Hot Math Tutoring
Study: Fuchs et al. (2008)
Summary
Hot Math Tutoring is a thirdgrade smallgroup tutoring program designed to enhance atrisk (AR) students’ wordproblem performance. Based on schema theory, Hot Math Tutoring provides explicit instruction on (a) solution strategies for four wordproblem types and (b) how to transfer those solution strategies to word problems with unexpected features, such as problems that include irrelevant information, or that present a novel question requiring an extra step, or that include relevant information presented in charts or graphs, or that combine problem types, and so on. Hot Math Tutoring centers on four wordproblem types, chosen from common thirdgrade curricula: “shopping list” word problems (e.g., Joe needs supplies for the science project. He needs 2 batteries, 3 wires, and 1 board. Batteries cost $4 each, wires cost $2 each, and boards cost $6 each. How much money does he need to buy supplies?), “half” problems (e.g., Marcy will buy 14 baseball cards. She’ll give her brother half the cards. How many cards will Marcy have?), stepup function or “buying bags” problems (e.g., Jose needs 32 party hats for his party. Party Hats come in bags of 4. How many bags of party hats does Jose need?), and 2step “pictograph” problems (e.g., Mary keeps track of the number of chores she does on this chart [pictograph is shown with label: each picture stands for 3 chores]. She also took her grandmother to the market 3 times last week. How many chores has Mary done?). The content of Hot Math Tutoring mirrors a companion, classroom Hot Math program, but randomized control trial efficacy data support the efficacy of Hot Math Tutoring when it is used with or without the classroom Hot Math program. Hot Math Tutoring relies on explicit instruction and selfregulated learning strategies. The program is divided into 3week units (3 2030 minute sessions per week); one unit is devoted to each of the four wordproblem types, and a 1 week review is conducted following winter break. Frequent cumulative review across wordproblem types is incorporated. During the first 5 sessions of each unit, problemsolution instruction is delivered. In Session 1, tutors address the underlying concepts and structural features for the problem type using concrete objects. Together with the students, tutors work several examples and, as they refer to the poster and the concrete objects, explain why and how each step of the solution method was applied in the examples. Next, students respond frequently to questions as they work 24 problems together with the tutor. Beginning in Session 2, students complete one problem independently, which the tutor reviews and scores. Sessions 69 in each unit are designed to teach students to transfer the solution strategy to problems with unexpected questions or irrelevant information. Tutors first teach the meaning of the word transfer and then teach about unexpected questions and irrelevant information. In Sessions 69, students continue to word on transfer and to complete problems independently. Throughout each tutoring session, tutors award points for attention to task and correct work. Once per week, students have an opportunity to trade points for small prizes. Tutors follow scripts to ensure consistency but are not permitted to read or memorize scripts.
 Target Grades:
 3
 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:

 Concepts and/or word problems
 Where to Obtain:
 Lynn Fuchs and Doug Fuchs
 228 Peabody Vanderbilt University, Nashville, TN 37220
 6153434782
 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). INCLUDED: Manual ($40), masters of all materials ($40) NOT INCLUDED: individual student copies of materials, concrete reinforcers
 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

Tutors are trained in one fullday session. Tutors are introduced to the program and its goals and provided instruction, demonstrations, and scripted materials. They are paired to practice the program. Then, they conduct one lesson for a trainer and are judged on a pointbypoint system for fidelity to treatment. A tutor who achieves 95% fidelity is considered reliable. A tutor who scores lower than 95% fidelity is coached on points he/she missed, asked to practice more, and then rerated at a later time on another lesson. At weekly meetings, tutors meet with a trainer for to solve problems that arise. At the beginning of each unit, a 3hour training sessions is conducted to orient tutors and distribute supporting materials.
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 1day workshop.
