Two Multi-Site Randomized Control Trials:
Bottom-Up vs. Top-Down Approaches
to Scaling Up PALS
Is Response to Word-Problem
Intervention among Students with MD
Moderated by Concurrent RD?
Doug Fuchs and Lynn Fuchs
Vanderbilt University
1
Bottom-Up vs. Top-Down Approaches
to Scaling Up PALS
Doug Fuchs, Kristen McMaster, Laura Saenz,
Devin Kearns, Lynn Fuchs, Loulee Yen,
Don Compton, and Chris Lemons
Vanderbilt University
Chris Schatschneider
Florida State University
R305G04104
Institute of Education Sciences
2
Purpose of PALS





Supplements the general education core program
Implemented 3 times per week in reading; 2 times per
week in math
Creates a “routine” for teachers to differentiate
instruction by creating many simultaneous peermediated lessons rather than one teacher-directed
lesson
PALS Reading: kindergarten, first grade, grades 2-6,
high school
PALS math: kindergarten, first grade, grades 2-6
3
PALS Research
•
•
•
•
•
•
•
Based on Juniper Gardens Classwide Peer Tutoring
Over 15 years of experimental research
Title I and Non-Title I schools
Urban and suburban schools
High, average, and low achievers
Students with learning disabilities
“Validated Practice” status (USDE, WWC, BEE)
4
Grades 2-6 PALS
Partner Reading
Paragraph Shrinking
Prediction Relay
5
Partner Reading
•
•
•
•
•
•
Conducted for 11-12 minutes
Stronger reader reads aloud for 5 minutes
Weaker reader reads same text aloud for 5 minutes
Weaker reader retells story for 1-2 minutes
Readers read quickly, correctly, and with expression
Coaches listen, correct mistakes, and mark points (1
point for each correctly read sentence and 10 points
for story retell)
6
Paragraph Shrinking
• Conducted for 10 minutes
• For 5 minutes:
• Stronger reader reads new text aloud,
summarizing paragraph by paragraph
– Name the most important who or what (1 point)
– Name the most important thing about the who or
what (1 point)
– Shrink it to 10 or fewer words (1 point)
• For next 5 minutes:
• Weaker reader reads new text aloud, summarizing
paragraph by paragraph (as above)
• Coach listens, corrects mistakes, and marks points
7
Prediction Relay

5 minutes, stronger reader read new text
−
−
−
−
−
−


Makes prediction (1)
Reads half page (1)
Checks prediction (1)
States main idea (3)
Makes new prediction
Continues to read
5 minutes, weaker reader continues on in new
text, with the same activities
Coach listens, corrects mistakes, and marks
points
8
Two Kinds of PALS Research
Randomized Controlled Trials
Study schools include Title I and no Title I.
Classrooms randomly assigned within
schools to PALS and control groups.
HA, AA, LA (including LD) students
targeted in each classroom.
Fidelity of treatment implementation.
Individually administered pre-/posttests by
trained examiners.
9
Improvement in Reading
Improvement
Over 16 Weeks
80
Experimental
Control
60
40
20
0
Learning
Disabled
Low
Achieving
Average
Achieving
High
Achieving
10
Two Kinds of PALS Research
School-Improvement Projects
Title I schools implement PALS school-wide.
Our TA funded by Nashville’s Title I office
No fidelity of treatment assessed.
Group administered high-stakes tests.
11
Report Card Scores Based on Students’
Performance on the TCAP (CTB/McGraw-Hill)
GOWER
Subject
‘93
‘94
MATH
76.0
(61)
107.8 (12)
READING
74.0
(60)
112.5 (25)
Language Arts
61.7
(60)
91.8
(33)
Science
74.4
(58)
95.6
(24)
Social Studies
60.1
(61)
81.4
(53)
Note 1: A score of 100 means that students of a school are progressing at a rate
equivalent to that of the national rate.
Note 2: The numbers in parentheses represent Gower’s standing in relation to the
Metro Schools’ other 66 elementary schools.
12
Typical Teacher Support
in PALS Research





