Spring Math
Study: VanDerHeyden et al. (2015)

Summary

Spring Math is a web-based RTI system for mathematics. Please note: As an RTI system, Spring Math include screening, progress monitoring, and intervention however, NCII has only reviewed the intervention component for the purposes of the Academic Intervention Tools Chart.

Target Grades:
K, 1, 2, 3, 4, 5, 6, 7, 8
Target Populations:
  • Any student at risk for academic failure
Area(s) of Focus:
  • Computation
  • Concepts and/or word problems
  • Whole number arithmetic
  • Comprehensive: Includes computation/procedures, problem solving, and mathematical concepts
  • Algebra
  • Fractions, decimals (rational number)
Where to Obtain:
Amanda VanDerHeyden / TIES
1667 Snelling Ave. N., St. Paul, MN 55108
(651) 999-6000
www.springmath.com
Initial Cost:
$7.00 per student
Replacement Cost:
$7.00 per student per year

There are no additional costs or requirements for implementation. The annual per student cost includes initial setup, universal screening and progress monitoring assessments, interventions, and related reporting. Support documentation is also included. Teachers and administrators interact with Spring Math online in a password protected account similar to other student assessment and intervention systems. When the teacher logs in to his or her account, the teacher dashboard provides a screening packet for the teacher to print. The packet contains assessments with standardized directions printed on each page in the form of a script for the teacher. The teacher administers and scores the screening measures using answer keys that are provided by the system and then enters the scores into the dashboard. Spring Math provides graphs of the students’ performance and if the criterion is met (median score in the risk range on the first two screening measures), recommends a classwide intervention. The teacher dashboard now directs classwide intervention, providing a printable intervention packet that contains the intervention protocol and all materials needed to conduct the classwide intervention for one week. Each week, the teacher enters scores from the 5th session, Spring Math graphs the performance of students, and advances the class to the next target skill or stays on the current skill level

Staff Qualified to Administer Include:
  • Special Education Teacher
  • General Education Teacher
  • Math Specialist
  • Interventionist
  • Paraprofessional
  • Other:
Training Requirements:
1 hour of training

Training is provided by video tutorials and an online user manual. Topics covered in the tutorial and manual include how to conduct the screening and how to conduct classwide and individual intervention. The research basis for the assessments and interventions are detailed in the online manual. An alignment study is provided detailing the alignment of the skills covered with Common Core State Standards. Users can access a full list of assessments and supplemental readings. An FAQ section is included that addresses questions like: Why are the assessments timed? How were the screening measures selected? How does Spring Math determine that a student is at risk or not? What does the “weeks with scores” metric mean? What are “tool skills” in math? Why are assessments given as part of the intervention? Why do the risk criteria differ across grades for the same skill? How do the assessments in Spring Math differ from other math assessments? Why do the screening measures seem so hard for my students? What research evidence supports the use of Spring Math? What research was used as the basis for developing the assessments?


The training instructions and materials were originally field tested in a district-wide trial of RtI that included use of classwide math intervention in all classes grades 1-8 in the district (VanDerHeyden & Burns, 2005; VanDerHeyden, Witt, & Gilbertson, 2007). These materials have been used in multiple research studies and implementation projects since 2002. A previous version of Spring Math, called Intervention Advisor, was pilot tested in the Boston public schools using the training materials and protocols that are now part of Spring Math.

Access to Technical Support:
Technical support is provided through our Zendesk support site. Systems can purchase support hours from TIES professional development and technical support teams. TIES hosts an annual conference in Minneapolis each December during which technological tools to support learning are featured (TIES and other publishers' products). Online support is provided on the site with short, embedded video tutorials explaining all aspects of implementation from screening to intervention selection and management.
Recommended Administration Formats Include:
  • Individual students
  • Small group of students
Minimum Number of Minutes Per Session:
15
Minimum Number of Sessions Per Week:
5
Minimum Number of Weeks:
15
Detailed Implementation Manual or Instructions Available:
Yes
Is Technology Required?
  • Computer or tablet
  • Internet connection

Program Information

Descriptive Information

Please provide a description of program, including intended use:

Spring Math is a web-based RTI system for mathematics. Please note: As an RTI system, Spring Math include screening, progress monitoring, and intervention however, NCII has only reviewed the intervention component for the purposes of the Academic Intervention Tools Chart.

