Sample size: 224 first grade students across 10 elementary schools. (771 students were initially screened. The final sample was comprised of 139 program students and 64 control students.)
Risk Status: Two main considerations drove sample selection: (a) maintaining sufficient power and (b) reliably assessing risk. Of the initial pool of students (N = 771), the lowest 35% (n = 269) was identified as being “atrisk” based on an initial administration of the Texas Early Mathematics InventoriesProgress Monitoring measures (TEMIPM; University of Texas System & Texas Education Agency, 2007a; refer to the Measures for further details about this test) in the fall (September). Students were administered four additional TEMIPM probes (alternate forms of the original measure used for student selection) over a 3week period to determine whether there were false positives among the initial pool of students. False positives are a particular concern given the generally “chaotic” nature of early achievement and the increased possibility of falsely identifying students as being “atrisk” when they were merely distracted, anxious, or unfamiliar with the testing protocols. Growth modeling (with continuous outcomes and autocorrelated residuals) was used to estimate caselevel factor scores for intercept and slope for each of the 238 cases using PLUS 4.1 (preliminary analyses suggested a statistically significant positive trend in scores over time, on average thus, a growth model approach was preferred over a confirmatory factor model). Intercept was conceptualized as the last of the four additional TEMIPM measures (beyond the TEMIPM used to initially identify the lowest 35%). Estimated time 4 scores were used to make final sample selection. The cut score was selected based on the probabilities of diagnostic accuracy (i.e., likelihood ratio [LR]) derived using receiver operator curve (ROC) analysis. Using this procedure, 14 students were found to be false positives and were eliminated from the sample.
A concern with accuracy and the need to maintain an adequate sample size both influenced our sampling strategy. Preliminary power analyses suggested a sample size of 240, with 160 in the treatment condition and 80 in the comparison group. The initial pool of eligible students was only 238, so our strategy was to identify students who clearly were not at risk, based on their estimated score at time 4 and a very conservative risk threshold (LR: negative of 0.70). The final sample (n = 224:151 treatment and 73 control) identified for treatment and control conditions was associated with a minimal detectable effect size of approximately 0.40, assuming 0.80 power and 45 instructional groups with five students in each group.
Demographics:

Program 
Control 
p of chi square 

Number 
Percentage 
Number 
Percentage 

Grade level 

Kindergarten 





Grade 1 
139 

64 

0.00 
Grade 2 





Grade 3 





Grade 4 





Grade 5 





Grade 6 





Grade 7 





Grade 8 





Grade 9 





Grade 10 





Grade 11 





Grade 12 





Raceethnicity 

AfricanAmerican 

26.6 

21.5 
0.006 
American Indian 





Asian/Pacific Islander 

3.6 

6.2 
0.091 
Hispanic 

33.0 

40.0 
0.003 
White 

36.6 

32.3 
0.002 
Other 





Socioeconomic status 

Subsidized lunch 

50.4 

52.3 
0.000 
No subsidized lunch 

49.6 

47.7 
0.000 
Disability status 

Speechlanguage impairments 





Learning disabilities 





Behavior disorders 





Intellectual disabilities 





Other 





Not identified with a disability 
139 
100 
64 
100 
0.000 
ELL status 

English language learner 





Not English language learner 





Gender 

Female 

43.9 

44.6 
0.000 
Male 

56.1 

55.4 
0.000 
Training of Instructors: The research team included two full time intervention coordinators and five graduate research assistants (GRAs) who were doctoral and master’s students in the Department of Special Education; all of the GRAs held teaching credentials or were completing a teaching certification program. This research team was also responsible for conducting the intervention.
At the beginning of the academic year, the principal investigator provided a 3hour training on the intervention lessons and accompanying instructional materials. This training consisted of an explanation of the content and review and modeling of systematic instruction. Following this training, the research team practiced the lessons with one another. Prior to intervention, the tutors taught a lesson and received feedback from experienced tutors who were using the same lessons with a group of students. Throughout the school year, training sessions were conducted before each intervention unit (seven total sessions). Tutors were visited weekly and team meetings were held to solve issues.