Pirate Math Individual Tutoring
Study: Fuchs et al. (2009)
Summary
Pirate Math Individual Tutoring is a tutoring program for remediating the calculation and wordproblem deficits and for promoting the algebraic cognition of thirdgrade students atrisk or with identified math disability. The program is based on schemabroadening instruction, with which students learn to think about word problems in terms of problem types and learn to classify word problems in terms of those problem types, even when the problems incorporate irrelevant information or involve money or incorporate relevant information in pictures, charts, or figures or combine problem types so that problems require 2step solutions. Students learn to represent the structure of each type of word problem using an algebraic equation and learn to solve those algebraic equations. The program is organized in terms of 4 units. The first unit teaches skills that are foundational skills to word problems (counting strategies for answering math facts, 2step procedural calculations, solving algebraic equations, and checking wordproblem solutions). Then, each of the next 3 units focuses on one problem type, with systematic cumulative review embedded throughout the units. The three problem types are two problems (where two quantities are combined to make a new amount), difference problems (where two quantities are compared), and change problems (where an event occurs to increase or decrease an initial amount). Sessions occur 3 times per week for 2030 minutes per sessions across 16 weeks on a onetoone basis. Tutors can be certified or noncertified teachers, each of whom is trained in a 1day session and then supervised with biweekly meetings. Pirate Math has been shown to improve outcomes on math fact fluency, procedural computational skill, wordproblem skill, and algebra skill.
 Target Grades:
 3
 Target Populations:

 Students with disabilities only
 Students with learning disabilities
 Any student at risk for academic failure
 Area(s) of Focus:

 Computation
 Concepts and/or word problems
 Algebra
 Where to Obtain:
 Lynn S. Fuchs, Pamela M. Seethaler, Sarah R. Powell, & Douglas Fuchs
 228 Peabody Vanderbilt University, Nashville, TN 37203
 6153434782
 www.kc.vanderbilt.edu/pals
 Initial Cost:
 $40.00 per school
 Replacement Cost:
 Free

Each Pirate Math Individual Tutoring manual costs $40. The Pirate Math manual contains 48 lessons. Each lesson has a tutor script (which is reviewed but not read verbatim) and templates for student worksheets. The manual also has templates for math fact flash cards, wordproblem sorting cards, graphs to monitor student progress, and treasure maps for motivation. All templates required for implementation are included in the manual. (The only additional materials required are pencils and highlighters.)
 Staff Qualified to Administer Include:

 Special Education Teacher
 General Education Teacher
 Reading Specialist
 Math Specialist
 EL Specialist
 Interventionist
 Student Support Services Personnel (e.g., counselor, social worker, school psychologist, etc.)
 Paraprofessional
 Other:
 Training Requirements:
 Training not required

One fullday workshop of instruction; practice implementing the procedures alone and with other tutors during the subsequent week; a practice session conducted with a supervisor who provides corrective feedback; tutors studying (not reading) scripts; and meetings among tutors and the supervisor every 23 weeks to address problems or questions are they arise. For additional details, please visist Fuchs Tutoring Professional Learning at https://www.air.org/fuchstutoringprofessionallearning.
The manuals guided implementation of tutoring during the series of studies conducted with Pirate Math both at the site proximal to the developers and at a site distal to the developers, with comparable effects at both sides. The training procedures were identical to those recommended above.
 Access to Technical Support:
 The manuals guided implementation of tutoring during the series of studies conducted with Pirate Math both at the site proximal to the developers and at a site distal to the developers, with comparable effects at both sides. The training procedures were identical to those recommended above.
 Recommended Administration Formats Include:

