS Math Scores
Grade 4: Top 5 and Lowest 5
0.87
1.91
2.44
4.37
5.79
16.80
17.29
18.67
21.32
29.47
-30.00 -20.00 -10.00 0.00 10.00 20.00 30.00
Change in Mean Percentile Ranking
Student Performance: ITBSChange in Mean Percentile Ranking
Fidelity of Curriculum Implementation (O’Donnell, 2008) Curriculum potential Teaching Curriculum-in-use Adaptation
Theoretical Framework
Fidelity of Curriculum Implementation (O’Donnell, 2008)
Guiding Questions
Curriculum profileWhat are the critical components of the curriculum? What ranges of variations are acceptable? What does it mean to implement the program with fidelity (as defined by school administrators and county supervisors)?
TeachingHow does one distinguish good teaching and fidelity of implementation to good teaching practices prompted by the curriculum material?
Curriculum-in-useHow is the curriculum and the perceived curriculum viewed and implemented by teachers? How are curriculum materials and instruction mutually supportive and reinforcing?
AdaptationDoes the curriculum promote variation and adaptation of curriculum implementation?
1. Survey Results
• Teachers, Kindergarten in particular, indicated a stronger affinity for and liked teaching mathematics at the end of the 2008-2009 school year than they had previously reported.
• Content knowledge of mathematics is important for effective teaching: teachers report some degree of understanding and confidence in teaching mathematics.
Survey Results, cont.
A degree of satisfaction with the training and resources for mathematics teaching in 2009 – i.e. Singapore Math training and mentoring initiatives were apparently noticed and appreciated by many teachers. Echoed in interview and journal data
2. Interview Results
A fluid integration of the new curriculum: a consequence of the training provided by the county and ongoing support delivered by school administration
Teachers reported manipulatives frequently integrated in the classroom
- value discs and number bonds cited as fostering learning
Interview Results, cont.
Teachers report students possessed a deeper understanding of mathematical concepts with the Singapore Math curriculum.
Teachers claimed that they have higher expectations of students in Singapore Math.
Parents’ reactions to Singapore Math ranged from enthusiasm to frustration.
3. Journal Results
Teachers wrote that students liked using place value disks a helpful hands-on manipulative to assist students
grasp the concept of place value.
Teachers wrote that students enjoyed activities, games, and manipulatives.
- the students showed enthusiasm in class.- Students described these parts of math class
as “fun”.
4. Classroom Observation
Some teachers tended to emphasize low-level cognitive
processes in their instruction rarely asked students to draw associations to
real-world contexts accountability pressure and time constraints? preponderance of teacher instruction at the expense
of higher cognitive instruction, deeper questioning, and more occasions for cooperative student learning?
Second Year, 2009-2010
No design changes in the second year of the study – i.e. same data collection instruments, teachers volunteer to participate, fifth grade classes added, compare first and second year data.
Data collected in the second year will - Determine student comprehension and
achievement, fidelity of curriculum implementation.
Theoretical Framework:Fidelity of Curriculum Implementation (O’Donnell, 2008)
Curriculum potential Teaching Curriculum-in-use Adaptation
CHART
Findings in Context
Sources of Data
Survey Data Journal Data Interview Data Observation Data Standardized Test
Scores