 Recommended Administration Formats Include:

 Individual students
 Small group of students
 Minimum Number of Minutes Per Session:
 20
 Minimum Number of Sessions Per Week:
 3
 Minimum Number of Weeks:
 13
 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:
Hot Math Tutoring is a thirdgrade smallgroup tutoring program designed to enhance atrisk (AR) students’ wordproblem performance. Based on schema theory, Hot Math Tutoring provides explicit instruction on (a) solution strategies for four wordproblem types and (b) how to transfer those solution strategies to word problems with unexpected features, such as problems that include irrelevant information, or that present a novel question requiring an extra step, or that include relevant information presented in charts or graphs, or that combine problem types, and so on. Hot Math Tutoring centers on four wordproblem types, chosen from common thirdgrade curricula: “shopping list” word problems (e.g., Joe needs supplies for the science project. He needs 2 batteries, 3 wires, and 1 board. Batteries cost $4 each, wires cost $2 each, and boards cost $6 each. How much money does he need to buy supplies?), “half” problems (e.g., Marcy will buy 14 baseball cards. She’ll give her brother half the cards. How many cards will Marcy have?), stepup function or “buying bags” problems (e.g., Jose needs 32 party hats for his party. Party Hats come in bags of 4. How many bags of party hats does Jose need?), and 2step “pictograph” problems (e.g., Mary keeps track of the number of chores she does on this chart [pictograph is shown with label: each picture stands for 3 chores]. She also took her grandmother to the market 3 times last week. How many chores has Mary done?). The content of Hot Math Tutoring mirrors a companion, classroom Hot Math program, but randomized control trial efficacy data support the efficacy of Hot Math Tutoring when it is used with or without the classroom Hot Math program. Hot Math Tutoring relies on explicit instruction and selfregulated learning strategies. The program is divided into 3week units (3 2030 minute sessions per week); one unit is devoted to each of the four wordproblem types, and a 1 week review is conducted following winter break. Frequent cumulative review across wordproblem types is incorporated. During the first 5 sessions of each unit, problemsolution instruction is delivered. In Session 1, tutors address the underlying concepts and structural features for the problem type using concrete objects. Together with the students, tutors work several examples and, as they refer to the poster and the concrete objects, explain why and how each step of the solution method was applied in the examples. Next, students respond frequently to questions as they work 24 problems together with the tutor. Beginning in Session 2, students complete one problem independently, which the tutor reviews and scores. Sessions 69 in each unit are designed to teach students to transfer the solution strategy to problems with unexpected questions or irrelevant information. Tutors first teach the meaning of the word transfer and then teach about unexpected questions and irrelevant information. In Sessions 69, students continue to word on transfer and to complete problems independently. Throughout each tutoring session, tutors award points for attention to task and correct work. Once per week, students have an opportunity to trade points for small prizes. Tutors follow scripts to ensure consistency but are not permitted to read or memorize scripts.
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 37220
 Phone Number
 6153434782
 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). INCLUDED: Manual ($40), masters of all materials ($40) NOT INCLUDED: individual student copies of materials, concrete reinforcersProgram 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?
24Program administration time
 Minimum number of minutes per session
 20
 Minimum number of sessions per week
 3
 Minimum number of weeks
 13
 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? Yes
 If yes, is the necessary training free or atcost?
 Atcost
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: Tutors are trained in one fullday session. Tutors are introduced to the program and its goals and provided instruction, demonstrations, and scripted materials. They are paired to practice the program. Then, they conduct one lesson for a trainer and are judged on a pointbypoint system for fidelity to treatment. A tutor who achieves 95% fidelity is considered reliable. A tutor who scores lower than 95% fidelity is coached on points he/she missed, asked to practice more, and then rerated at a later time on another lesson. At weekly meetings, tutors meet with a trainer for to solve problems that arise. At the beginning of each unit, a 3hour training sessions is conducted to orient tutors and distribute supporting materials.
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 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 1day 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., Fuchs, D., Craddock, C., Hollenbeck, K. N., Hamlett, C. L. & Schatschneider, C. (2008). Effects of smallgroup tutoring with and without validated classroom instruction on atrisk students' math problem solving: Are two tiers of prevention better than one?. Journal of Educational Psychology, 100() 491509.