 Individual students
 Minimum Number of Minutes Per Session:
 20
 Minimum Number of Sessions Per Week:
 3
 Minimum Number of Weeks:
 16
 Detailed Implementation Manual or Instructions Available:
 Yes
 Is Technology Required?
 No technology is required.
Program Information
Descriptive Information
Please provide a description of program, including intended use:
Pirate Math Individual Tutoring is a tutoring program for remediating the calculation and wordproblem deficits and for promoting the algebraic cognition of thirdgrade students atrisk or with identified math disability. The program is based on schemabroadening instruction, with which students learn to think about word problems in terms of problem types and learn to classify word problems in terms of those problem types, even when the problems incorporate irrelevant information or involve money or incorporate relevant information in pictures, charts, or figures or combine problem types so that problems require 2step solutions. Students learn to represent the structure of each type of word problem using an algebraic equation and learn to solve those algebraic equations. The program is organized in terms of 4 units. The first unit teaches skills that are foundational skills to word problems (counting strategies for answering math facts, 2step procedural calculations, solving algebraic equations, and checking wordproblem solutions). Then, each of the next 3 units focuses on one problem type, with systematic cumulative review embedded throughout the units. The three problem types are two problems (where two quantities are combined to make a new amount), difference problems (where two quantities are compared), and change problems (where an event occurs to increase or decrease an initial amount). Sessions occur 3 times per week for 2030 minutes per sessions across 16 weeks on a onetoone basis. Tutors can be certified or noncertified teachers, each of whom is trained in a 1day session and then supervised with biweekly meetings. Pirate Math has been shown to improve outcomes on math fact fluency, procedural computational skill, wordproblem skill, and algebra skill.
The program is intended for use in the following age(s) and/or grade(s).
Age 35
Kindergarten
First grade
Second grade
Third grade
Fourth grade
Fifth grade
Sixth grade
Seventh grade
Eighth grade
Ninth grade
Tenth grade
Eleventh grade
Twelth grade
The program is intended for use with the following groups.
Students with learning disabilities
Students with intellectual disabilities
Students with emotional or behavioral disabilities
English language learners
Any student at risk for academic failure
Any student at risk for emotional and/or behavioral difficulties
Other
If other, please describe:
ACADEMIC INTERVENTION: Please indicate the academic area of focus.
Early Literacy
Alphabet knowledge
Phonological awareness
Phonological awarenessEarly writing
Early decoding abilities
Other
If other, please describe:
Language
Grammar
Syntax
Listening comprehension
Other
If other, please describe:
Reading
Phonics/word study
Comprehension
Fluency
Vocabulary
Spelling
Other
If other, please describe:
Mathematics
Concepts and/or word problems
Whole number arithmetic
Comprehensive: Includes computation/procedures, problem solving, and mathematical concepts
Algebra
Fractions, decimals (rational number)
Geometry and measurement
Other
If other, please describe:
Writing
Spelling
Sentence construction
Planning and revising
Other
If other, please describe:
BEHAVIORAL INTERVENTION: Please indicate the behavior area of focus.
Externalizing Behavior
Verbal Threats
Property Destruction
Noncompliance
High Levels of Disengagement
Disruptive Behavior
Social Behavior (e.g., Peer interactions, Adult interactions)
Other
If other, please describe:
Internalizing Behavior
Anxiety
Social Difficulties (e.g., withdrawal)
School Phobia
Other
If other, please describe:
Acquisition and cost information
Where to obtain:
 Address
 228 Peabody Vanderbilt University, Nashville, TN 37203
 Phone Number
 6153434782
 Website
 www.kc.vanderbilt.edu/pals
Initial cost for implementing program:
 Cost
 $40.00
 Unit of cost
 school
Replacement cost per unit for subsequent use:
 Cost
 $0.00
 Unit of cost
 Duration of license
Additional cost information:
Describe basic pricing plan and structure of the program. Also, provide information on what is included in the published program, as well as what is not included but required for implementation (e.g., computer and/or internet access)
Each Pirate Math Individual Tutoring manual costs $40. The Pirate Math manual contains 48 lessons. Each lesson has a tutor script (which is reviewed but not read verbatim) and templates for student worksheets. The manual also has templates for math fact flash cards, wordproblem sorting cards, graphs to monitor student progress, and treasure maps for motivation. All templates required for implementation are included in the manual. (The only additional materials required are pencils and highlighters.)Program Specifications
Setting for which the program is designed.
Small group of students
BI ONLY: A classroom of students
If groupdelivered, how many students compose a small group?
Program administration time
 Minimum number of minutes per session
 20
 Minimum number of sessions per week
 3
 Minimum number of weeks
 16
 If intervention program is intended to occur over less frequently than 60 minutes a week for approximately 8 weeks, justify the level of intensity:
Does the program include highly specified teacher manuals or step by step instructions for implementation? Yes
BEHAVIORAL INTERVENTION: Is the program affiliated with a broad school or classwide management program?
If yes, please identify and describe the broader school or classwide management program: 
Does the program require technology?  No