Support was ongoing and on-site: RAs gave in-class
assistance 1x or 2x per wk during training and
implementation.
RA support is costly, unlikely in wider implementations,
an obstacle to scaling up.
Absent such support, quality of implementations suffer.
How to separate an intervention from its support
system? How to scale-up (“export” the intervention from
A to B) without researchers’ nurturance?
There’s also a matter of transcending time….
13
Purpose of the Present Study


With Grades 2-6 PALS as a “prop,” and
students’ reading achievement as the
criterion, does a “bottom-up” approach
beat a “top-down” approach to scaling up?
Do these approaches affect teachers’
sustainability of PALS?
14
METHOD
15
Participating Sites
Vanderbilt
University
(Nashville)
University of
Minnesota (Twin
Cities Area)
The University of
Texas Pan
American
(Hidalgo County)
Where K-PALS was
developed and
researched
Large urban area,
diverse student
population
Southern-most
region of TX along
the U.S. Mexico
Border
Has K-PALS
“expertise”(Project
Director,
Coordinators)
Schools had some
prior experience
with PALS
Schools had no
prior experience
with PALS
“PALS” has brandname recognition
Schools regularly
participate in
University research
projects
Schools had no
prior experience
participating in
research
16
Participating Teachers

Two cohorts of 3rd-, 4th-, and 5th-grade teachers :
− Cohort 1
 Entered study in 2006-07
− Cohort 2
 Entered study in 2007-08

Two years of study participation:
− Year 1
 Assigned randomly to PALS or Control
− Year 2
 PALS Teachers selected Top Down or Bottom Up PALS
 Control Teachers remained in Control group
17
Teachers by Study Group in
Year 2
Cohort 1
Tennessee
Minnesota
Texas
Total
Top Down
Bottom Up
Control
5
5
6
16
5
5
7
17
7
4
7
18
Cohort 2
12
8
9
Tennessee
6
9
12*
Minnesota
8
4
7
Texas
26
21
28*
Total
TOTAL
42
38
46*
Teachers
*This number is based on all MN controls; 10 were eliminated, right?
18
Students by Study Group in
Year 2
Cohort 1
Tennessee
Minnesota
Texas
Total
Cohort 2
Tennessee
Minnesota
Texas
Total
TOTAL
Students
Top Down
Bottom Up
Control
60
61
61
182
60
65
90
215
68
49
88
205
136
72
95
303
86
109
46
241
102
151*
73
326*
485
456
531*
19
Study Conditions: Year 1


Control – Teachers implemented core language
arts curriculum
PALS – Teachers implemented with fidelity:
− 3 times/week for 35-40 min (about 54 sessions)
− Coaches and Readers: higher-performing readers
paired with lower-performing readers
− Four PALS Activities:
 Partner Reading (10 min)
 Retell (2 min)
 Paragraph Shrinking (10 min)
 Prediction Relay (10 min)
20
Study Conditions: Year 2



Control – Teachers implemented core language arts
curriculum
“Top Down” (TD) PALS
− Teachers did PALS “by the book”
− Fidelity of PALS implementation was emphasized
“Bottom Up” (BU) PALS
− Teachers implemented core components of PALS
− Customization was strongly encouraged and
supported
21
BU PALS: Core Elements

48 sessions minimum
35 minutes per session minimum
10 minutes of Partner Reading
10 minutes of Paragraph Shrinking
A motivational peer reinforcement system
22
22




BU PALS: Requirements

23
Teachers asked to:
− Conduct core elements of PALS as designed
− Develop changes
 Match to curriculum, students’ needs, teaching
style
 Create a type of PALS for the long term
23
Student Measures
Academic Measures






