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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
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 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
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
9
2
 Number bonds

operations and part-whole relationships
 Mental math

7
6,325 + 400 = 6,725
leverages and reinforces place value
 Bar models

helps conceptualize arithmetic operations,
fractions, ratios, algebraic thinking
“12 of Jack’s
marbles are red,
which is 2/9 of
his collection…”
Example:
Place Value Disks
Thousands
Hundreds
100
100
100
537
+ 184
Tens
10
100 100
10
100
7
10
10
Ones .
10
1
1
1
1
10
10
10
10
2
10
100
10
10
1
1
1
1
1
1
1
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?”
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.
Algebraic Ideas – Before Algebra
 Three more than twice a number is eleven.
What is the number ?
8
4
1 1 1
11
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
3 Parts
Jesse
4 Parts
Ratios
 Ratio of cards was 3:4
 Clinton bought 40 more cards and
Before
Clinton
8
8
8
3 Parts
then had twice as many as Jesse.
 How many did Clinton have at first?
8 x 3 = 24
Jesse
Clinton had 24
cards to begin with
40 Cards
4 Parts
After
8
Clinton
2 Parts
Jesse
1 Part
40/5 = 8
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
40 %
2 gal
+
60 %
3 gal
=
?%
16/30 = 53 1/3 %
The final concentration is 53 1/3 % acid.
Classroom Best Practices
 Concrete  Pictorial  Abstract
3
+
4
3
4
 Emphasis on place value, mental math
 Conceptual approach, not rule-based
 Spiral approach to topics
Research Questions
1. Has the implementation of Singapore Math resulted
2.
3.
4.
5.
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?
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)
–
vii.
Analysis: TPR (Teaching Performance Record)
Standardized test scores
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.
1. Teacher Survey Items
(strongly disagree / disagree / agree / strongly agree)
•
•
I like mathematics.
I like teaching mathematics.
Survey Response by Teacher Grade Level – 2009
Survey Response by Teacher Grade Level – 2008
K
1
2
3
4
5
K
1
2
3
4
5
80.0%
70.0%
70.0%
60.0%
60.0%
50.0%
50.0%
40.0%
40.0%
30.0%
30.0%
20.0%
20.0%
10.0%
10.0%
0.0%
0.0%
Strongly Disagree
Disagree
Agree
"I like teaching mathematics"
Strongly Agree
Strongly Disagree
Disagree
Agree
Strongly Agree
"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)
•
I believe I have the training and resources to
effectively teach mathematics.
Survey Response by Teacher Grade Level – 2009
K
Survey Response by Teacher Grade Level – 2008
K
1
2
3
4
5
1
2
3
4
5
90.0%
80.0%
70.0%
70.0%
60.0%
60.0%
50.0%
50.0%
40.0%
40.0%
30.0%
30.0%
20.0%
20.0%
10.0%
10.0%
0.0%
0.0%
Strongly Disagree
Disagree
Agree
Strongly Agree
"I believe I have the training and resources to effectively teach math"
Strongly Disagree
Disagree
Agree
Strongly Agree
"I believe I have the training and resources to effectively teach math"
Major shift toward teachers feeling that they had
necessary training and resources
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.
1. Teacher Survey Items
(strongly disagree / disagree / agree / strongly agree)
•
I believe that ordinarily, elementary students
cannot 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…
Survey Response by Teacher Grade Level – 2009
Survey Response by Teacher Grade Level – 2008
K
1
2
3
4
5
70.0%
60.0%
50.0%
40.0%
30.0%
20.0%
10.0%
0.0%
K-5 only
K-8 only
K-10 only
1
2
3
4
5
100.0%
90.0%
80.0%
70.0%
60.0%
50.0%
40.0%
30.0%
20.0%
10.0%
0.0%
90.0%
80.0%
K-2 only
K
K-12 only
College level
"I am confident that I can effectively teach mathematics concepts covered at..."
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..."
