WWC review of this study

Testing the Efficacy of a Tier 2 Mathematics Intervention: A Conceptual Replication Study [Whole number understanding intervention vs. control]

Doabler, Christian T.; Clarke, Ben; Kosty, Derek B.; Kurtz-Nelson, Evageline; Fien, Hank; Smolkowski, Keith; Baker, Scott K. (2016). Exceptional Children, v83 n1 p92-110. Retrieved from: https://eric.ed.gov/?id=EJ1116305

  • Randomized Controlled Trial
    , grade

Reviewed: February 2020

At least one finding shows promising evidence of effectiveness
At least one statistically significant positive finding
Meets WWC standards with reservations
General Mathematics Achievement outcomes—Statistically significant positive effect found for the domain
Comparison Period Sample Intervention
Significant? Improvement

Test of Early Mathematics Ability (TEMA-3)

Targeted Math Intervention vs. Business as usual

0 Months

Full sample;
301 students




More Outcomes

Stanford Early School Achievement Test (SESAT)

Targeted Math Intervention vs. Business as usual

5 Months

Full sample;
275 students




Show Supplemental Findings

Stanford Achievement Test- Tenth Edition (SAT-10): Math

Targeted Math Intervention vs. Business as usual

11 Months

Full sample;
256 students





Evidence Tier rating based solely on this study. This intervention may achieve a higher tier when combined with the full body of evidence.

Characteristics of study sample as reported by study author.

  • 24% English language learners

  • Female: 50%
    Male: 50%

  • Suburban, Urban
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  • Race
    Native American
    Other or unknown
  • Ethnicity
    Not Hispanic or Latino    


The study took place in urban and suburban schools in 2 school districts in the Boston, Massachusetts metropolitan area.

Study sample

Kindergarten students were screened for eligibility for the ROOTS intervention and then the 10 students with the lowest scores on the screening assessment were randomly assigned to one of three conditions within classroom: (1) a ROOTS small group with 2 students to 1 teacher; (2) a ROOTS large group with 5 students to 1 teacher; or (3) the comparison (business as usual) condition. In some instances, classrooms did not have 10 ROOTS-eligible students so classrooms were combined to create “virtual ROOTS classrooms”. The study was conducted in 36 kindergarten classrooms in 9 schools across 2 school districts. A total of 319 students were randomly assigned to one of the conditions in the study (162 to the ROOTS large group intervention, 67 to the ROOTS small group intervention, and 90 to the control condition). The average age in the baseline sample was 5.2 years. Approximately half of the students were male, 10 percent were eligible for special education, and 24 percent were limited English proficient. The racial and ethnic background of students was 89 percent white, 6 percent black, 1 percent Asian, 3 percent multi-racial, and 50 percent Hispanic. The analytic sample size varied depending on the outcome measure.

Intervention Group

Students assigned to the ROOTS intervention received 50 lessons focused on whole numbers concepts and skills. ROOTS is a Tier 2 supplemental intervention that uses explicit and systematic instruction, including modeling, practice, visual representations, and academic feedback. Students are also encouraged to discuss their mathematical thinking and methods for problem solving. The intervention took place 5 times per week for 10 weeks, and each session lasted for 20 minutes. The intervention was delivered in small groups of 2 or 5 students. The intervention began in November and ended in March of the 2013–2014 school year. Similar to the comparison condition, intervention students also received daily core (Tier 1) mathematics instruction. The authors combined the two intervention groups for analysis, so the focus of this review is on the contrast between ROOTS large and small groups versus the comparison group.

Comparison Group

Students assigned to the comparison group received core (Tier 1) mathematics instruction from their kindergarten classroom teacher which was primarily Scott Foresman mathematics curriculum in one district and enVisionMath curriculum in the other. Based on teacher-reported data, the average math lesson in comparison classrooms was 46 minutes long.

Support for implementation

Interventionists received 2 professional workshops each lasting 5 hours long that covered content, instructional practice, and small group management techniques. Interventionists practiced the curriculum and received feedback from coaches during the workshop. They were also visited one to four times depending on need while implementing the intervention by coaches who observed their lessons and provided feedback. Across all observations, observers recorded an average of 4.26 out of 5 activities were delivered during lessons. On average, interventionists also met lesson objectives (scoring 3.46 of out 4 on a Likert scale), followed teacher scripting (3.37 out of 4), and used prescribed math models (3.58 out of 4).

In the case of multiple manuscripts that report on one study, the WWC selects one manuscript as the primary citation and lists other manuscripts that describe the study as additional sources.

  • Doabler, C. T., Clarke, B., Kosty, D., Kurtz-Nelson, E., Fien, H., Smolkowski, K., & Baker, S. K. (2019). Examining the impact of group size on the treatment intensity of a tier 2 mathematics intervention within a systematic framework of replication. Journal of learning disabilities, 52(2), 168-180.


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