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
selected Sixth grade
selected Seventh grade
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
selected Whole number arithmetic
selected Comprehensive: Includes computation/procedures, problem solving, and mathematical concepts
selected Algebra
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
1667 Snelling Ave. N., St. Paul, MN 55108
Phone Number
(651) 999-6000
Website
www.springmath.com

Initial cost for implementing program:

Cost
$7.00
Unit of cost
student

Replacement cost per unit for subsequent use:

Cost
$7.00
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)

There are no additional costs or requirements for implementation. The annual per student cost includes initial setup, universal screening and progress monitoring assessments, interventions, and related reporting. Support documentation is also included. Teachers and administrators interact with Spring Math online in a password protected account similar to other student assessment and intervention systems. When the teacher logs in to his or her account, the teacher dashboard provides a screening packet for the teacher to print. The packet contains assessments with standardized directions printed on each page in the form of a script for the teacher. The teacher administers and scores the screening measures using answer keys that are provided by the system and then enters the scores into the dashboard. Spring Math provides graphs of the students’ performance and if the criterion is met (median score in the risk range on the first two screening measures), recommends a classwide intervention. The teacher dashboard now directs classwide intervention, providing a printable intervention packet that contains the intervention protocol and all materials needed to conduct the classwide intervention for one week. Each week, the teacher enters scores from the 5th session, Spring Math graphs the performance of students, and advances the class to the next target skill or stays on the current skill level

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?

  

Program administration time

Minimum number of minutes per session
15
Minimum number of sessions per week
5
Minimum number of weeks
15
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
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:
Although all materials are provided to the teacher via an online interface, the actual administration of the assessments and interventions within Spring Math do not require technology because they are printed and delivered via paper and pencil. Spring Math classwide math intervention can be delivered in small groups, as could the individual interventions (so long as there is a small group of students who require the same individual intervention, which would adjust weekly).

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 hour of training

Describe the format and content of the instructor or interventionist training:
Training is provided by video tutorials and an online user manual. Topics covered in the tutorial and manual include how to conduct the screening and how to conduct classwide and individual intervention. The research basis for the assessments and interventions are detailed in the online manual. An alignment study is provided detailing the alignment of the skills covered with Common Core State Standards. Users can access a full list of assessments and supplemental readings. An FAQ section is included that addresses questions like: Why are the assessments timed? How were the screening measures selected? How does Spring Math determine that a student is at risk or not? What does the “weeks with scores” metric mean? What are “tool skills” in math? Why are assessments given as part of the intervention? Why do the risk criteria differ across grades for the same skill? How do the assessments in Spring Math differ from other math assessments? Why do the screening measures seem so hard for my students? What research evidence supports the use of Spring Math? What research was used as the basis for developing the assessments?

What types or professionals are qualified to administer your program?

selected Special Education Teacher
selected General Education Teacher
not selected Reading Specialist
selected Math Specialist
not selected EL Specialist
selected Interventionist
not 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 training instructions and materials were originally field tested in a district-wide trial of RtI that included use of classwide math intervention in all classes grades 1-8 in the district (VanDerHeyden & Burns, 2005; VanDerHeyden, Witt, & Gilbertson, 2007). These materials have been used in multiple research studies and implementation projects since 2002. A previous version of Spring Math, called Intervention Advisor, was pilot tested in the Boston public schools using the training materials and protocols that are now part of Spring Math.

