Number Rockets
Study: Fuchs et al. (2005)

Summary

Number Rockets is a small-group tutoring program based on the concrete-representational-abstract model (Butler et al., 2003; Cass, Cates, Smith, & Jackson, 2003; Mercer, Jordan, & Miller, 1996), which relies on concrete objects to promote conceptual learning. Lessons followed a sequence of 17 scripted topics, and each topic includes worksheet and manipulative (e.g., base-10 blocks for place value instruction) activities. The sequence of topics is: identifying and writing numbers to 99; identifying more, less, and equal with objects; sequencing numbers; using <, >, and = symbols; skip counting by 10s, 5s, and 2s; understanding place value (introduction); identifying operations; place value (0-50); writing number sentences; place value (0-99); addition facts (sums to 18); subtraction facts (minuends to 18); review of addition and subtraction facts; place value; 2-digit addition (no regrouping); 2-digit subtraction (no regrouping); and missing addends. Review of topics 1-4 is conducted after winter break. Thirteen topics are each addressed in three sessions; the remaining four topics, in six sessions. Mastery of the topic is assessed each day. If every student in the group achieves mastery prior to the last day of the topic, the group moves to the next topic. For mastery assessment, students complete worksheets independently, with percentage of correct answers determining mastery (for most topics, 90% accuracy). After the last day on a topic, the group progresses to the next topic regardless of mastery status. On the first day of each topic, the students complete a cumulative review worksheet covering previous topics. Mastery assessment and cumulative review takes approximately 10 min and provides additional practice. Throughout each tutoring session, tutors award points to students for appropriate behavior. As point sheets are completed, students trade points for prizes (e.g., pencils, erasers, stickers). Tutors follow scripts to ensure consistency but are not permitted to read or memorize scripts. During the final 10 min of each intervention session, students complete drill and practice activities to help students develop automatic retrieval of math facts, and students are taught efficient counting strategies as backups to automatic retrieval.

Target Grades:
1
Target Populations:
  • Students with disabilities only
  • Students with learning disabilities
  • Students with intellectual disabilities
  • Students with emotional or behavioral disabilities
  • Any student at risk for academic failure
Area(s) of Focus:
  • Computation
  • Concepts and/or word problems
Where to Obtain:
Lynn Fuchs, Kim Paulsen, Doug Fuchs, Joan Bryant
228 Peabody Vanderbilt University, Nashville, TN 37220
615-343-4782
www.peerassistedlearningstrategies.net
Initial Cost:
$80.00 per tutor
Replacement Cost:
$25.00 per student per year

Initial cost per student for implementing program: $80 per tutor plus ~$25 per student in copying. Replacement cost per student for subsequent use: ~$25. The manual provides all information necessary for implementation and include masters of all materials. Schools need to make copies of materials (we recommend lamination for posters and reusable materials) and provide concrete reinforcers and manipulatives involved in the program. INCLUDED: Manual ($40), masters of all materials ($40) NOT INCLUDED: individual student copies of materials, concrete reinforcers, manipulatives

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:
1 day of training plus follow up by school or district staff

In a 1-day training session for tutors, (a) an overview of the tutoring program, goals, and topics is presented, and (b) the tutoring procedures are explained for each activity in the first 4 tutoring topics. After presentation of each activity, tutors practice the activity with a partner, with more practice completed in the next 2 weeks. One week later, in a second session, tutors learn the drill/practice math fact activities. At the end of that week, a review session is held. Tutoring begins one week later. Also, tutors attend weekly meetings to learn about and practice upcoming tutoring topics. In these weekly sessions, tutors also discuss difficulties they face. These sessions are supervised by a building or district instructional support person.


The manuals have already been used widely, and users report high levels of satisfaction.