Test of Word Reading Efficiency
(TOWRE)
Woodcock Reading Mastery TestRevised (WRMT-R)
− Word Identification Subtest
Wide Range Achievement Test (WRAT)
− Letter and Word Identification
Subtests
Comprehensive Reading Assessment
Battery (CRAB; 2 passages)
− Oral reading (1 min & 3 min)
− Comprehension (10 open-ended
questions)
CBM Maze Task (2 passages)
− Correct maze choices made in 2.5
min
Iowa Test of Basic Skills (ITBS)
− Reading Comprehension
− Vocabulary
Student Characteristics
 Demographics
 SWAN
− Teachers rated each
student’s abilities to focus
attention, control activity,
and inhibit impulses

Teacher ratings
− Teachers rated each
student’s effort in reading
and behavior in the
classroom
24
Teacher Measures
Classroom Measures





PALS Calendars
PALS Fidelity
Language Arts Observation
Classroom Atmosphere Rating
Scale (Wehby)
Survey of Enacted Curriculum
(SEC): English and Language
Arts
Teacher Characteristics


Demographics
Berends teacher survey
(assesses school climate,
teacher professional
development, teacher efficacy,
etc.)
25
Procedures


Pretesting (September-October)
PALS Workshops (September-October)
− Year 1: All teachers attend same workshop
− Year 2: Separate TD and BU workshops

PALS Implementation (~18 weeks)
−
−
−
−

Teachers implemented 3 times per week for 35-40 min
Weekly classroom visits from project staff
Three “booster” sessions for TD and BU PALS teachers
Two fidelity observations
Language arts observations in PALS and Control classrooms
− 45-60 min
− Momentary time sampling of a variety of reading instructional
components
− Supplementary field notes

Posttesting (March-May)
26
Scaling-Up PALS for Grades
2-6
Results
27
Organization of Study
Year 1
(2006-07)
COHORT 1
(1st YEAR)
Top-Down
PALS (W +
Year 2
(2007-08)
COHORT 1
(2nd YEAR)
B +
Top-Down PALS
B
Bottom-Up PALS
Year 3
(2008-09)
COHORT 2
(1st YEAR)
COHORT 2
(2nd YEAR)
Top-Down PALS
Top-Down PALS
Tutor)
Top-Down
PALS (W +
Control
Bottom-Up PALS
+ Helpers)
Control
Control
Control
28
Analysis Procedures