Do you provide fidelity of implementation guidance such as a checklist for implementation in your manual?
Yes

Can practitioners obtain ongoing professional and technical support?
Yes

If yes, please specify where/how practitioners can obtain support:

Technical support is provided through our Zendesk support site. Systems can purchase support hours from TIES professional development and technical support teams. TIES hosts an annual conference in Minneapolis each December during which technological tools to support learning are featured (TIES and other publishers' products). Online support is provided on the site with short, embedded video tutorials explaining all aspects of implementation from screening to intervention selection and management.

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.

VanDerHeyden, A. M., McLaughlin, T., Algina, J., & Snyder, P. (2012). Randomized evaluation of a supplemental grade-wide mathematics intervention. American Education Research Journal, 49, 1251-1284. http://aer.sagepub.com/cgi/reprint/49/6/1251?ijkey=CHbWMLJp8/kRc&keytype=ref&siteid=spaer

 

VanDerHeyden, A. M. & Codding, R. (2015). Practical effects of class wide mathematics intervention. School Psychology Review, 44, 169-190. doi: http://dx.doi.org/10.17105/spr-13-0087.1

 

Codding, R., VanDerHeyden, Martin, R. J., & Perrault, L. (2016). Manipulating treatment dose: Evaluating the frequency of a small group intervention targeting whole number operations. Learning Disabilities Research & Practice, 31, 208-220

Study Information

Study Citations

1) VanDerHeyden, A. M., McLaughlin, T., Algina, J. & Snyder, P. (2012). Randomized evaluation of a supplemental grade-wide mathematics intervention. American Education Research Journal, 49(6) 1251-1284; 2) VanDerHeyden, A. M. & Codding, R. (2015). Practical effects of classwide mathematics intervention. School Psychology Review, 44(2) 169-190.

Participants Full Bobble

Describe how students were selected to participate in the study:
All fourth and fifth grade students attending any of the 7 schools in a southeastern U.S. city were eligible for participation. Inclusion criteria were (1) enrolled in the system at the time of spring testing in the spring of the intervention year (spring score available), (2) not categorized as limited English proficient according to state criteria, and (3) participating in general education mathematics instruction. From the original sample, 254 fifth graders and 283 fourth graders met inclusion criteria. Among these included students, 186 fifth graders and 188 fourth graders had a preceding year’s spring test score available (pre-test score) on the year-end state test. Thus the final sample for the distal measure outcomes was 186 5th graders and 188 4th graders. The final sample for the proximal outcome measures was 254 fifth graders and 283 fourth graders.

Describe how students were identified as being at risk for academic failure (AI) or as having emotional or behavioral difficulties (BI):
Classes for which the median score was in the at-risk range on the fall occasion proximal measures were considered as eligible for intervention. 100% of classes screened met the risk criterion in both the control and intervention groups.