Participants
 Describe how students were selected to participate in the study:
 This study was conducted across four years, with 30 classrooms participating each year, for a total of 120 thirdgrade classrooms. We refer to each year’s sample as a “cohort.” Stratifying so that each condition was represented approximately equally in each school, we randomly assigned 40 classrooms to control (i.e., teacherdesigned math problemsolving instruction) and 80 classrooms to Hot Math SBI (i.e., researcherdesigned SBI). One Hot Math SBI teacher dropped out due to personal reasons during the first month of the study. To obtain a representative sample, we screened 2,023 students on whom we had consent. That is, in the 119 thirdgrade classrooms, we randomly sampled 1,200 students for participation, blocking within classroom and within three strata: (a) 25% of students with scores 1 SD below the mean of the entire distribution on the Test of Computational Fluency (Fuchs, Hamlett, & Fuchs, 1990); (b) 50% of students with scores within 1 SD of the mean of the entire distribution on the Test of Computational Fluency; and (c) 25% of students with scores 1 SD above the mean of the entire distribution on the Test of Computational Fluency. Of these 1,200 students, 59 moved prior to posttesting (including 45 AR students). The 59 children who moved prior to posttesting were demographically comparable to the pupils who remained in the study. Among these students, we identified 288 students as AR of poor problemsolving outcomes. To derive a parsimonious equation for predicting problemsolving outcomes, we conducted regression analyses on a previous database (Fuchs, Fuchs, Prentice, Hamlett, Finelli, & Courey, 2004) of thirdgrade students who had received Hot Math SBI. The final prediction equation included pretest performance on the immediate transfer problemsolving measure (see Measures) and pretest performance on the Test of Computational Fluency (Fuchs et al., 1990). For each cohort, we rank ordered students on the predicted score and selected the lowest 72 students in that year’s sample. All of these students scored below the district criterion designating risk for math learning disabilities on the Test of Computation Fluency. These students were randomly assigned to tutoring conditions, while stratifying by classroom condition. In this way, some AR students received neither classroom nor tutoring Hot Math SBI; some received classroom but not tutoring Hot Math SBI; some received tutoring but not classroom Hot Math SBI; and some received classroom and tutoring Hot Math SBI. Of the 288 AR students, 45 moved prior to posttesting. On demographic and pretest performance variables, the 45 children who moved prior to posttesting were comparable to the 243 pupils who remained in the study, and there were no significant interactions between AR students’ tutoring condition and attrition status. See Table 1 for student demographics and pretreatment intelligence, reading, and math standard scores by group for the “program” and “control” groups. The demographics of the two groups relevant to the TRC review were comparable. (NOTE: In the research report, classrooms were randomly assigned to control (teacherdesigned wordproblem instruction; onethird of classrooms) or Classroom Hot Math (twothirds of classrooms). Within these wholeclass conditions, atrisk students were randomly assigned to control (no tutoring; onethird of students within each classroom condition) or Hot Math Tutoring (twothirds of students within each classroom condition). In this way, AR students received one of four conditions: (1) no Classroom Hot Math and no Hot Math Tutoring (we refer to this as “control” in this protocol), (2) Classroom Hot Math and no Hot Math Tutoring (not addressed in this protocol), (3) no Classroom Hot Math with Hot Math Tutoring (referred to as the “program” condition in this protocol), and (4) Classroom Hot Math and Hot Math Tutoring (not addressed in this protocol). In the tables in the attached research report, look under “Classlevel Condition: Control: Tutoringlevel condition” (i.e., left side of tables). Then look at “AR tutor” for the program condition (second column) and at “AR control” for the control condition (third column). This contrasts AR students who did not receive Hot Math Tutoring against AR students who did receive Hot Math Tutoring. None of the students in these two conditions received Classroom Hot Math.)