If yes, what technology is required to implement your program? 
Computer or tablet
Internet connection
Other technology (please specify)
If your program requires additional technology not listed above, please describe the required technology and the extent to which it is combined with teacher smallgroup instruction/intervention:
Training
 How many people are needed to implement the program ?
Is training for the instructor or interventionist required? No
 If yes, is the necessary training free or atcost?
Describe the time required for instructor or interventionist training: 48 hours of training
Describe the format and content of the instructor or interventionist training: One fullday workshop of instruction; practice implementing the procedures alone and with other tutors during the subsequent week; a practice session conducted with a supervisor who provides corrective feedback; tutors studying (not reading) scripts; and meetings among tutors and the supervisor every 23 weeks to address problems or questions are they arise. For additional details, please visist Fuchs Tutoring Professional Learning at https://www.air.org/fuchstutoringprofessionallearning.
What types or professionals are qualified to administer your program?
General Education Teacher
Reading Specialist
Math Specialist
EL Specialist
Interventionist
Student Support Services Personnel (e.g., counselor, social worker, school psychologist, etc.)
Applied Behavior Analysis (ABA) Therapist or Board Certified Behavior Analyst (BCBA)
Paraprofessional
Other
If other, please describe:
 Does the program assume that the instructor or interventionist has expertise in a given area?