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?
0.0%

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:
Classwide mathematics intervention. A sequence of skills was identified for each grade level. A standard protocol was followed to conduct a 15-min classwide intervention each day. Within treatment classes, students were grouped into dyads based on the beginning of year screening data such that higher-performing students were matched with lower-performing students and middle-performing students were matched with each other. The standard protocol included a period of guided practice with peer coaching and feedback for each member of the dyad, a timed interval of independent practice, corrective feedback (including teacher-led re-teaching, error correction, and “think aloud” problem solving where the student had to explain to his/her math buddy how he or she corrected an error), goal setting, and a group contingency for improved class performance. On Friday of each week, a probe of the skill being targeted during intervention was administered following standard CBM procedures. If the class median score surpassed 80 digits correct per 2 min (Deno & Mirkin, 1977), the entire class advanced to the next level of intervention difficulty (i.e., the next skill in the sequence) and intervention continued at that level the following week. When the class was working on a basic fact (e.g., multiplication 0-12), flashcards were used during the guided practice period of the intervention as indicated by the intervention protocol. When the class was working on a skill that was not a basic fact (e.g., multi-digit addition and subtraction), practice worksheets were used during the guided practice interval as indicated by the intervention protocol. At each grade level, the intervention skill sequence included 14 skills. In theory, classes could have finished the intervention in 14 weeks but this would have represented very rapid progress (VanDerHeyden & Burns, 2008). Out of 26 intervention classes, only 3 completed all 14 skills during the 29 weeks allotted to intervention. The intervention was similar in format to classwide peer tutoring (Greenwood, 1991) and peer assisted learning strategies (Fuchs, Fuchs, Mathes, & Simmons, 1997), which have been experimentally evaluated and shown moderate effects on mathematics achievement (e.g., +.24 and +.33, Slavin & Lake, 2008). The intervention strategies emphasized explicit, direct instruction on computation and procedural mathematics skills emphasizing whole number operations, numbers and operations in base ten, and numbers and operations with fractions and decimals. The use of guided practice, immediate corrective feedback, multiple opportunities to respond, incentives for improved performance, and gradually increased task difficulty based on mastery of easier, related skills are strategies that have been widely studied with moderate to strong effect sizes on achievement (Hattie, 2009; Slavin & Lake, 2008) for all children and for children who are at risk (Kavale & Forness, 1999). When these strategies are implemented as part of an intervention package to advance mathematics performance, users might reasonably expect to observe performance improvements (Bryant et al., 2011). Classwide math intervention is a component of Spring Math (www.springmath.com). Spring Math is a web-based system that directs screening for students K-8 in fall, winter, and spring; summarizes and interprets the data by grade and class; recommends a classwide intervention if needed; and recommends individual students for intervention. Spring Math provides all follow-up assessment and follows decision trees to identify the intervention skill difficulty level and the type of intervention needed (acquisition versus fluency-building). Spring Math provides all materials needed to conduct the intervention for one week including the intervention protocol with a teacher script, scripted activities to develop and expand conceptual understanding, and a follow-up assessment for a targeted and generalization skill. Spring Math graphs weekly performance gains, interprets data, and adjusts the intervention packet for the following week. An administrator and coach dashboard tracks implementation metrics and recommends actions to support high-quality intervention use in all classrooms. The classwide intervention emphasizes fluency building for essential skills that are foundational for progress at a given grade level. Individual intervention is the next layer for students who require more assistance to attain key understandings. Individual interventions include both acquisition protocols and fluency-building protocols. The protocol used depends upon the student’s assessment(s).

Specify which condition is the control condition:
Control classrooms

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
Grade 4 168 115 0.02
Grade 5 148 106 0.02
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 123 79 0.08
American Indian
Asian/Pacific Islander 16 14 0.12
Hispanic 20 6 0.44
White 157 122 0.12
Other

Socioeconomic Status

Demographic Program
Number
Control
Number
Effect Size: Cox Index
for Binary Differences
Subsidized Lunch 182 124 0.05
No Subsidized Lunch 132 97 0.05

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 33 29 0.18
Not Identified With a Disability 282 192 0.12

ELL Status

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

Gender

Demographic Program
Number
Control
Number
Effect Size: Cox Index
for Binary Differences
Female 156 108 0.00
Male 160 113 0.00

Mean Effect Size

0.10

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.

In data analyses conducted for the paper, CBM pre-test program and control comparisons were conducted using a multilevel model, which took nesting into account. None of these comparisons were significant. This is reported on page 1269 of the article: “Of note, treatment and control groups were not statistically different on the CBMs at the first time point before intervention,” and these data are shown in Table 7. There were no significant pre-test (time 1) differences on any of the CBMs at grade 4 or 5. Please note that “simplify fractions” is referred to as “reduce fractions” in the article.