 Describe how students were identified as being at risk for academic failure (AI) or as having emotional or behavioral difficulties (BI):
 All of these students scored below the district criterion designating risk for math learning disabilities on the Test of Computation Fluency. The atrisk sample was at the 24th percentile (lowest 72 of each cohort’s 300 students). The 300 students were a representative sample on a combination of the pretest immediate transfer measure of math problem solving (a reliable index that correlates well with commercial measures of math problem solving) and pretest performance on the Test of Computational Fluency, a reliable and widely used measure of mathematics skill. I use the term “representative sample” 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,
 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:
 In the research report, classrooms were randomly assigned to control (teacherdesigned wordproblem instruction; onethird of classrooms) or Classroom Hot Math (twothirds of classrooms). Within these wholeclass conditions, atrisk students were randomly assigned to control (no tutoring; onethird of students within each classroom condition) or Hot Math Tutoring (twothirds of students within each classroom condition). In this way, AR students received one of four conditions: (1) no Classroom Hot Math and no Hot Math Tutoring (we refer to this as “control” in this protocol), (2) Classroom Hot Math and no Hot Math Tutoring (not addressed in this protocol), (3) no Classroom Hot Math with Hot Math Tutoring (referred to as the “program” condition in this protocol), and (4) Classroom Hot Math and Hot Math Tutoring (not addressed in this protocol). In the tables in the attached research report, look under “Classlevel Condition: Control: Tutoringlevel condition” (i.e., left side of tables). Then look at “AR tutor” for the program condition (second column) and at “AR control” for the control condition (third column). This contrasts AR students who did not receive Hot Math Tutoring against AR students who did receive Hot Math Tutoring. None of the students in these two conditions received Classroom Hot Math
 Specify which condition is the control condition:
 In the research report, classrooms were randomly assigned to control (teacherdesigned wordproblem instruction; onethird of classrooms) or Classroom Hot Math (twothirds of classrooms). Within these wholeclass conditions, atrisk students were randomly assigned to control (no tutoring; onethird of students within each classroom condition) or Hot Math Tutoring (twothirds of students within each classroom condition). In this way, AR students received one of four conditions: (1) no Classroom Hot Math and no Hot Math Tutoring (we refer to this as “control” in this protocol), (2) Classroom Hot Math and no Hot Math Tutoring (not addressed in this protocol), (3) no Classroom Hot Math with Hot Math Tutoring (referred to as the “program” condition in this protocol), and (4) Classroom Hot Math and Hot Math Tutoring (not addressed in this protocol). In the tables in the attached research report, look under “Classlevel Condition: Control: Tutoringlevel condition” (i.e., left side of tables). Then look at “AR tutor” for the program condition (second column) and at “AR control” for the control condition (third column). This contrasts AR students who did not receive Hot Math Tutoring against AR students who did receive Hot Math Tutoring. None of the students in these two conditions received Classroom Hot 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  56  28  0.78 
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  35  17  0.12 
American Indian  0  0  0.00 
Asian/Pacific Islander  0  0  0.00 
Hispanic  2  3  0.78 
White  16  6  0.31 
Other  3  3  0.45 
Socioeconomic Status
Demographic  Program Number 
Control Number 
Effect Size: Cox Index for Binary Differences 

Subsidized Lunch  43  21  0.18 
No Subsidized Lunch  13  7  0.03 
Disability Status
Demographic  Program Number 
Control Number 
Effect Size: Cox Index for Binary Differences 

SpeechLanguage Impairments  
Learning Disabilities  6  4  0.18 
Behavior Disorders  
Emotional Disturbance  
Intellectual Disabilities  
Other  
Not Identified With a Disability  50  24  0.37 
ELL Status
Demographic  Program Number 
Control Number 
Effect Size: Cox Index for Binary Differences 

English Language Learner  0  1  2.08 
Not English Language Learner  56  27  0.95 
Gender
Demographic  Program Number 
Control Number 
Effect Size: Cox Index for Binary Differences 

Female  26  16  0.17 
Male  30  12  0.32 
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.
 In a southeastern metropolitan school district, 120 thirdgrade classrooms participated in this study. Stratifying so that each condition was represented approximately comparably in each school, we randomly assigned 40 classrooms to the control condition (i.e., 3 weeks of researcherdesigned general math problemsolving instruction) and assigned 80 classrooms to the Hot Math SBI condition (i.e., 3 weeks of researcherdesigned general math problem solving plus 13 weeks of researcherdesigned SBI). The study occurred over 4 school years during a time when the school district was relatively stable. One quarter of the sample entered the study each year. During the first 3 years, SBI classrooms were randomly assigned to Hot Math SBI or to a variant designed to strengthen Hot Math SBI. In the first three cohorts, the effects of the two SBI conditions were not statistically significantly different, but both were reliably better than control. Therefore, we did not test a variant in Cohort 4 (all Cohort 4 teachers were randomly assigned to control or to the standard version of SBI). We considered all student in the SBI classrooms to have participated in one SBI condition; however, to assess SBI variants, we included cohort effects in the analytic model. One Cohort 3 classroom in the SBI condition left the study during the first month of participation because of the classroom teacher’s personal reasons.

What was the unit of assignment?  Teachers
 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
 3
 Minimum group size
 2
 Maximum group size
 4
What was the duration of the intervention (If duration differed across participants, settings, or behaviors, describe for each.)?
 Weeks
 13.00
 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?