Access to Technical Support:
Contact Flora.Murray@vanderbilt.edu for information on how to arrange a 1-day workshop.
Recommended Administration Formats Include:
  • Individual students
  • Small group of students
Minimum Number of Minutes Per Session:
40
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:

Number Rockets is a small-group tutoring program based on the concrete-representational-abstract model (Butler et al., 2003; Cass, Cates, Smith, & Jackson, 2003; Mercer, Jordan, & Miller, 1996), which relies on concrete objects to promote conceptual learning. Lessons followed a sequence of 17 scripted topics, and each topic includes worksheet and manipulative (e.g., base-10 blocks for place value instruction) activities. The sequence of topics is: identifying and writing numbers to 99; identifying more, less, and equal with objects; sequencing numbers; using <, >, and = symbols; skip counting by 10s, 5s, and 2s; understanding place value (introduction); identifying operations; place value (0-50); writing number sentences; place value (0-99); addition facts (sums to 18); subtraction facts (minuends to 18); review of addition and subtraction facts; place value; 2-digit addition (no regrouping); 2-digit subtraction (no regrouping); and missing addends. Review of topics 1-4 is conducted after winter break. Thirteen topics are each addressed in three sessions; the remaining four topics, in six sessions. Mastery of the topic is assessed each day. If every student in the group achieves mastery prior to the last day of the topic, the group moves to the next topic. For mastery assessment, students complete worksheets independently, with percentage of correct answers determining mastery (for most topics, 90% accuracy). After the last day on a topic, the group progresses to the next topic regardless of mastery status. On the first day of each topic, the students complete a cumulative review worksheet covering previous topics. Mastery assessment and cumulative review takes approximately 10 min and provides additional practice. Throughout each tutoring session, tutors award points to students for appropriate behavior. As point sheets are completed, students trade points for prizes (e.g., pencils, erasers, stickers). Tutors follow scripts to ensure consistency but are not permitted to read or memorize scripts. During the final 10 min of each intervention session, students complete drill and practice activities to help students develop automatic retrieval of math facts, and students are taught efficient counting strategies as backups to automatic retrieval.

The program is intended for use in the following age(s) and/or grade(s).

not selected Age 0-3
not selected Age 3-5
not selected Kindergarten
selected First grade
not selected Second grade
not selected Third grade
not selected Fourth grade
not selected Fifth grade
not selected Sixth grade
not selected Seventh grade
not selected Eighth grade
not selected Ninth grade
not selected Tenth grade
not selected Eleventh grade
not selected Twelth grade


The program is intended for use with the following groups.

selected Students with disabilities only
selected Students with learning disabilities
selected Students with intellectual disabilities
selected Students with emotional or behavioral disabilities
not selected English language learners
selected Any student at risk for academic failure
not selected Any student at risk for emotional and/or behavioral difficulties
not selected Other
If other, please describe:

ACADEMIC INTERVENTION: Please indicate the academic area of focus.

Early Literacy

not selected Print knowledge/awareness
not selected Alphabet knowledge
not selected Phonological awareness
not selected Phonological awarenessEarly writing
not selected Early decoding abilities
not selected Other

If other, please describe:

Language

not selected Expressive and receptive vocabulary
not selected Grammar
not selected Syntax
not selected Listening comprehension
not selected Other
If other, please describe:

Reading

not selected Phonological awareness
not selected Phonics/word study
not selected Comprehension
not selected Fluency
not selected Vocabulary
not selected Spelling
not selected Other
If other, please describe:

Mathematics

selected Computation
selected Concepts and/or word problems
not selected Whole number arithmetic
not selected Comprehensive: Includes computation/procedures, problem solving, and mathematical concepts
not selected Algebra
not selected Fractions, decimals (rational number)
not selected Geometry and measurement
not selected Other
If other, please describe:

Writing

not selected Handwriting
not selected Spelling
not selected Sentence construction
not selected Planning and revising
not selected Other
If other, please describe:

BEHAVIORAL INTERVENTION: Please indicate the behavior area of focus.

Externalizing Behavior

not selected Physical Aggression
not selected Verbal Threats
not selected Property Destruction
not selected Noncompliance
not selected High Levels of Disengagement
not selected Disruptive Behavior
not selected Social Behavior (e.g., Peer interactions, Adult interactions)
not selected Other
If other, please describe:

Internalizing Behavior

not selected Depression
not selected Anxiety
not selected Social Difficulties (e.g., withdrawal)
not selected School Phobia
not selected Other
If other, please describe:

Acquisition and cost information

Where to obtain:

Address
228 Peabody Vanderbilt University, Nashville, TN 37220
Phone Number
615-343-4782
Website
www.peerassistedlearningstrategies.net