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.
Experimental Design and Group Assignment: This study used a nested, between-groups experimental design to evaluate the effects of an intervention on (a) year-end statewide accountability test scores, and (b) differences in growth on three curriculum-based measures (CBM) administered on three occasions. Assignment occurred at the classroom level. Classrooms were randomly assigned to the intervention or control group within each grade within each school. In cases where the number of classes at a given grade level represented an odd number, a greater number of classes were assigned to intervention than control. Class assignments and pre-intervention average scores on experimental measures are shown in Table 3. Assignment procedures resulted in 10 control classrooms and 13 intervention classrooms for both the fourth and fifth grade samples. In the fourth grade sample, there were 16 teachers for the 23 classrooms. Five teachers taught only the control curriculum, six teachers taught only the intervention curriculum, and five teachers taught both curricula. In the fifth grade sample there were 15 teachers for the 23 classrooms. Five teachers taught only the control curriculum, six teachers taught only the intervention curriculum, and four teachers taught both curricula. Thus, for some of the teachers treatment was crossed with teachers and for other teachers, teachers were nested in treatment. See Table 3 on p. 1259 of the AERJ manuscript.

What was the unit of assignment?
Other
If other, please specify:
Classes. For some teachers, treatment was crossed with teachers, whereas for other teachers, teachers were nested in treatment. Please see details at bottom of p. 1258 of AERJ manuscript.

Please describe the unit of assignment:
Assignment procedures resulted in 10 control classrooms and 13 intervention classrooms for both the fourth and fifth grade samples. In the fourth grade sample, there were 16 teachers for the 23 classrooms. Five teachers taught only the control curriculum, six teachers taught only the intervention curriculum, and five teachers taught both curricula. In the fifth grade sample there were 15 teachers for the 23 classrooms. Five teachers taught only the control curriculum, six teachers taught only the intervention curriculum, and four teachers taught both curricula. Thus, for some of the teachers treatment was crossed with teachers and for other teachers, teachers were nested in treatment.

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
not selected Small Group
selected Classroom

If small group, answer the following:

Average group size
10
Minimum group size
4
Maximum group size
16

What was the duration of the intervention (If duration differed across participants, settings, or behaviors, describe for each.)?

Weeks
29.00
Sessions per week
5.00
Duration of sessions in minutes
15.00
What were the background, experience, training, and ongoing support of the instructors or interventionists?
Teachers, RtI coordinators, and administrators were trained to implement the intervention using a combination of antecedent and live coaching strategies. Following a series of trainings specific to principals, the first author traveled to each school to conduct a 1-hour training with teachers whose classes were assigned to the intervention condition. Additionally, each school had an RtI coordinator and that person was charged with receiving and organizing weekly data to provide to the first author via an electronic spreadsheet program designed to organize the data and present graphs of class progress each week during the intervention. In the didactic training session, an overview of the rationale for the intervention program was shared with teachers using the district’s data reflecting low mathematics achievement. Details of the intervention were provided, including sharing the intervention protocol, describing how the intervention would progress based on student mastery of skills within a pre-established hierarchy of skills, showing effects on mathematics achievement obtained in other districts using the same intervention, and showing short video clips of the intervention being implemented in classrooms in other districts. An opportunity to discuss and troubleshoot intervention implementation was provided to teachers at this time. Teachers were provided all materials needed to implement the intervention each week by the on-site RtI coordinators. School principals agreed to conduct implementation integrity checks via direct observation as part of the intervention plan (described in greater detail in the next section). The consultant organized feedback on district progress for district administrators and school principals bimonthly during the year. Graphed feedback on each class’s progress with the intervention was provided to principals and district administrators. The consultant met in person with the district leaders and principals, reporting the number of skills mastered by teacher and identifying implementation errors. Additionally, the consultant communicated directly with principals and RtI coordinators providing a list of teachers whose classes were growing at a slower pace relative to other classes in the same school and encouraged an intervention integrity check in those classes. Finally, on a bimonthly basis (four total occasions), the consultant conducted integrity observations in classrooms with each principal and modeled for school principals how to troubleshoot intervention implementation with the classroom teacher. School principals agreed to conduct implementation integrity checks via direct observation as part of the intervention plan. Principals or on-site RtI coordinators agreed to conduct four integrity observations each week with approximately half of those occurring during regular mathematics instruction within control classrooms in an attempt to capture contamination between control and intervention conditions. The intervention integrity checklist listed each step of the intervention in observable terms and administrators were trained to observe and note the occurrence of each step of the intervention. The trained observer used the scripted intervention protocol to note correctly and independently completed steps of the intervention. Where deviations from the protocol were observed in intervention classrooms, principals and/or RtI coordinators provided corrective feedback on implementation and assisted the teacher to troubleshoot barriers to effective implementation.