Create latent pretest and posttest variables combining 5 reading
measures into 1
Create a latent change score
− Produces an “error-free” change value
Run 2-level HLM analyses
− Outcome: Latent change score
− Variables: Treatment condition (TD, BU, Control); Site (TN, MN,
TX); latent pretest score
− Random effects: Level 2 teacher effects; ICC = .10
Test comparability of groups on variables plausibly related to
selection of TD or BU
29
Descriptive Statistics
Table 1. Pretest-posttest raw score gains
Reading Measure
Top-Down
Bottom-Up
Control
M
SD
M
SD
M
SD
5.08
11.51
5.41
12.29
4.47
11.55
5.45
12.67
6.08
12.26
4.95
12.02
3.15
18.68
3.39
8.79
2.88
8.75
22.18
44.91
23.78
42.30
20.19
43.80
4.72
8.25
4.78
8.30
4.52
8.31
-0.03
0.97
0.18
0.95
-0.17
1.05
WRMT-R WID
words correct
TOWRE SWE
words correct
ITBS RC
items correct
CRAB Fluency
words correct
CBM Maze
correct completions
Latent change
score (z-scored)
Note: WRMT-R WID = Woodcock Reading Mastery Test, Revised, Word Identification subtest; TOWRE SWE = Test of
Word Reading Efficiency, Sight Word Efficiency subtest; ITBS RC = Iowa Test of Basic Skills, Reading Comprehension
subtest; CRAB = Comprehensive Reading Assessment Battery; CBM = Curriculum-Based Measurement
30
Regression Analysis
Table 2. Multilevel Regression Effects
Comparison
Estimate
SE
PALS vs. Control
TD vs. Control
BU vs. Control
TD vs. BU
0.247
0.150
0.343
-0.193
Random Effects
Variance
Teacher
Residual
0.102
0.872
0.087
0.097
0.100
0.095
SE
0.024
0.035
t
2.85 **
1.54
3.42 ***
2.03 *
z
4.20
24.79
Note: Degrees of freedom for fixed effects = 109. * = p <.05; ** =
p <.01; *** = p <.001
31
Effects for Study Groups by LA, AA,
and HA Students
Table 3. Child-level effect sizes for PALS (Hedges' g )
Student type
Overall
Low Achieving
Average Achieving
High Achieving
PALS
v. Control
TD v.
Control
BU v. Control
BU v. TD
.25
.26
.23
.28
.15
.08
.19
.20
.34
.43
.27
.37
.19
.35
.08
.18
Note: Hedges' g effect sizes calculated using recommendations for What Works Clearinghouse
reporting (IES, 2007) BU=Bottom-Up; TD=Top-Down; PALS = Peer-Assisted Learning Strategies.
32
Effects for Study Groups by LA, AA,
and HA Students
Effect Size (Hedges' g)
Effect Sizes for PALS
.50
.45
.40
.35
.30
*
.25
Overall
*
.20
.15
*
Low
Average
High
.10
.05
.00
B U P A LS
TD P A LS
vs.C ontrol vs.C ontrol
B U P A LS
vs.TD
P A LS
P A LS
vs.C ontrol
33
Is Response to Word-Problem
Intervention among Students with MD
Moderated by Concurrent RD?
Lynn Fuchs, Sarah Powell, Pamela Seethaler, Paul Cirino,
Jack Fletcher, Doug Fuchs,
Carol Hamlett, and Rebecca Zumeta
Vanderbilt University and University of Houston
Journal of Educational Psychology, 2009
Grant #P01046261
National Institute of
Child Health and Human Development
34
35
Study Purposes



Examine the efficacy of tutoring protocols for
remediating
− Math fact deficits
− Word problem deficits
Assess whether treatment efficacy is different for
− Students with MD alone versus
− Students with MDRD
Determine whether effects are comparable as a function
of site
− Nashville, where the tutoring protocols were
developed
− Houston, a site distal to the developers
36
Participants

924 students screened in 63 classrooms in 18 schools in Nashville and
Houston (similar sample size at each site)

Inclusion criteria:
− WRAT-A: < 26th percentile
− 5-item word-problem measure: score < 2
− At least 1 (of 2) WASI subtest T score: > 36

162 students eligible for the study; 133 students remained at posttesting

Blocking on site (Nashville and Houston) and MD status (MD vs. MDRD),
students randomly assigned to tutoring conditions:
− Math Facts Tutoring (“Math Flash”)
− Word Problem Tutoring (“Pirate Math”)
− Control
37
Participants


Treatment groups comparable on all variables
MD vs. MDRD differences (across treatment
groups) as expected
Age
Female
Sub. Lunch
Spec. Ed.
WASI IQ
WRAT-A
WRAT-R
MD
9
40%
68%
8%
92
88
105
MDRD
9
48%
90%
28%
85
81
78
38
Examined Efficacy
of Two Tutoring Protocols
Both Tutoring Protocols






Delivered individually
48 sessions: 3 per week for 16 weeks
20-30 minutes per session
Scripted lessons, which tutors studied (not read)
Motivational system to ensure on-task behavior and
hard, accurate work
Each session audiotaped; tapes sampled and coded for
fidelity, which was high for both tutoring conditions
39
Examined Efficacy
of Two Tutoring Protocols

The exclusive focus of Math Flash was
math facts

The primary focus of Pirate Math was
word problems
− but it also addressed foundational skills
(math facts, procedural calculations, and
algebra skills)
40
Pirate Math Tutoring
48 sessions: 3 per week for 16 weeks
20-30 minutes per session
Scripted lessons, which tutors study (not read)
Four units
Foundational Skills for Word Problems
Total Word Problems
Difference Word Problems
Change Word Problems
41
Pirate Math: Introductory Unit