Trend: Slight increase in teachers’ self-reported
ability levels in mathematics and mathematics
teaching, especially among grade 3-5 teachers.
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 Observation
6. 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 Observation
6. 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: CRCT
School Mean Math Score by Grade
Change in CRCT Math Mean Score
Grade 1
Decreased
20%
Change in CRCT Math Mean Score
Grade 2
Increased
80%
Decreased
15%
Increased
85%
Student Performance: CRCT
School Mean Math Score by Grade
Change in CRCT Math Mean Score
Grade 3
Change in CRCT Math Mean Score
Grade 4
Decreased
30%
Increased
70%
Decreased
15%
Increased
85%
Student Performance: CRCT
Percent Change in Mean Math Score
Percent Change in Math CRCT Mean Score
Grade 1 - Top 5 vs. Lowest 5
1.54%
1.35%
1.32%
1.04%
1.01%
0.03%
-0.13%
-0.15%
-0.16%
-0.62%
-5.00%
-4.00%
-3.00%
-2.00%
-1.00%
0.00%
1.00%
Mean Score Change
2.00%
3.00%
4.00%
5.00%
Student Performance: CRCT
Percent Change in Mean Math Score
Percent Change in Math CRCT Mean Score
Grade 2 - Top 5 vs. Lowest 5
2.34%
1.40%
1.22%
0.96%
0.83%
0.11%
0.02%
-0.01%
-0.13%
-0.28%
-5.00%
-4.00%
-3.00%
-2.00%
-1.00%
0.00%
1.00%
Mean Score Change
2.00%
3.00%
4.00%
5.00%
Student Performance: CRCT
Percent Change in Mean Math Score
Percent Change in Math CRCT Mean Score
Grade 3 - Top 5 vs. Lowest 5
4.32%
2.33%
1.92%
1.86%
1.77%
-0.24%
-0.49%
-0.51%
-0.93%
-2.64%
-5.00%
-4.00%
-3.00%
-2.00%
-1.00%
0.00%
1.00%
Mean Score Change
2.00%
3.00%
4.00%
5.00%
Student Performance: CRCT
Percent Change in Mean Math Score
Percent Change in Math CRCT Mean Score
Grade 4 - Top 5 vs. Lowest 5
3.72%
2.52%
2.10%
1.50%
1.37%
0.17%
0.01%
-0.30%
-0.83%
-0.86%
-5.00%
-4.00%
-3.00%
-2.00%
-1.00%
0.00%
1.00%
Mean Score Change
2.00%
3.00%
4.00%
5.00%
Student Performance: CRCT
Students Meeting Min. Requirements
Change in Percentage of Students
Meeting CRCT Math Minimum Requirement
Grade 1
Decreased
15%
Change in Percentage of Students
Meeting CRCT Math Minimum Requirement
Grade 2
Increased
85%
Decreased
5%
Increased
95%
Student Performance: CRCT
Students Meeting Min. Requirements
Change in Percentage of Students
Meeting CRCT Math Minimum Requirement
Grade 3
Change in Percentage of Students
Meeting CRCT Math Minimum Requirement
Grade 4
Decreased
25%
Increased
75%
Decreased
40%
Increased
60%
Students Meeting CRCT Math Req.’s
Change in Percentage Points
Change in Percentage of Students
Meeting Minimum Math CRCT Requirements
Grade 1: Top 5 and Lowest 5
15.4
13.9
12.3
9.4
8.2
2.3
0.1
-1.9
-2.5
-3.1
-40.0
-30.0
-20.0
-10.0
0.0
10.0
Change in Percentage
20.0
30.0
40.0
Students Meeting CRCT Math Req.’s
Change in Percentage Points
Change in Percentage of Students
Meeting Minimum Math CRCT Requirements
Grade 2: Top 5 and Lowest 5
24.5
9.8
9.6
9.1
8.9
0.3
0.2
0.2
0.1
-1.4
-40.0
-30.0
-20.0
-10.0
0.0
10.0
Change in Percentage
20.0
30.0
40.0
Students Meeting CRCT Math Req.’s