Initial cost for implementing program:

Cost
$80.00
Unit of cost
tutor

Replacement cost per unit for subsequent use:

Cost
$25.00
Unit of cost
student
Duration of license
year

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)

Initial cost per student for implementing program: $80 per tutor plus ~$25 per student in copying. Replacement cost per student for subsequent use: ~$25. The manual provides all information necessary for implementation and include masters of all materials. Schools need to make copies of materials (we recommend lamination for posters and reusable materials) and provide concrete reinforcers and manipulatives involved in the program. INCLUDED: Manual ($40), masters of all materials ($40) NOT INCLUDED: individual student copies of materials, concrete reinforcers, manipulatives

Program Specifications

Setting for which the program is designed.

selected Individual students
selected Small group of students
not selected BI ONLY: A classroom of students

If group-delivered, how many students compose a small group?

   2-3

Program administration time

Minimum number of minutes per session
40
Minimum number of sessions per week
3
Minimum number of weeks
16
not selected N/A (implemented until effective)

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 class-wide management program?

If yes, please identify and describe the broader school- or class-wide management program:

Does the program require technology?
No

If yes, what technology is required to implement your program?
not selected Computer or tablet
not selected Internet connection
not selected 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 small-group instruction/intervention:
There are two options for delivering math fact practice, one with and one without computers. So use of computers is optional; if computers are selected, iBooks or other MAC computers are needed.

Training

How many people are needed to implement the program ?

Is training for the instructor or interventionist required?
Yes
If yes, is the necessary training free or at-cost?

Describe the time required for instructor or interventionist training:
1 day of training plus follow up by school or district staff

Describe the format and content of the instructor or interventionist training:
In a 1-day training session for tutors, (a) an overview of the tutoring program, goals, and topics is presented, and (b) the tutoring procedures are explained for each activity in the first 4 tutoring topics. After presentation of each activity, tutors practice the activity with a partner, with more practice completed in the next 2 weeks. One week later, in a second session, tutors learn the drill/practice math fact activities. At the end of that week, a review session is held. Tutoring begins one week later. Also, tutors attend weekly meetings to learn about and practice upcoming tutoring topics. In these weekly sessions, tutors also discuss difficulties they face. These sessions are supervised by a building or district instructional support person.

What types or professionals are qualified to administer your program?

selected Special Education Teacher
selected General Education Teacher
selected Reading Specialist
selected Math Specialist
selected EL Specialist
selected Interventionist
selected Student Support Services Personnel (e.g., counselor, social worker, school psychologist, etc.)
not selected Applied Behavior Analysis (ABA) Therapist or Board Certified Behavior Analyst (BCBA)
selected Paraprofessional
not selected 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 field-tested with the target population of instructors or interventionist and students:
The manuals have already been used widely, and users report high levels of satisfaction.

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:

Contact Flora.Murray@vanderbilt.edu for information on how to arrange a 1-day workshop.

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., Compton, D. L., Fuchs, D., Paulsen, K., Bryant, J. D. & Hamlett, C. L. (2005). The prevention, identification, and cognitive determinants of math difficulty.. Journal of Educational Psychology, 97() 493-513.