Teach students:
− Efficient counting strategies to answer math
facts
− 2-digit procedural calculations
− How to solve for X in addition and
subtraction equations (a+b=c; x-y=z)
− How to check work
42
Introductory Unit:
Counting Up
COUNTING UP
Addition
COUNTING UP
Subtraction
1. Put the bigger number in your head
and say it.
1. Put the minus number in your head
and say it.
2. Count up the smaller number on your
fingers.
2. Count up on your fingers to the
number you started with.
3. Your answer is the last number you
say.
To ADD, you CAN reverse the numbers!
3. Your answer is the number of fingers
you have up.
To SUBTRACT, do NOT reverse the numbers. The
minus number always goes first.
Example: 5 - 2 = ?
Example: 5 + 2 = ?
1.
2.
3.
“5.”
(Hold up 1 finger.) “6.”
(Hold up 2 fingers.) “7.”
“The answer is 7.”
Example: 2 + 5 = ?
1.
2.
3.
“5.”
(Hold up 1 finger.) “6.”
(Hold up 2 fingers.) “7.”
“The answer is 7.”
1.
2.
3.
“2.”
(Hold up 1 finger.) “3.”
(Hold up 2 fingers.) “4.”
(Hold up 3 fingers.) “5.”
“The answer is 3.”
43
Introductory Unit:
Finding X in All 3
Positions of Equation



If X is at the end of a number sentence, do
what the problem tells you to do (e.g., 3 +
2 = X; 6 – 2 = X)
If X is not at the end, and it’s an “X minus”
problem, add (e.g., X – 2 = 4).
If X is not at the end, and it’s not a X
minus problem, subtract (e.g., X + 2 = 8; 5
– X = 2; 7 + X = 12).
44
Introductory Unit:
Checking Work
CHECKING YOUR WORK
1. Sense
Does the work make sense?
2. Lining Up
Did I line up the numbers correctly?
3. Math
Did I add or subtract correctly?
4. Labels
Did I use a label?
5. Signs
Did I use signs correctly?
45
Remaining Units:
Word-Problem Lessons
Following Unit 1, four activities per session.
1. Flash-card warm up
2. Conceptual/strategic lesson using schema-broadening
instruction
3. Sorting practice on identifying problem types
4. Paper/pencil review
46
1. Math Fact Flash Card Warm Up
Math Fact flash cards comprise 200 addition and 11
subtraction facts
- 6
− Sums 0-18
− Subtrahends 0-18
 Tutor shows flash card to student: Know it or Count Up!
− If student answers correctly, flash card placed in
correct pile.
− If student answers incorrectly, tutor asks student to
4
“Count Up”; once correct, goes in correct pile.
+ 5
− Student graphs score on graph.

47
2. Lesson
Pirate Math RUN

Students use “RUN”
strategy for every
word problem.
RUN!
1. Read the problem.
2. Underline the question.
3. Name the problem type.

Students learn to
circle relevant
information directly
in the text or
picture/graph/chart.
48
2. Lesson
Pirate Math Setting Up Work






Write the equation that goes with the problem type.
Figure out what’s missing. Write X in your equation in
the appropriate slot.
Figure out what numbers are known. Write those
numbers in the appropriate slots.
Write the math signs.
Find X.
Make sure your answer has a number and a label.
49
2. Lesson
Problem Types with Transfer


Problem types at grade 2:
Total, Difference, and
Change
Transfer features:
− Irrelevant
information
− Money
− Double-digit
calculations
− Finding relevant
information in graphs
and pictures.
− Combining problem
types.
50
2. Lesson
Pirate Math Change