No
If yes, please describe:
Are training manuals and materials available? Yes

Describe how the training manuals or materials were fieldtested with the target population of instructors or interventionist and students:  The manuals guided implementation of tutoring during the series of studies conducted with Pirate Math both at the site proximal to the developers and at a site distal to the developers, with comparable effects at both sides. The training procedures were identical to those recommended above.
Do you provide fidelity of implementation guidance such as a checklist for implementation in your manual?
Can practitioners obtain ongoing professional and technical support? 
Yes
If yes, please specify where/how practitioners can obtain support:
The manuals guided implementation of tutoring during the series of studies conducted with Pirate Math both at the site proximal to the developers and at a site distal to the developers, with comparable effects at both sides. The training procedures were identical to those recommended above.
Summary of Evidence Base
 Please identify, to the best of your knowledge, all the research studies that have been conducted to date supporting the efficacy of your program, including studies currently or previously submitted to NCII for review. Please provide citations only (in APA format); do not include any descriptive information on these studies. NCII staff will also conduct a search to confirm that the list you provide is accurate.
Study Information
Study Citations
Fuchs, L. S., Powell, S. R., Seethaler, P. M., Cirino, P. T., Fletcher, J. M., Fuchs, D., Hamlett, C. L. & Zumeta, R. O. (2009). Remediating Number Combination and Word Problem Deficits among Students with Mathematics Difficulties: A Randomized Control Trial . Journal of Educational Psychology, 101() 561576.
Participants
 Describe how students were selected to participate in the study:
 The study was conducted at two sites, both large urban school districts. Houston was distal and Nashville was proximal to the developers of the tutoring protocols. Thirdgrade students (n=924) were screened for inclusion in 63 classrooms in 18 schools. Seven schools and 23 classrooms were in Houston; 11 schools and 40 classrooms were in Nashville. Because tutoring focused on NCs or on WPs, we included students with low performance on a calculations screening measure or a WP screening measure. (Screening occurred in stepwise fashion; so students did not receive every measure.) The criterion applied for low performance on the calculations measure was < the 26th percentile. The criterion applied to the 5item wordproblem measure was a score of 0 or 1. (See measures for description of the screening measures.) All 924 students were administered the calculations measure; 302 (33%) scored < the 26th percentile. We administered the 5item WP screener to 598 students; 170 (28%) scored 0 or 1. Of the 598 students who took the calculations and the WP screening measures, 291 (49%) did not meet the inclusion criterion on either measure; 67 (11%) met only the WP criterion; 137 (23%) met only the calculations criterion; and 103 (17%) met both criteria. The 307 students who met either or both criteria were eligible for further screening on a reading and an abbreviated IQ measure. We excluded students who scored between the 25th and 40th percentiles in reading and students with a Tscore below 30 on both IQ subtests. Students scoring < the 26th percentile on the reading measure were classified as having math and reading difficulty (MDRD). Those scoring > 39th percentile were classified as math difficulty alone (MD). Two hundred and two students took all measures. Of these students, 32 (16%) were excluded due to reading scores between the 25th and 40th percentiles; two students were excluded due to low IQ scores; and one student was excluded for both reasons. Thus, 165 students were eligible for tutoring. However, 162 students comprised the actual assignment sample because three students who met all criteria were accidentally not included in the assignment sample. Blocking on site, type of screening difficulty (WPs, calculations, or both), and difficulty status (MD or MDRD), we randomly assigned students to one of three treatment conditions (NC tutoring, WP tutoring, or control). So, the composition of each treatment group was similar in terms of the three blocking variables. Of the 162 students, 13 (8%) moved after randomization but prior to the onset of tutoring, 7 (4%) moved during the school year, 5 (3%) were excluded by parents or schools prior to the onset of tutoring, and 4 (2%) were withdrawn by parents or schools during the school year, leaving 133 who were evaluated at posttest.
 Describe how students were identified as being at risk for academic failure (AI) or as having emotional or behavioral difficulties (BI):
 The study was conducted at two sites, both large urban school districts. Houston was distal and Nashville was proximal to the developers of the tutoring protocols. Thirdgrade students (n=924) were screened for inclusion in 63 classrooms in 18 schools. Seven schools and 23 classrooms were in Houston; 11 schools and 40 classrooms were in Nashville. Because tutoring focused on NCs or on WPs, we included students with low performance on a calculations screening measure or a WP screening measure. (Screening occurred in stepwise fashion; so students did not receive every measure.) The criterion applied for low performance on the calculations measure was < the 26th percentile. The criterion applied to the 5item wordproblem measure was a score of 0 or 1. (See measures for description of the screening measures.) All 924 students were administered the calculations measure; 302 (33%) scored < the 26th percentile. We administered the 5item WP screener to 598 students; 170 (28%) scored 0 or 1. Of the 598 students who took the calculations and the WP screening measures, 291 (49%) did not meet the inclusion criterion on either measure; 67 (11%) met only the WP criterion; 137 (23%) met only the calculations criterion; and 103 (17%) met both criteria. The 307 students who met either or both criteria were eligible for further screening on a reading and an abbreviated IQ measure. We excluded students who scored between the 25th and 40th percentiles in reading and students with a Tscore below 30 on both IQ subtests. Students scoring < the 26th percentile on the reading measure were classified as having math and reading difficulty (MDRD). Those scoring > 39th percentile were classified as math difficulty alone (MD). Two hundred and two students took all measures. Of these students, 32 (16%) were excluded due to reading scores between the 25th and 40th percentiles; two students were excluded due to low IQ scores; and one student was excluded for both reasons. Thus, 165 students were eligible for tutoring. However, 162 students comprised the actual assignment sample because three students who met all criteria were accidentally not included in the assignment sample. Blocking on site, type of screening difficulty (WPs, calculations, or both), and difficulty status (MD or MDRD), we randomly assigned students to one of three treatment conditions (NC tutoring, WP tutoring, or control). So, the composition of each treatment group was similar in terms of the three blocking variables. Of the 162 students, 13 (8%) moved after randomization, but prior to the onset of tutoring, 7 (4%) moved during the school year, 5 (3%) were excluded by parents or schools prior to the onset of tutoring, and 4 (2%) were withdrawn by parents or schools during the school year, leaving 133 who were evaluated at posttest.