 None of the tutors was a certified teacher; only one tutor had previous experience tutoring. Tutors were trained in one fullday session. Tutors were introduced to the program and its goals and provided instruction, demonstrations, and scripted materials. They were paired to practice the program. Then, they condcuted one lesson for a trainer and were judged on a pointby point system for fidelity to treatment. A tutor who achieved 95% fidelity was considered reliable. A tutor who scored lower than 95% fidelity was coached on points he/she missed, asked to practice more, and then rerated at a later time on another lesson. At weekly meetings, tutors met with a trainer to solve problems that arose. At the beginning of each unit, a 3hour training session was conducted to orient tutors and distribute supporting materials. Across the four years of the study, the typical tutor was one to two years beyond undergraduate education, studying for a graduated degree in education, special education, counseling, or education policy. The majority of tutors worked for the project one year, with three tutors working for more than one year. Each year of the study, two fulltime project coordinators, typically with bachelor's or master's level degrees typically outside of education, also tutored. Each year, five or six tutors were needed. (None of the tutors conducted Classroom Hot Math and Hot Math Tutoring).
 Describe when and how fidelity of treatment information was obtained.
 Each tutoring session was audiotaped. At the study’s end, four research assistants independently listened to tapes while completing a checklist to identify the percentage of points addressed. We sampled tapes so that, within conditions, tutors, groups, and session numbers were sampled equitably. For each of 64 tutoring small groups, 20% of sessions were sampled (78 tapes distributed equally across the four units). Intercoder agreement, calculated on 20% of the sampled tapes, was 96.4%.
 What were the results on the fidelityoftreatment implementation measure?
 The mean percentage of points addressed across all units was 98.12 (SD = 1.28).
 Was the fidelity measure also used in control classrooms?
Measures and Results
Measures Broader :
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 wordattack skills, a targeted measure would be decoding of pseudo words. If a program taught comprehension of causeeffect passages, a targeted measure would be answering questions about causeeffect 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 wordlevel 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 ontask behavior in one classroom, a broader measure would be academic performance in that setting or ontask 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? 
Full sample
Students at or below the 20th percentile
English language learners
Racial/ethnic subgroups
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 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 converted scores on the three problemsolving measures to percentage correct so performance on the three measures could be compared. To examine how much of the total variance in improvement on the three problemsolving measures was explained by the clustering of children in classrooms and in tutoring groups, we estimated variance components with SAS PROC MIXED (Littell, 2006). The resulting intraclass correlations showed that the effect for classroom clustering explained 16.10% of the variance (p <.001) and the effect for tutoringgroup clustering explained 4.10% of the variance (p = .006). We therefore incorporated each as a random effect into our model, which also included four fixed effects: one withinsubjects factor (problemsolving measure) and three betweensubjects factors (classroom condition, tutoring condition, and cohort). To assess pretreatment comparability, we fit a full model that included all main effects, 2way, 3way, and 4way interactions as well as estimated the impact of classroom as a random effects factor. To index learning as a function of study condition, we used improvement on the three problemsolving measures. (Fitting a model using improvement scores produces identical effects as would considering the interaction between test occasion [pre vs. posttest] and study conditions. We opted for improvement scores because their interpretation is more straightforward.) In this full model, the variance component for tutoring group decreased to zero (indicating that all of the variance associated with tutoring group clusters was explained in the model). So we fixed the random effects of tutoring group to zero and also eliminated from the final model all higherorder interactions that were not statistically significant. To followup significant effects, we Bonferronicorrected pvalues by the number of followup tests we ran for that significant effect. To compute effect sizes (ESs), we subtracted the difference between improvement means and then divided by the pooled standard deviation of the improvement/square root of 2(1rxy) (Glass, McGaw, & Smith, 1981). 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(1rxy) (Glass, McGaw, & Smith, l981).
Additional Research
 Is the program reviewed by WWC or EESSA?
 WWC & EESSA
 Summary of WWC / EESSA Findings :
What Works Clearingouse
WWC only reviewed the report “Effects of smallgroup tutoring with and without validated classroom instruction on atrisk students’ math problem solving: Are two tiers of prevention better than one?” The findings from this review do not reflect the full body of research evidence on Hot Math Tutoring.
WWC Rating: Meets WWC standards without reservations.
Evidence for ESSA
No studies considered met Evidence for ESSA's inclusion requirements.
 How many additional research studies are potentially eligible for NCII review?
 0
 Citations for Additional Research Studies :
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