Math Recovery
Study: Smith et al. (2007)

Summary

Math Recovery (MR) is an early intervention program designed to change the long-term mathematical development of initially low-performing children. The program identifies children who are falling behind in mathematics and provides intensive one-to-one tutoring designed to help them “catch up” to their higher performing peers. Although targeted for first grade, the diagnostic assessments can be applied K-5. The MR program comprises both an elaborated body of theory and research-based strategies for supporting the development of children’s numerical reasoning, and an innovative set of techniques for supporting instructors’ acquisition and use of this knowledge to work effectively with children. The developers of MR have codified this knowledge in a Learning Framework and an Instructional Framework that instructors use to assess children’s arithmetical knowledge and tailor instruction to their current levels of arithmetical reasoning. MR tutoring is diagnostic rather than scripted in nature and is consistent with current theory and evidence on effective mathematics teaching. Instructors are expected to select instructional tasks and to adjust probes and questions as informed by their initial and ongoing assessment of students’ numerical competence. The MR program can be implemented with virtually any curricula as the 12-month teacher development program is grounded in gaining a deep understanding of the teaching and learning of elementary mathematics.

Target Grades:
K, 1, 2, 3, 4, 5
Target Populations:
  • Any student at risk for academic failure
Area(s) of Focus:
  • Computation
  • Concepts and/or word problems
  • Algebra
Where to Obtain:
US Math Recovery Council
205 Powell Place Brentwood, TN 37027
615-369-0700
www.mathrecovery.org
Initial Cost:
Contact vendor for pricing details.
Replacement Cost:
Contact vendor for pricing details.

There are no per-student costs. The cost of the program is the professional development for the Intervention Specialist. The Math Recovery Intervention Specialist professional development program includes two (2) weeks of course work, three additional individual on-site coaching sessions and / or distance video-coaching , and three (3) facilitated collegial team meetings. The program includes a detailed understanding of the Learning Framework in Number and the Instructional Framework in Early Number. It incorporates a powerful staff development model that builds communities of practice for teachers, leader/trainers and coaching teams. The cost of the Math Recovery Intervention Specialist 12-month course is Math Recovery Teacher Specialist is $5500 per person, with discounts for additional teachers from the same district. The fees include: Access to Math Recovery tools and copyrighted material; Assessment and teaching kits, textbooks and program handbooks; All travel and consulting costs for on-site coaching; Membership to the US Math Recovery Council for two years. Each coaching session is individualized to meet the needs of the instructor, giving insight to specific issues that arise as the instructor begins to work with students. The MR tutoring program is personalized for each child and highly interactive. The instructor is trained to meet the child at his or her current level of math understanding and provides specific activities to raise the child’s ability.

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.)
Training Requirements:
12 month PD course with onsite mentoring

The Math Recovery Intervention Specialist training is 10 days of face to face instruction with a trained Math Recovery Leader. The Specialist receives 5 individual coaching sessions over the course of the year training


The math recovery assessments and teaching exemplars were created as part of a 3 year study (1992-1995) funded by the Australian Research Council. Twenty teachers working in 18 Australian primary schools participated in videotaped teaching and assessment episodes followed by discussion with principal researcher Robert Wright. The result of this study were two books currently used as a part of the Math Recovery Intervention Specialist training, Math Recovery assessments, teaching procedures and models for analyzing student performance on the assessments.

Access to Technical Support:
Ongoing support is provided through Regional Leaders as well as through web resources, the National Conference and Annual Summer Institute
Recommended Administration Formats Include:
  • Individual students
  • Small group of students
Minimum Number of Minutes Per Session:
30
Minimum Number of Sessions Per Week:
4
Minimum Number of Weeks:
12
Detailed Implementation Manual or Instructions Available:
Yes
Is Technology Required?
  • Computer or tablet
  • Internet connection
  • Other technology: The program requires a video camera to record the tutoring sessions for subsequent analysis. A computer is required for playback, to compile data for lesson plans and to create an assessment and teaching case study incorporating video clips. A computer camera is required for video conferences. After the training period, video cameras are used to record and analyze student performance.