ACADEMIC INTERVENTION: What percentage of participants were at risk, as measured by one or more of the following criteria:
 below the 30th percentile on local or national norm, or
 identified disability related to the focus of the intervention?
 %

BEHAVIORAL INTERVENTION: What percentage of participants were at risk, as measured by one or more of the following criteria:
 emotional disability label,
 placed in an alternative school/classroom,
 nonresponsive to Tiers 1 and 2, or
 designation of severe problem behaviors on a validated scale or through observation?
 %
 Specify which condition is the submitted intervention:
 WP tutoring or Pirate Math (referred to both ways in study)
 Specify which condition is the control condition:
 There was a notutoring (Tier 1 only) condition, which was the businessasusual condition, as well as a competing condition, which was an active tutoring condition devoted entirely to number combination (i.e., math facts). This competing condition controlled for tutoring time and for the motivational component of Pirate Math.
 If you have a third, competing condition, in addition to your control and intervention condition, identify what the competing condition is (data from this competing condition will not be used):
Using the tables that follow, provide data demonstrating comparability of the program group and control group in terms of demographics.
Grade Level
Demographic  Program Number 
Control Number 
Effect Size: Cox Index for Binary Differences 

Age less than 1  
Age 1  
Age 2  
Age 3  
Age 4  
Age 5  
Kindergarten  
Grade 1  
Grade 2  
Grade 3  89.4%  97.9%  1.09 
Grade 4  
Grade 5  
Grade 6  
Grade 7  
Grade 8  
Grade 9  
Grade 10  
Grade 11  
Grade 12 
Race–Ethnicity
Demographic  Program Number 
Control Number 
Effect Size: Cox Index for Binary Differences 

African American  51.1%  68.8%  0.46 
American Indian  
Asian/Pacific Islander  
Hispanic  23.4%  18.8%  0.15 
White  6.4%  8.3%  0.19 
Other  8.5%  2.1%  0.96 
Socioeconomic Status
Demographic  Program Number 
Control Number 
Effect Size: Cox Index for Binary Differences 

Subsidized Lunch  68.1%  75.0%  0.21 
No Subsidized Lunch  21.3%  22.9%  0.07 
Disability Status
Demographic  Program Number 
Control Number 
Effect Size: Cox Index for Binary Differences 

SpeechLanguage Impairments  
Learning Disabilities  14.9%  16.7%  0.09 
Behavior Disorders  
Emotional Disturbance  
Intellectual Disabilities  
Other  
Not Identified With a Disability  74.5%  81.3%  0.24 
ELL Status
Demographic  Program Number 
Control Number 
Effect Size: Cox Index for Binary Differences 

English Language Learner  17.0%  14.6%  0.09 
Not English Language Learner  72.3%  83.3%  0.39 
Gender
Demographic  Program Number 
Control Number 
Effect Size: Cox Index for Binary Differences 

Female  40.4%  33.3%  0.18 
Male  48.9%  64.6%  0.40 
Mean Effect Size
For any substantively (e.g., effect size ≥ 0.25 for pretest or demographic differences) or statistically significant (e.g., p < 0.05) pretest differences between groups in the descriptions below, please describe the extent to which these differences are related to the impact of the treatment. For example, if analyses were conducted to determine that outcomes from this study are due to the intervention and not demographic characteristics, please describe the results of those analyses here.
Design
 What method was used to determine students' placement in treatment/control groups?
 Random
 Please describe the assignment method or the process for defining treatment/comparison groups.
 Blocking on site, type of screening difficulty (WPs, calculations, or both), and difficulty status (MD or MDRD), we randomly assigned students to one of three treatment conditions (NC tutoring, WP tutoring, or control).

What was the unit of assignment?  Students
 If other, please specify:

Please describe the unit of assignment: 
What unit(s) were used for primary data analysis? 
Schools
Teachers
Students
Classes
Other
If other, please specify:

Please describe the unit(s) used for primary data analysis:
Fidelity of Implementation
 How was the program delivered?

