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

Evaluating Countywide Adoption and Implementation of K-5

Singapore Math A 2-Year Study in 21 Elementary Schools

Dianna SpenceJames Badger

North Georgia College & State UniversityJanuary 28, 2010

AMTE

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

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?”

666666666

12 6 x 7 = 42

Whole collection

?

Answer: 42 marbles in Jake’s collection are not red.

Algebraic Ideas – Before Algebra

Three more than twice a number is eleven. What is the number ?

11

8

4 1 1 1

The number is 4

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

3 Parts

4 Parts

Ratios

Clinton

Jesse

Clinton

Jesse

After

3 Parts

4 Parts

Before

40 Cards

2 Parts

1 Part

8

40/5 = 8

8 x 3 = 24

8 8 8

Clinton had 24 cards to begin with

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?

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.

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. Teacher surveys – fall/spring

ii. Student surveys – fall/spring

iii. Interviews with teachers

iv. Participating teachers’ journals

v. Classroom observations

vi. Video-taping of mathematics lesson (4 per year) – Analysis: TPR (Teaching Performance Record)

vii. Standardized test scores

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.

Our Data: Things to Keep in Mind

• 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.

1. Teacher Survey Items (strongly disagree / disagree / agree / strongly agree)

Survey Response by Teacher Grade Level – 2008

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

Strongly Disagree Disagree Agree Strongly Agree

"I like teaching mathematics"

K 1 2 3 4 5


0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%


"I like teaching mathematics"

K 1 2 3 4 5

• I believe I have the training and resources to effectively teach mathematics.

Major shift toward teachers feeling that they had necessary training and resources



0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%


"I believe I have the training and resources to effectively teach math"

K 1 2 3 4 5


0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

90.0%


"I believe I have the training and resources to effectively teach math"

K 1 2 3 4 5


• 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.


• 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.

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

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.


0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

90.0%

K-2 only K-5 only K-8 only K-10 only K-12 only College level

"I am confident that I can effectively teach mathematics concepts covered at..."

K 1 2 3 4 5


0.0%10.0%20.0%30.0%40.0%50.0%60.0%70.0%80.0%90.0%

100.0%

K-2 only K-5 only K-8 only K-10 only K-12 only College level

"I am confident that I can effectively teach mathematics concepts covered at..."

K 1 2 3 4 5

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

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

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

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.

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

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.”

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

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

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)

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

Student Performance: CRCTSchool Mean Math Score by Grade

Change in CRCT Math Mean ScoreGrade 1

Increased80%

Decreased20%


Increased85%

Decreased15%

Student Performance: CRCTSchool Mean Math Score by Grade


Increased70%

Decreased30%


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



-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


-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



-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: CRCTStudents Meeting Min. Requirements

Change in Percentage of Students Meeting CRCT Math Minimum Requirement

Grade 1

Increased85%

Decreased15%


Grade 2

Increased95%

Decreased5%

Student Performance: CRCTStudents Meeting Min. Requirements


Grade 3

Increased75%

Decreased25%


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



-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





-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





-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



Student Performance: ITBSMean Percentile Ranking in Math

Change in ITBS Mean Percentile Ranking in Math

Grade 2

Increased70%

Decreased30%


Grade 3

Increased100%

Decreased0%


Grade 4

Increased100%

Decreased0%

Student Performance: ITBSChange in Mean Percentile Ranking

Change in Mean Percentile Ranking on ITBS Math Scores


-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



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





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



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?

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 Interview Data Journal Data Observation Data Standardized Test

Scores

Preliminary Observations

Teacher training and support are essential

Not a “drop-in” solution, especially at higher grades (need phased approach)

Parent “buy-in” is important

Will take time to see full impact

Going Forward

Year 2 now in progress Same design and data collection plan Fifth grade classes added First and second year data to be compared

Years 3 and 4? Grant funding proposal submitted December ‘09 Additional instruments proposed

Teacher curriculum and content knowledge Classroom observation (fidelity of implementation)

Questions/Discussion

Oh Yeah…The Beads! In a jar filled with beads, 2/5 of the beads are blue, 1/3 of them are red, and the

rest are green and yellow. The total number of red, green and yellow beads is 126. There are ¾ as many green beads as there are yellow beads. How many yellow beads are there?

Beads

1/3 Red2/5 Blue Rest Green and Yellow

126 Red, Green, and Yellow

14 126/9 = 14

“There are ¾ as many green beads as there are yellow beads.”

4 Yellow 3 Green

56

There are 4 x 14 = 56Green and Yellow Beads

8There are 8 x 4 = 32Yellow Beads

56/7 = 8

Documents

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