Describe when and how fidelity of treatment information was obtained.
We examined fidelity in three ways. (1) We conducted a survey at the midpoint of the intervention of all treatment and control teachers. The survey documented by teacher report characteristics of core instruction in mathematics (number of minutes, type of supplemental intervention if any, number of minutes supplemental intervention was provided, etc.). These findings are reported on p. 1257 of the manuscript under the heading, “Instructional Context” and in Table 2 on p. 1258. Contamination was documented with two teachers in the control group reporting that they had implemented the classwide intervention. (2) We also examined use of the intervention in treatment classrooms using permanent products. We examined the number of skills mastered during intervention by class since classes were equivalent at the start of intervention and the intervention used a standard protocol with classes advancing through a fixed sequence of skills as a class to a new skill based upon the median score reaching a mastery criterion associated with the skill. Because a weekly score was recorded for all students in all treatment classes and the class was expected to advance based upon a specific decision rule, we also computed number of deviations from the treatment plan during the 29 weeks of the study (intervention score recorded, class advanced or did not advance as prescribed). (3) Trained observers (coach or principal) conducted a total of 406 direct observations of the intervention across all classrooms (treatment and control) during math lessons and documented occurrence of the steps in the standard protocol for classwide intervention. Each step was coded as having been implemented or not and the total number of steps implemented was divided by the total number of intervention steps in the protocol and the quotient was multiplied by 100%. 281 observations were conducted in treatment classrooms representing about 8% of opportunities for intervention among intervention teachers (26 weeks of intervention completed on average times 5 sessions per week times 26 intervention teachers). 125 observations were conducted in control classrooms. Average integrity in treatment classrooms was 96.69% (83.5%-100%) and estimated average implementation in control classrooms was 2.69% (0-20%). No feedback was provided to teachers following completion of the observation checklist. What we learned from direct observation data was that the most common integrity error was failing to use the intervention at all, which we suspected direct observation was less sensitive to given that the presence of the observer likely cued or reminded the teacher to implement the intervention. When the intervention was used, teachers tended to implement all of the steps of the intervention correctly. Thus, in our two published articles, we emphasized permanent product estimates of integrity including weeks of intervention and skill progression (which we thought of as trials to criterion data).

What were the results on the fidelity-of-treatment implementation measure?
Teachers completed on average 26.1 weeks of intervention (range, 20-29). Intervention teachers deviated from the intervention plan on average 1.4 times during the intervention (range, 0-5). On average, correct decisions (advance a skill level or not) were made for 94% of decision-making occasions (range, 80-100%). These permanent product indicators indicated that the intervention was sufficiently used to measure its effect on average although between teacher differences were apparent. Results on p. 1272 of the article under the heading “Intervention Integrity Effects” indicate that fourth grade classes successfully mastered more skills compared to fifth grade classes. There was a positive, but not statistically significant relationship between integrity estimates and post-intervention year-end state accountability scores. There was a positive and statistically significant relationship between integrity estimates and CBM growth in the intervention group.

Was the fidelity measure also used in control classrooms?
The survey fidelity measure was used in the control classroom. Direct observations were conducted 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.