Participants Full Bobble

Describe how students were selected to participate in the study:
All first-grade teachers (n = 41) in six Title 1 and four non-Title 1 schools in a southeastern metropolitan school district agreed to participate. From these 41 classrooms, we identified not-at-risk (NAR) and at-risk (AR) students in September using the following procedure. In whole-class format, we tested the 667 (89% of) students for whom we received parent consent. The measures were Curriculum-Based Measurement (CBM) Computation, Addition Fact Fluency, Subtraction Fact Fluency, and CBM Concept/Applications. Based on a factor score computed across these measures, we identified the 308 lowest-scoring students for individual testing, all of whom failed the local benchmark for designating risk status in math using the CBM Computation measure. Staff shared the names of these students with teachers, who nominated 11 additional students as potentially AR. Staff administered an individual battery to these 319 children. Then, based on the Week 4 CBM score, we identified the lowest 139 performing students as AR (i.e., 21% of the consented students); scores for all 139 students fell below the CBM benchmark for risk in math. These 139 students were randomly assigned to control or tutoring conditions, blocking by classrooms to ensure comparable distribution of AR students in the control and tutoring conditions within classrooms. This created two pools of students relevant to the TRC review: 69 AR control students and 70 AR tutored students (a comparison group of NAR students was also followed, but is not relevant to the TRC review). Because some students moved to other schools, the size of these two groups decreased from September to May, respectively, to 63 and 64. See Table 1 for student demographics and pretreatment intelligence, reading, and math standard scores by group for these 63 and 64 students. The demographics of the groups were comparable. As expected, on the intelligence and academic measures, the NAR students performed higher than the AR students, but the AR control and AR tutored groups performed comparably. NOTE: Standard scores on the Woodcock-Johnson III (WJ III; Woodcock, McGrew, & Mather, 2001) achievement measures placed the AR students near average (i.e., 93-98). By contrast, on measures for which standard scores are relative to classmates, performance fell substantially lower (85-93). (Note that the high scores on the Woodcock measures, relative to locally-normed measures, are surprising because our sample was drawn from an urban district, including six high-poverty schools, which can be expected to perform lower than a nationally representative sample. So, it is important to consider three points. First, other researchers [e.g., Speece & Case, 2001; Vellutino, Scanlon, Small, & Fanuele, in press] have also documented Woodcock measures’ inadequate sensitivity to reading difficulty in first grade. Second and relatedly, performance floors on the Woodcock measures make discrimination among low-performing first graders difficult. At the beginning of first grade on WJ III Calculation, for example, a raw score of 2 (e.g., Make the number 1; Make the number 3) corresponds to a standard score of 87. With one additional correct item (e.g., 1+1=), the standard score increases to 93; with one more correct item [e.g., 2+2=], to 99. Third, research at third grade [Fletcher, Cirino, & Fuchs, 2004] has also documented a pattern of high WJ III Calculation standard scores for low-performing students relative to another norm-referenced measure [i.e., WJ III Calculation scores were 8-10 points higher than Wide Range Achievement Test – Arithmetic scores]. All of this raises questions about the structure and/or norming of the Woodcock tests and lends credence to the locally normed figures. Moreover, with respect to the generalizability of findings, it is important to consider that many response-to-intervention models of prevention and identification and the studies underpinning those models [e.g., McMaster, Fuchs, Fuchs, & Compton, in press; Speece & Case, 2001] incorporate local normative frameworks to designate risk, as was done in this study.)

Describe how students were identified as being at risk for academic failure (AI) or as having emotional or behavioral difficulties (BI):
In whole-class format, we tested the 667 (89% of) students for whom we received parent consent. The measures were Curriculum-Based Measurement (CBM) Computation, Addition Fact Fluency, Subtraction Fact Fluency, and CBM Concept/Applications. Based on a factor score computed across these measures, we identified the 308 lowest-scoring students for individual testing, all of whom failed the local benchmark for designating risk status in math using the CBM Computation measure. Staff shared the names of these students with teachers, who nominated 11 additional students as potentially AR. Staff administered an individual battery to these 319 children. Then, based on the Week 4 CBM score, we identified the lowest 139 performing students as AR (i.e., 21% of the consented students); scores for all 139 students fell below the CBM benchmark for risk in math. These 139 students were randomly assigned to control or tutoring conditions, blocking by classrooms to ensure comparable distribution of AR students in the control and tutoring conditions within classrooms. The at-risk sample was at the 21st percentile of a representative sample on pretest (Week 4 was before intervention, but having provided students with sufficient time to acclimate to the assessment) Curriculum-Based Measurement-Calculations (a reliable assessment of overall math competence at beginning of first grade). The term “representative sample” is used in the research design sense, i.e., representing the full range of performance (e.g., not among a sample of students selected low or high performing). In the case of this study/sample, students were in a metropolitan area with a high proportion of subsidized lunch students. So in terms of a national sample, it is safe to assume the samples are below the 25th percentile of a nationally representative sample in the demographic sense.