Change in Percentage Points
Change in Percentage of Students
Meeting Minimum Math CRCT Requirements
Grade 3: Top 5 and Lowest 5
34.0
28.4
13.9
13.7
12.8
-2.8
-3.5
-6.7
-8.0
-24.0
-40.0
-30.0
-20.0
-10.0
0.0
10.0
Change in Percentage
20.0
30.0
40.0
Students Meeting CRCT Math Req.’s
Change in Percentage Points
Change in Percentage of Students
Meeting Minimum Math CRCT Requirements
Grade 4: Top 5 and Lowest 5
27.8
27.7
19.2
11.5
7.7
-5.4
-5.6
-6.4
-7.0
-7.9
-40.0
-30.0
-20.0
-10.0
0.0
10.0
Change in Percentage
20.0
30.0
40.0
Student Performance: ITBS
Mean Percentile Ranking in Math
Change in ITBS Mean
Percentile Ranking in Math
Grade 4
Change in ITBS Mean
Percentile Ranking in Math
Grade 2
Decreased
30%
Change in ITBS Mean
Percentile Ranking in Math
Grade 3
Increased
70%
Decreased
0%
Increased
100%
Decreased
0%
Increased
100%
Student Performance: ITBS
Change in Mean Percentile Ranking
Change in Mean Percentile Ranking
on ITBS Math Scores
Grade 2: Top 5 and Lowest 5
11.39
10.32
9.11
8.41
8.20
-0.86
-1.79
-2.23
-6.00
-6.35
-30.00
-20.00
-10.00
0.00
10.00
Change in Mean Percentile Ranking
20.00
30.00
Student Performance: ITBS
Change in Mean Percentile Ranking
Change in Mean Percentile Ranking
on ITBS Math Scores
Grade 3: Top 5 and Lowest 5
17.29
15.83
12.44
12.11
11.91
5.70
4.65
2.43
1.08
0.98
-30.00
-20.00
-10.00
0.00
10.00
Change in Mean Percentile Ranking
20.00
30.00
Student Performance: ITBS
Change in Mean Percentile Ranking
Change in Mean Percentile Ranking
on ITBS Math Scores
Grade 4: Top 5 and Lowest 5
29.47
21.32
18.67
17.29
16.80
5.79
4.37
2.44
1.91
0.87
-30.00
-20.00
-10.00
0.00
10.00
Change in Mean Percentile Ranking
20.00
30.00
Theoretical Framework
Fidelity of Curriculum Implementation
(O’Donnell, 2008)
 Curriculum potential
 Teaching
 Curriculum-in-use
 Adaptation
Fidelity of Curriculum Implementation
(O’Donnell, 2008)
Guiding Questions
Curriculum profile
What 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)?
Teaching
How does one
distinguish good
teaching and
fidelity of
implementation to
good teaching
practices
prompted by the
curriculum
material?
Curriculum-in-use
How is the
curriculum and the
perceived
curriculum viewed
and implemented
by teachers? How
are curriculum
materials and
instruction
mutually
supportive and
reinforcing?
Adaptation
Does the curriculum
promote variation
and adaptation of
curriculum
implementation?
Findings in Context
Sources of Data
 Survey Data
 Interview Data
 Journal Data
 Observation Data
 Standardized Test
Scores
Theoretical Framework:
Fidelity of Curriculum
Implementation
(O’Donnell, 2008)
 Curriculum potential
 Teaching
 Curriculum-in-use
 Adaptation
CHART
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?
126 Red, Green, and Yellow
Beads
14
2/5 Blue
“There are ¾ as many green
beads as there are yellow
beads.”
1/3 Red
Rest Green
and Yellow
56
There are 4 x 14 = 56
Green and Yellow Beads
56/7 = 8
8
4 Yellow
126/9 = 14
3 Green
There are 8 x 4 = 32
Yellow Beads