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What populations are you submitting outcome data for?
selected Full sample
selected Students at or below the 20th percentile
not selected English language learners
selected Racial/ethnic subgroups
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.
In data analyses conducted for the paper, CBM pre-test program and control comparisons were conducted using a multilevel model, which took nesting into account. None of these comparisons were significant. This is reported on page 1269 of the article: “Of note, treatment and control groups were not statistically different on the CBMs at the first time point before intervention,” and these data are shown in Table 7. There were no significant pre-test (time 1) differences on any of the CBMs at grade 4 or 5. Please note that “simplify fractions” is referred to as “reduce fractions” in the article. Year-end test scores were analyzed with multilevel ANCOVA with the covariate (pre-test means) centered. This provides the best analysis for the structure of the nesting in which “class means are used as the basic observations and treatment effects are tested against variations in these means” (Campbell & Stanley, 1971, p. 23). Given a randomized cluster design, determining pre-test differences on the basis of mean differences analyses that ignore the nested structure of the dataset may be misleading.
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:
Please see pp. 1262-1266 of the AERJ article for the complete description including models and model terms: Multilevel linear modeling (MLM) was used to account for the nesting of students within classes and classes within teachers. Fourth- and fifth-grade data were analyzed separately. The statewide test analyses were designed to investigate a treatment difference on students’ 2009 statewide test math scores while controlling for 2008 statewide test score. Follow-up analyses examined the difference between groups on students’ numbers and operations subscale of the statewide test while controlling for 2008 statewide test score. Students with a 2008 and 2009 statewide test math score were included in these analyses (referred to as sample b in this application). We used two different dependent variables for each of the fourth-grade and fifth-grade samples. The following descriptions apply to both samples and both dependent variables. Our final specification of residuals included a residual for the teacher level for the intercept and a within-class residual for the Level 1 model. For each of the four combinations of dependent variable and grade, the final model resulted in the smallest Akaike Information Criterion (AIC) fit index (Akaike, 1974) among the models for which estimation converged. Group mean centering (GPMC) based on classroom mean was used at Level 1 to protect against spurious cross-level interactions (Enders & Tofighi, 2007). A multilevel repeated measures analysis, including treatment and occasion as factors, was used to test for a Treatment x Time interaction and account for scores nested within students across occasions, students nested within classrooms, and classrooms nested within teachers for each CBM in each grade. An unstructured covariance matrix (UCM) was specified for each component of the model. That is, for each component the variances were permitted to be unequal for different occasions and the covariances were permitted to be unequal for different pairs of occasions. For models that did not converge with unstructured covariance matrices for student, class, and teacher components, we estimated new models that allowed either UCMs for student and teacher components of the residual and a compound symmetric covariance matrix (CSCM) for the class component or UCMs for the student and class components and a CSCM for the teacher component. We used the AIC fit index (Akaike, 1974) to select the model with the most appropriate variance-covariance structure. For models with a significant Treatment x Occasion interaction, we estimated treatment effects at each occasion. When the Time x Treatment interaction was significant, we estimated an MLM with a treatment effect and a Treatment x Pretest interaction at each of the last two occasions to evaluate if the treatment effect varied with the pretest score. The covariance structure was selected by following the same steps that we used for the repeated measures analysis. To evaluate the relationship of student scores to intervention integrity, the number of skills mastered and the percentage of correctly followed decision rules were used as indicators of correct intervention implementation. To investigate the relationship of 2009 statewide test scores to intervention integrity, we estimated two-level means-as outcomes (MAO) models (Raudenbush & Bryk, 2002) for students in the treatment group only. To investigate the difference in CBM scores by intervention integrity, we estimated two three-level intercepts-and-slopes-as-outcomes (ISAO) models for each CBM probe for students in the treatment group only. Occasion was the predictor at Level 1, and an intervention integrity indicator was used as the predictor at Level 2 for each model. In the first model, the number of skills mastered was the intervention integrity indicator; in the second, percentage of correctly followed decision rules was the indicator.

Additional Research

Is the program reviewed by WWC or E-ESSA?
No
Summary of WWC / E-ESSA Findings :
This program was not reviewed by What Works Clearinghouse.
How many additional research studies are potentially eligible for NCII review?
0
Citations for Additional Research Studies :
This program was not reviewed by Evidence for ESSA.

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