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,
  • non-responsive 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:
“AR tutored” who received the Number Rockets program

Specify which condition is the control condition:
“AR control” who received business-as-usual (i.e., no tutoring)

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 63 64 0.00
Grade 2
Grade 3
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 32 31 0.05
American Indian
Asian/Pacific Islander
Hispanic 3 4 0.26
White 29 28 0.05
Other

Socioeconomic Status

Demographic Program
Number
Control
Number
Effect Size: Cox Index
for Binary Differences
Subsidized Lunch 36 32 0.15
No Subsidized Lunch 23 26 0.11

Disability Status

Demographic Program
Number
Control
Number
Effect Size: Cox Index
for Binary Differences
Speech-Language Impairments
Learning Disabilities
Behavior Disorders
Emotional Disturbance
Intellectual Disabilities
Other
Not Identified With a Disability 63 64 0.00

ELL Status

Demographic Program
Number
Control
Number
Effect Size: Cox Index
for Binary Differences
English Language Learner
Not English Language Learner 63 64 0.00

Gender

Demographic Program
Number
Control
Number
Effect Size: Cox Index
for Binary Differences
Female 33 31 0.10
Male 30 33 0.10

Mean Effect Size

0.08

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 Full Bobble

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.
These 139 students were randomly assigned to control or tutoring conditions, blocking by classrooms to ensure comparable distribution of AR students in the control and tutoring conditions within classrooms.

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?
not selected Schools
not selected Teachers
selected Students
not selected Classes
not selected Other
If other, please specify:

Please describe the unit(s) used for primary data analysis:

Fidelity of Implementation Full Bobble

How was the program delivered?
not selected Individually
selected Small Group
not selected Classroom

If small group, answer the following:

Average group size
3
Minimum group size
2
Maximum group size
3

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
40.00
What were the background, experience, training, and ongoing support of the instructors or interventionists?
None of the tutors was a certified teacher; only one tutor had previous experience tutoring. Training occurred as follow. In a 1-day training session for tutors, (a) an overview of the tutoring program, goals, and topics was presented, and (b) the tutoring procedures were explained for each activity in the first four tutoring topics. After presentation of each activity, tutors practiced the activity with a partner, with more practice completed in the next two weeks. One week later, in a second session, tutors learned to use the drill/practice math fact activities. At the end of that week, a review session was held. Tutoring began one week later. Also, tutors attended weekly meetings to learn about and practice upcoming tutoring topics. In these weekly sessions, tutors also discussed difficulties they faced. Supervisors facilitated the weekly meetings and helped tutors problem solve.

Describe when and how fidelity of treatment information was obtained.
All tutoring sessions were audiotaped. Tutors did not know which audiotapes would be checked for fidelity. We checked tapes for all 27 tutoring groups for Topic 4 (Day 1 or 2) and Topic 16 (Day 1) using a checklist that corresponded to the steps included in the lesson’s script, with 9-19 items (mean: 12) per checklist. Each checklist item was marked as observed, not observed, or not applicable. Fidelity was indexed as percentage of items implemented (observed divided by the sum of observed + not observed). A second coder re-checked fidelity for a random sample of 25% of the audiotapes. Agreement between coders was 88.3%.

What were the results on the fidelity-of-treatment implementation measure?
Across tutors and sessions, the percentage of fidelity for the first check was 95.6; for the second check, 93.5.

Was the fidelity measure also used in control classrooms?

Measures and Results

Measures Targeted : Full Bobble
Measures Broader : Full Bobble

Study measures are classified as targeted, broader, or administrative data according to the following definitions:

  • Targeted measures
    Assess outcomes, such as competencies or skills that the program was directly targeted to improve.
    • In the academic domain, targeted measures typically are not the very items taught but rather novel items structured similarly to the content addressed in the program. For example, if a program taught word-attack skills, a targeted measure would be decoding of pseudo words. If a program taught comprehension of cause-effect passages, a targeted measure would be answering questions about cause-effect passages structured similarly to those used during intervention, but not including the very passages used for intervention.
    • In the behavioral domain, targeted measures evaluate aspects of external or internal behavior the program was directly targeted to improve and are operationally defined.
  • Broader measures
    Assess outcomes that are related to the competencies or skills targeted by the program but not directly taught in the program.
    • In the academic domain, if a program taught word-level reading skill, a broader measure would be answering questions about passages the student reads. If a program taught calculation skill, a broader measure would be solving word problems that require the same kinds of calculation skill taught in the program.
    • In the behavioral domain, if a program taught a specific skill like on-task behavior in one classroom, a broader measure would be academic performance in that setting or on-task behavior in another setting.
  • Administrative data measures apply only to behavioral intervention tools and are measures such as office discipline referrals (ODRs) and graduation rates which do not have psychometric properties as do other, more traditional targeted or broader measures.