Program Information

Descriptive Information

Please provide a description of program, including intended use:

Math Recovery (MR) is an early intervention program designed to change the long-term mathematical development of initially low-performing children. The program identifies children who are falling behind in mathematics and provides intensive one-to-one tutoring designed to help them “catch up” to their higher performing peers. Although targeted for first grade, the diagnostic assessments can be applied K-5. The MR program comprises both an elaborated body of theory and research-based strategies for supporting the development of children’s numerical reasoning, and an innovative set of techniques for supporting instructors’ acquisition and use of this knowledge to work effectively with children. The developers of MR have codified this knowledge in a Learning Framework and an Instructional Framework that instructors use to assess children’s arithmetical knowledge and tailor instruction to their current levels of arithmetical reasoning. MR tutoring is diagnostic rather than scripted in nature and is consistent with current theory and evidence on effective mathematics teaching. Instructors are expected to select instructional tasks and to adjust probes and questions as informed by their initial and ongoing assessment of students’ numerical competence. The MR program can be implemented with virtually any curricula as the 12-month teacher development program is grounded in gaining a deep understanding of the teaching and learning of elementary mathematics.

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
selected Kindergarten
selected First grade
selected Second grade
selected Third grade
selected Fourth grade
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.

not selected Students with disabilities only
not selected Students with learning disabilities
not selected Students with intellectual disabilities
not 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
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
205 Powell Place Brentwood, TN 37027
Phone Number
615-369-0700
Website
www.mathrecovery.org

Initial cost for implementing program:

Cost
Unit of cost

Replacement cost per unit for subsequent use:

Cost
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)

There are no per-student costs. The cost of the program is the professional development for the Intervention Specialist. The Math Recovery Intervention Specialist professional development program includes two (2) weeks of course work, three additional individual on-site coaching sessions and / or distance video-coaching , and three (3) facilitated collegial team meetings. The program includes a detailed understanding of the Learning Framework in Number and the Instructional Framework in Early Number. It incorporates a powerful staff development model that builds communities of practice for teachers, leader/trainers and coaching teams. The cost of the Math Recovery Intervention Specialist 12-month course is Math Recovery Teacher Specialist is $5500 per person, with discounts for additional teachers from the same district. The fees include: Access to Math Recovery tools and copyrighted material; Assessment and teaching kits, textbooks and program handbooks; All travel and consulting costs for on-site coaching; Membership to the US Math Recovery Council for two years. Each coaching session is individualized to meet the needs of the instructor, giving insight to specific issues that arise as the instructor begins to work with students. The MR tutoring program is personalized for each child and highly interactive. The instructor is trained to meet the child at his or her current level of math understanding and provides specific activities to raise the child’s ability.

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?

   3-4

Program administration time

Minimum number of minutes per session
30
Minimum number of sessions per week
4
Minimum number of weeks
12
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?
Yes

If yes, what technology is required to implement your program?
selected Computer or tablet
selected Internet connection
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:
The program requires a video camera to record the tutoring sessions for subsequent analysis. A computer is required for playback, to compile data for lesson plans and to create an assessment and teaching case study incorporating video clips. A computer camera is required for video conferences. After the training period, video cameras are used to record and analyze student performance.

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?
At-cost

Describe the time required for instructor or interventionist training:
12 month PD course with onsite mentoring

Describe the format and content of the instructor or interventionist training:
The Math Recovery Intervention Specialist training is 10 days of face to face instruction with a trained Math Recovery Leader. The Specialist receives 5 individual coaching sessions over the course of the year training

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)
not selected Paraprofessional
selected Other

If other, please describe:

Teaching experience preferred, but not required.
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 math recovery assessments and teaching exemplars were created as part of a 3 year study (1992-1995) funded by the Australian Research Council. Twenty teachers working in 18 Australian primary schools participated in videotaped teaching and assessment episodes followed by discussion with principal researcher Robert Wright. The result of this study were two books currently used as a part of the Math Recovery Intervention Specialist training, Math Recovery assessments, teaching procedures and models for analyzing student performance on the assessments.