Individually
Small Group
Classroom
If small group, answer the following:
 Average group size
 Minimum group size
 Maximum group size
What was the duration of the intervention (If duration differed across participants, settings, or behaviors, describe for each.)?
 Weeks
 16.00
 Sessions per week
 3.00
 Duration of sessions in minutes
 25.00
 What were the background, experience, training, and ongoing support of the instructors or interventionists?
 The tutors were parttime or fulltime employees of the research project. In Houston, tutors were not certified teachers, and they were drawn from the community. Each tutor had an undergraduate degree, but the degrees were not necessarily in educationrelated fields. In Nashville, tutors were graduate students across departments at Vanderbilt University (3 were certified teachers; 9 were not). The graduate students were not necessarily in education programs. Tutors were trained as follows: 1 session of instruction; practice implementing the procedures alone and with each other during the subsequent week; a practice session conducted with a supervisor who provides corrective feedback; tutors studying (not reading) scripts; and meeting among tutors and the supervisor every 23 weeks to address problems or questions as they arise.
 Describe when and how fidelity of treatment information was obtained.
 Every tutoring session was audiotaped. Four research assistants independently listened to tapes while completing a checklist to identify the percentage of essential points in that lesson. We sampled 16.8 of tapes such that treatments, tutors, and lesson types at each site were examined comparably.
 What were the results on the fidelityoftreatment implementation measure?
 At the site where the protocols had been developed (Nashville), the mean percentage of points addressed was 98.1 (SD=2.06) for number combinations (competing) tutoring and 98.4 (SD=2.79) for WP (Pirate Math) tutoring. In Houston, the mean percentage of points addressed was 99.5 (SD=0.47) for number combinations (competing) tutoring and 99.2 (SD=0.68) for WP (Pirate Math) tutoring.
Tutors also recorded the duration of each session. In Nashville, tutoring min averaged 1032 (SD=85.08) for number combinations (competing) tutoring and 997 (SD=130.25) for WP (Pirate Math) tutoring. In Houston, total tutoring min averaged 1155 (SD=130.09) for number combinations (competing) tutoring and 1158 (SD=184.69) for WP (Pirate Math) tutoring. Analysis of variance revealed a significant effect for site, F(1,82)=15.68, p<.001, with more time in Houston than Nashville. More pertinently, the effect for treatment condition was not significant, F(1,82)=0.18, p=.669; neither was the interaction between treatment and site, F(1,82)=0.27, p =.603.
 Was the fidelity measure also used in control classrooms?
Measures and Results
Measures Broader :
Targeted Measure  Reverse Coded?  Reliability  Relevance  Exposure 

Broader Measure  Reverse Coded?  Reliability  Relevance  Exposure 

Administrative Data Measure  Reverse Coded?  Relevance 

Effect Size
Effect size represents the how much performance changed because of the intervention. The larger the effect size, the greater the impact participating in the intervention had.
According to guidelines from the What Works Clearinghouse, an effect size of 0.25 or greater is “substantively important.” Additionally, effect sizes that are statistically significant are more trustworthy than effect sizes of the same magnitude that are not statistically significant.
Effect Size Dial
The purpose of the effect size dial is to help users understand the strength of a tool relative to other tools on the Tools Chart.
 The range represents where most effect sizes fall within reading or math based on effect sizes from tools on the Tools Chart.
 The orange pointer shows the average effect size for this study.
Targeted Measures (Full Sample)
Average Math Effect Size
Measure  Sample Type  Effect Size 

Average across all targeted measures  Full Sample  4.85* 
* = p ≤ 0.05; † = Vendor did not provide necessary data for NCII to calculate effect sizes. 
Broader Measures (Full Sample)
Average Math Effect Size
Measure  Sample Type  Effect Size 

Average across all broader measures  Full Sample  3.16* 
* = p ≤ 0.05; † = Vendor did not provide necessary data for NCII to calculate effect sizes. 
Administrative Measures (Full Sample)
Measure  Sample Type  Effect Size 

Average across all admin measures  Full Sample   
* = p ≤ 0.05; † = Vendor did not provide necessary data for NCII to calculate effect sizes. 
Targeted Measures (Subgroups)
Measure  Sample Type  Effect Size 

