This article uses two samples in grades 4 and 5. Sample a includes all students with proximal measure scores in the intervention year for intervention and control students. Sample b includes students with two consecutive years of state accountability test scores in mathematics
Sample size: 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 (pretest score) on the yearend 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.
Risk Status: Classes for which the median score was in the atrisk 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.
Demographics:

Program 
Control 
Cox Index 

Number 
Percentage 
Number 
Percentage 

Grade level 

Kindergarten 





Grade 1 





Grade 2 





Grade 3 





Grade 4 
168^{a} 105^{b} 
53^{a} 50^{b} 
115^{a} 83^{b} 
52^{a} 51^{b} 
0.02 0.02 
Grade 5 
148^{a} 107^{b} 
47^{a} 50^{b} 
106^{a} 79^{b} 
48^{a} 49^{b} 
0.02 0.02 
Grade 6 





Grade 7 





Grade 8 





Grade 9 





Grade 10 





Grade 11 





Grade 12 





Raceethnicity 

AfricanAmerican 
123^{a} 79^{b} 
39^{a} 37^{b} 
79^{a} 53^{b} 
36^{a} 33^{b} 
0.08 0.11 
American Indian 





Asian/Pacific Islander 
16^{a} 12^{b} 
5^{a} 6^{b} 
14^{a} 11^{b} 
5^{a} 7^{b} 
0.00 0.10 
Hispanic 
20^{a} 12^{b} 
6^{a} 6^{b} 
6^{a} 5^{b} 
3^{a} 3^{b} 
0.44 0.44 
White 
157^{a} 109^{b} 
50^{a} 51^{b} 
122^{a} 93^{b} 
55^{a} 57^{b} 
0.12 0.15 
Other 





Socioeconomic status 

Subsidized lunch 
182^{a} 121^{b} 
58^{a} 57^{b} 
124^{a} 90^{b} 
56^{a} 56^{b} 
0.05 0.02 
No subsidized lunch 
132^{a} 91^{b} 
42^{a} 43^{b} 
97^{a} 72^{b} 
44^{a} 44^{b} 
0.05 0.02 
Disability status 

Speechlanguage impairments 





Learning disabilities 





Behavior disorders 





Intellectual disabilities 





Other 
33^{a} 20^{b} 
10^{a} 9^{b} 
29^{a} 20^{b} 
13^{a} 12^{b} 
0.18 0.19 
Not identified with a disability 
282^{a} 191^{b} 
89^{a} 90^{b} 
192^{a} 142^{b} 
87^{a} 88^{b} 
0.12 0.12 
ELL status 

English language learner 





Not English language learner 





Gender 

Female 
156^{a} 100^{b} 
49^{a} 47^{b} 
108^{a} 76^{b} 
49^{a} 47^{b} 
0.00 0.00 
Male 
160^{a} 112^{b} 
51^{a} 53^{b} 
113^{a} 86^{b} 
51^{a} 53^{b} 
0.00 0.00 
^{a}Full Sample which was used for the CBM or targeted measures. ^{b}Sample included students with a pretest state accountability test score in math and a posttest state accountability test score in math (two consecutive years).
Training of Instructors: 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 1hour 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 preestablished 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 onsite 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 onsite 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.