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:

Ongoing support is provided through Regional Leaders as well as through web resources, the National Conference and Annual Summer Institute

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

Smith, T., Cobb, P., Farran, D., Cordray, D., Munter, C. & Dunn, A. (2007). Evaluating Math Recovery: Evaluating the Causal Impact of Math Recovery on Student Achievement. Vanderbilt University.

Participants Empty Bobble

Describe how students were selected to participate in the study:
A 10-minute interview was conducted where each first grade student was asked to complete eight tasks. The tasks included counting visual objects, forward and backward number sequence, numeral identification and sequencing and elementary addition and subtraction. In addition, each student completed Woodcock Johnson III math tests including Math Fluency, Applied Problems, Quantitative Concepts and Math Reasoning instruments.

Describe how students were identified as being at risk for academic failure (AI) or as having emotional or behavioral difficulties (BI):
Those students that scored in the twenty-fifth percentile or below in both the MR and the WJIII protocols were identified as at-risk for academic failure.

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:
The students in the treatment group received 4 to 5 one-on-one tutoring sessions for 12 weeks from tutors trained in the Math Recovery method.

Specify which condition is the control condition:
The control group received normal classroom instruction with 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 1 343 684 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
American Indian
Asian/Pacific Islander
Hispanic
White 194 347 0.15
Other 148 337 0.15

Socioeconomic Status

Demographic Program
Number
Control
Number
Effect Size: Cox Index
for Binary Differences
Subsidized Lunch 220 445 0.03
No Subsidized Lunch 123 236 0.03

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

ELL Status

Demographic Program
Number
Control
Number
Effect Size: Cox Index
for Binary Differences
English Language Learner 43 109 0.15
Not English Language Learner 300 575 0.15

Gender

Demographic Program
Number
Control
Number
Effect Size: Cox Index
for Binary Differences
Female 188 366 0.02
Male 155 318 0.02

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 Half 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.
By randomly assigning the students selected for participation in the study each year to one of the three treatment cohorts or the wait list, we can establish the essential characteristics of an experimental design

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

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?
selected Individually
not selected Small Group
not selected 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
11.00
Sessions per week
5.00
Duration of sessions in minutes
30.00
What were the background, experience, training, and ongoing support of the instructors or interventionists?
The tutors were trained for one year in the Math Recovery. The training consisted of two weeks of coursework with three additional on site coaching sessions or distance video coaching. The training program includes a detailed explanation of the Learning Framework in Number and the Instructional Framework in Early number. Each tutor was released from half of their classroom duties to administer the math tutoring program.

Describe when and how fidelity of treatment information was obtained.
Charles Munter conducted a separate Master’s Thesis to test the fidelity of the MR study against other instruments. The videos of 107 program subjects were studied by five experienced MR instructors. Each video was independently coded with an instrument designed for the study. The MR scores were then compared to scores on Woodcock Johnson III testing instruments.

What were the results on the fidelity-of-treatment implementation measure?
The results in the Thesis study showed a 0.84 correlation between the MR instructor’s scores and the Woodcock Johnson III instruments where a 1.0 would be perfect fidelity.

Was the fidelity measure also used in control classrooms?

Measures and Results

Measures Targeted : Empty 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:
Throughout the program, students were observed by both intervention and outside MR tutors. The results were plotted into a three tier hierarchical linear growth model to show increasing or decreasing learning rates.

Additional Research

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

What Works Clearinghouse Review

This program was not reviewed by What Works Clearinghouse.

 

Evidence for ESSA

Program Outcomes: A large evaluation of Math Recovery found positive outcomes on Woodcock Johnson III Math Reasoning measures averaging an effect size of +0.30, in comparison to non-tutored students. The study was set up to be randomized, which would have qualified Math Recovery for the ESSA “Strong” category, but some students from the control group were moved into the experimental group during the study, making this a matched study and therefore qualifying for the ESSA “Moderate” category.

Number of Studies: 1

Average Effect Size: 0.31

Full Report

 

How many additional research studies are potentially eligible for NCII review?
0
Citations for Additional Research Studies :

Disclaimer

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