* = p ≤ 0.05; † = Vendor did not provide necessary data for NCII to calculate effect sizes. 
Broader Measures (Subgroups)
Measure  Sample Type  Effect Size 

* = p ≤ 0.05; † = Vendor did not provide necessary data for NCII to calculate effect sizes. 
Administrative Measures (Subgroups)
Measure  Sample Type  Effect Size 

* = p ≤ 0.05; † = Vendor did not provide necessary data for NCII to calculate effect sizes. 
 For any substantively (e.g., effect size ≥ 0.25 for pretest or demographic differences) or statistically significant (e.g., p < 0.05) pretest differences, please describe the extent to which these differences are related to the impact of the treatment. For example, if analyses were conducted to determine that outcomes from this study are due to the intervention and not pretest characteristics, please describe the results of those analyses here.
 Please explain any missing data or instances of measures with incomplete pre or posttest data.
 If you have excluded a variable or data that are reported in the study being submitted, explain the rationale for exclusion:
 Describe the analyses used to determine whether the intervention produced changes in student outcomes:
 We conducted distributional exploration of each measure via statistical (e.g., skewness, kurtosis) and graphical (e.g., box plots, stem and leaf plots) means. Generally, the standardized variables were normally distributed at both time points. However, Vanderbilt Story Problems was positively skewed and kurtotic at both time points, and Find X was negatively skewed at pretest and bimodal at posttest. In the case of Vanderbilt Story Problems, a squareroot transformation was completed, which improved distribution; however, because results for the original and the transformed variables were similar, results of the original variable are presented for ease of interpretation. Similarly, for Find X, logistic analyses (dichotomizing scores into high and low) yielded similar results as the original variables; so we retained the original form. Number Sentences at pretest and procedural computations at posttest also showed some skewness, but transformations did not generally improve distributions. Age was unrelated to pre or posttest performance. Also, tutoring time was unrelated to all but two outcomes, and in this case, the relation was small and did not interact with other effects or change conclusions. Therefore, these variables are not reported. The factors of interest were difficulty status (MD vs. MDRD), site (Houston vs. Nashville), and tutoring condition (number combinations, i.e., competing condition, tutoring vs. WP, i.e., Pirate Math, tutoring vs. control).
Additional Research
 Is the program reviewed by WWC or EESSA?
 EESSA
 Summary of WWC / EESSA Findings :
What Works Clearinghouse Review
This program was not reviewed by What Works Clearinghouse.
Evidence for ESSA
Program Outcomes: One qualifying study of Pirate Math took place in Nashville and Houston. Lowachieving students in Pirate Math were compared to similar control students. On Key Math, students in Pirate Math scored significantly higher than controls, with an effect size of +0.37. This qualified Pirate Math for the ESSA “Strong” category.
Number of Studies: 1
Average Effect Size: 0.37
 How many additional research studies are potentially eligible for NCII review?
 3
 Citations for Additional Research Studies :
Fuchs, L.S., Powell, S.R., Seethaler, P.R., Cirino, P.T., Fletcher, J.M., Fuchs, D., & Hamlett, C.L. (2010). The effects of strategic counting instruction, with and without deliberate practice, on number combinations skill among students with mathematics difficulties. Learning and Individual Differences, 20, 89100. doi:10.1016/j.lindif.2009.09.003
Fuchs, L.S., Powell, S.R., Seethaler, P.M., Cirino, P.T., Fletcher, J.M., Fuchs, D., Hamlett, C.L., & Zumeta, R.O. (2009). Remediating number combination and word problem deficits among students with mathematics difficulties: A randomized control trial. Journal of Educational Psychology, 101, 561576. doi:10.1037/a0014701
Fuchs, L.S., Seethaler, P.M., Powell, S.R., Fuchs, D., Hamlett, C.L., & Fletcher, J.M. (2008) Effects of preventative tutoring on the mathematical problem solving of thirdgrade students with math and reading difficulties. Exceptional Children, 74, 155173.
Data Collection Practices
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