Field Studies of RTI Effectiveness Standard-Protocol Mathematics Model (SPMM)

Study Citation

Ardoin, S. P., Witt, J. C., Connell, J. E., & Koenig, J. L. (2005). Application of a three-tiered response to intervention model for instructional planning, decision making, and the identification of children in need of services. Journal of Psychoeducational Assessment, 23, 362–380.


Program Description

The standard-protocol mathematics model (SPMM) focuses on mathematics outcomes and relies on the universal screening of level of achievement rather than on progress monitoring of achievement. Ardoin, Witt, Connell, and Koenig (2005) identified three tiers of the SPMM: a) universal classwide screening, b) classwide intervention, c) individual intervention and special education referral process.

Within this study, general education teachers were responsible for universal screening (e.g., administering curriculum-based measurement [CBM] probes in multiplication, addition, and subtraction). The classwide intervention (i.e., modeling the target skill, guided practice with frequent opportunities to respond and immediate feedback, timed independent practice to yield a score for progress monitoring, and use of delayed error correction with a verbal rehearsal strategy) was implemented by Ardoin and four graduate students. Students below the class mean received the individual intervention (e.g., peer tutoring; cover, copy, compare [CCC] + instruction) implemented by graduate students.

The first author conducted training of school personnel and graduate students in the SPMM model.

Purpose of Study


The authors conducted the study to present a demonstration of a Response-to-Intervention (RTI) model derived from the more complex models described in the special education and school psychology literature. Specifically, the purpose of the study was to answer the following question: To what degree does a classwide intervention and individual intervention improve student mathematics outcomes?


Study Method

Fourteen 4th grade students from an elementary school serving 514 students in Grades K–5 participated in the study. The school was not using an RTI model for identifying students for special education services. Participants were enrolled in one of two classrooms whose teachers chose to team-teach. The two teachers divided their classes into three math sections; participants in this study were in the lowest of the three math sections. In Phase I of the RTI model, all students were screened using multiplication, addition, and subtraction probes. Phase II consisted of the implementation of a classwide intervention because the screening data indicated a classwide skills deficit. Following the classwide intervention, 5 students needed further intervention. A combination of two interventions was implemented in Phase III (peer tutoring and CCC + instruction).

All math CBM (M-CBM) probes and CCC probes were developed using Intervention Central. Calculation problems on M-CBM and CCC probes were presented vertically. Performance on the M-CBM probes was used as the dependent measure across study phases (baseline and intervention conditions).

Study Results

Question 1: With regard to the effectiveness of the classwide intervention, Ardoin et al. (2005) reported that 9 students made improvements over baseline, but that 5 showed little or no progress. When peer tutoring was used with these 5 students, they showed some progress but only showed adequate improvement when the CCC + instruction intervention was implemented.

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