Change problems with
a starting amount that
increases or decreases
(a change) to make it a
new amount.
“Sarah had 10 pencils.
Then she gave 4 pencils
to Pamela. How many
pencils does Sarah have
now?”
St +/- C = E
CHANGE
1. How many do you start with? (St)
2. How many do you change? (C)
Is there an increase? +
Is there a decrease? 3. How many do you end with? (E)
St
+ or -
C
=
E
4. Write the number sentence.
5. Find X!
51
“Sarah had 10 pencils. Then, she gave 4 pencils to Pamela.
How many pencils does Sarah have now?”
52
“Sarah had 10 pencils. Then, she gave 4 pencils to Pamela.
How many pencils does Sarah have now?”
Recognize problem type: Change problem.
Write equation for Change problems: St +/- C = E.
Identify missing information (E). Write that in the appropriate slot
St +/- C = E
X
Identify the important given numbers (St and C). Write those in the
appropriate slots.
St +/- C = E
10
4 X
Write math signs.
St +/- C = E
10 - 4 = X
Find X: X is at end so do what problem tells me to do: 10 – 4 = 6;
X=6.
Label answer: 6 pencils.
53
Lexie had some comic books in her desk. Then she bought 8
more. Now, she has 12 comic books. How many comic
books did Lexie have in her desk to begin with?
54
Lexie had some comic books in her desk. Then she bought 8
more. Now, she has 12 comic books. How many comic
books did Lexie have in her desk to begin with?
Recognize problem type: Change problem.
Write equation for Change problems: St +/- C = E.
Identify missing information (St). Write that in the appropriate slot
St +/- C = E
X
Identify the important given numbers (St and C). Write those in the
appropriate slots.
St +/- C = E
X
8 12
Write math signs.
St +/- C = E
X + 8 = 12
Find X: X is not at end and it’s not an X minus problem, so subtract: 12
– 8 = 4; X=4.
Label answer: 4 comic books.
55
Alicia has 3 friends in her math class. The
chart shows how many stars Alicia and her
friends earned on Monday. On Tuesday,
Alicia lost 3 stars for talking. How many
stars does she have now?
Monday’s Star Chart
Milo
Trish
David
Alicia
0
2
4
6
8
10
Number of Gold Stars
56
Recognize problem type: Change problem.
Identify transfer features: Irrelevant information (cross it out) and
relevant information in a graph (number the graph).
Write equation for Change problems: St +/- C = E.
Identify missing information (St). Write that in the appropriate slot
St +/- C = E
X
Identify the important given numbers (St and C). Write those in the
appropriate slots.
St +/- C = E
8
3 X
Write math signs.
St +/- C = E
8 - 3=X
Find X: X is at end, so do what the problem says: 8 – 3 = 5; X=5.
Label answer: 5 stars.
57
2. Lesson
Pirate Math Total




Total problems have two
parts that are combined
for a total.
Total amount is the entire
or combined amount.
“Sarah has 5 pencils.
Pamela has 3 pencils.
How many pencils do the
girls have in all?”
P1 + P2 = T
58
2. Lesson
Pirate Math Difference



Difference problems
compare two amounts to
find the difference
between them.
“Sarah has 7 pencils.
Pamela has 12 pencils.
How many more pencils
does Pamela have than
Sarah?”
B–s=D
59
3. Sorting




Student sorts word problems by problem type for
2 minutes.
Tutor reads cards to student.
Student places cards on Sorting Mat.
At end of 2 minutes, tutor counts number of
correctly sorted cards and uses correction
procedure for up to 3 incorrectly sorted cards.
60
3. Sorting
Sorting Mat
Total
Difference
Change
?
61
3. Sorting
Maria and Jackie picked
16 flowers. Jackie
picked 7 flowers. How
many flowers did Maria
pick?
Maria picked 8 more
flowers than Jackie.
Jackie picked 4 flowers.
How many flowers did
Maria pick?
Maria picked 11 flowers.
Then Jackie took 4 of
them for her Mom. How
many flowers does
Maria have now?
62
4. Paper/pencil review
* 10 math facts
* 4 double-digit calculations
* 1 word problem
63
Motivation during Pirate Math