Click here for more information on effect size.


What populations are you submitting outcome data for?
not selected Full sample
not selected Students at or below the 20th percentile
not selected English language learners
not selected Racial/ethnic subgroups
not selected Economically disadvantaged students (low socioeconomic status)
Targeted Measure Reverse Coded? Reliability Relevance Exposure
Broader Measure Reverse Coded? Reliability Relevance Exposure
Administrative Data Measure Reverse Coded? Relevance

Posttest Data

Targeted Measures (Full Sample)

Measure Sample Type Effect Size P

Broader Measures (Full Sample)

Measure Sample Type Effect Size P

Administrative Measures (Full Sample)

Measure Sample Type Effect Size P

Targeted Measures (Subgroups)

Measure Sample Type Effect Size P

Broader Measures (Subgroups)

Measure Sample Type Effect Size P

Administrative Measures (Subgroups)

Measure Sample Type Effect Size P
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 post-test 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:
One-way analyses of variance (ANOVAs) were applied to pretest, posttest, and improvement scores on the seven mathematics dependent variables, using condition (NAR vs. AR control vs. AR tutored) as the factor. In Table 2, we report raw score means and SDs by condition, as well as omnibus F values, Fisher LSD post hoc follow-up tests (Seaman, Levin, & Serlin, 1991) for significant effects, and effect sizes (ESs) comparing the conditions. To compute ESs for pre- and posttreatment scores, we subtracted the difference between means and divided by the pooled SD (Hedges & Olkin, 1985). For improvement scores, we corrected for the correlation between the pre- and posttest: difference between improvement means, divided by the pooled SD of improvement/square root of 2(1-rxy) (Glass, McGaw, & Smith, l981).

Additional Research

Is the program reviewed by WWC or E-ESSA?
E-ESSA
Summary of WWC / E-ESSA Findings :

What Works Clearinghouse Review

WWC only reviewed the report “The prevention, identification, and cognitive determinants of math difficulty.” The findings from this review do not reflect the full body of research evidence on Number Rockets.

 

WWC Rating: Meets WWC standards without reservations.

 

Full Report

 

Evidence for ESSA

Program Outcomes: One qualifying study evaluated Number Rockets with students below the 38th percentile in math. Students in the control group did not receive any tutoring or organized remediation. On TEMA-3 tests, students in Number Rockets scored significantly higher than controls, with an effect size of +0.34. This qualifies the program for the ESSA “Strong” category. An earlier study of Number Rockets also showed positive effects, but the tutors were the authors’ graduate students, so that study did not meet inclusion standards.

Number of Studies: 1

Average Effect Size: 0.34

Full Report

How many additional research studies are potentially eligible for NCII review?
2
Citations for Additional Research Studies :

Fuchs, L. S., Geary, D. C., Compton, D. L., Fuchs, D., Schatschneider, C., Hamlett, C. L., & Changas, P. (2013). Effects of First-Grade Number Knowledge Tutoring with Contrasting Forms of Practice. Journal of Educational Psychology, 105, 58-77.

Rolfhus, E., Gersten, R., Clarke, B., Decker, L., Wilkins, C., & Dimino, J. (20120). An Evaluation of Number Rockets: a Tier-2 Intervention for Grade 1 Students At Risk for Difficulties in Mathematics (NCEE 2012-4007). Washington, D.C.: National Center for Educational Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education.

Disclaimer

Most tools and programs evaluated by the NCII are branded products which have been submitted by the companies, organizations, or individuals that disseminate these products. These entities supply the textual information shown above, but not the ratings accompanying the text. NCII administrators and members of our Technical Review Committees have reviewed the content on this page, but NCII cannot guarantee that this information is free from error or reflective of recent changes to the product. Tools and programs have the opportunity to be updated annually or upon request.