Students earn coins
throughout lesson for
listening well, working hard,
following directions, and
correct work.
At end of lesson, students
color footsteps on treasure
map equaling amount of
coins earned.
When students color 16
footsteps, they pick a prize
from treasure box and
receive a new map.
64
Examined Efficacy
of Two Tutoring Programs

The exclusive focus of math facts tutoring
was math facts

The primary focus of Pirate Math tutoring
was word problems
− but it also addressed foundational skills
(math facts, procedural calculations, and
algebra skills)
65
Efficacy:
Fluency with Math Facts and
Procedural Calculations

On math facts, Pirate Math effects superior improvement
compared to control group. No difference between
Pirate Math and math facts tutoring. Notable, because
Pirate Math only allocates an initial lesson and then 4-6
minutes per session on number combinations.

On procedural calculations, Pirate Math effects superior
improvement compared to control group and compared
to math facts tutoring. Again, little time spent on
procedural calculations.
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Efficacy:
Algebra

On algebra, Pirate Math effects superior outcomes
compared to control group and compared to math facts
tutoring.

Algebraic cognition improved even though students
were severely deficient in math and young.

Given strong focus on algebra in high schools, given
graduation requirements for algebra, and given
emphasis in NMAP, introducing algebra earlier in the
curriculum may represent a productive innovation.
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Correct Representation
68
Correct Representation
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Incorrect Representation
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Over Efficacy Results: Word Problems

Work on these foundation skills (MFs, procedural calculations,
algebra), combined with schema-broadening instruction, also
produced differential growth on WP outcomes compared to MF
tutoring group and compared to control group.

MF tutoring did not result in improvement on WPs.

Lack of transfer suggests that source of difficulty is not diverting
attention from the complex mathematics to the MFs embedded in
those problems, but rather failing to comprehend the relations
among the numbers embedded in the narratives or to process the
language in those stories adequately.

Suggests that MFs may not be the bottleneck for WP performance.
Instead, mathematics disability represents a more complicated
pattern of difficulty, implicating language (as has been suggested
elsewhere).
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Is Tutoring Differentially Efficacious
Depending on MD Status (MD vs. MDRD)?

Why We Hypothesized MD students would be more
responsive to tutoring than MDRD students
For MFs
− A key deficit among students with reading difficulty is
phonological processing and
− Phonological processing deficits are linked with difficulty in
automatic retrieval of MFs.

For WPs
− Using text to construct a WP model involves language
− Language profiles of students with MDRD are depressed
compared to students with MD.
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Is Tutoring Differentially Efficacious
Depending on MD Status (MD vs. MDRD)?

No evidence of differential responsiveness to
intervention as a function of difficulty status on any
outcome.

Raises questions about the tenability of the MD/MDRD
subtyping scheme and suggests the need to pursue
other avenues for subtyping mathematics disability.

Even so, across tutoring conditions and sites, students
with MD outperformed students with MDRD at pre- and
posttest.

Additional work to examine the tenability of the
MD/MDRD subtyping scheme is warranted, even as
research pursuing alternative frameworks proceeds.
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These Tutoring Protocols
Are Transportable
No MD/MDRD by treatment by site effects.
No treatment by site effects.
Tutoring protocols were comparably
effective in Nashville and Houston, for MD
and for MDRD students.
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Overall Conclusions

MF tutoring enhances fluency with MFs
with transfer to procedural calculations but
without transfer to algebra or WPs.

For a comparable amount of tutoring time,
WP tutoring (with work on foundational
skills) enhances WP skill, fluency with
MFs, procedural calculations, and algebra.
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For Materials, Contact:
Flora Murray
flora.murray@vanderbilt.edu
Vanderbilt University
228 Peabody College
Department of Special Education
Nashville, TN 37203
(615) 343-4782
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