THE EFFECTS OF A CONCRETE, REPRESENTATIONAL, ABSTRACT (CRA) INSTRUCTIONAL MODEL ON TIER 2 FIRST-GRADE MATH STUDENTS IN A RESPONSE TO INTERVENTION MODEL: EDUCATIONAL IMPLICATIONS FOR NUMBER SENSE AND COMPUTATIONAL FLUENCY

Abstract

This study was designed to evaluate the effects of a Concrete Representational Abstract (CRA) instructional model on Tier 2 first-grade mathematics students in a Response to Intervention model. Twelve students were instructed three times a week using the Expeditions to Numeracy program. The Test of Early Mathematics Ability-3rd edition results overwhelmingly indicated dramatic student growth. A t-test, which included all twelve students in the study, was found to be statistically significant (t=5.79, p<.01). The effects of a CRA instructional model on students' computational fluency were measured through the use of the curriculum based assessments given weekly to all first-grade students. Only those students who had not yet met the first-grade benchmark were included in the analysis of growth over time. All intervention students showed significant growth on their CBM scores throughout the study, exceeding the recommended weekly growth of 0.35. Two-thirds of the students exceed the recommended growth by two or more points. A single-subject analysis of the CBM data all indicated the strong student growth. The analyses of the student growth on the CBMs, as well as the variables that affect this change, were also analyzed using Growth Curve Modeling. The final model of analysis indicated the treatment group's slope was statistically significantly greater than the slope for other members of the study, including those students progressing at a typical first-grade level and therefore not eligible for services. These results indicate a statistically significant affect of a CRA instructional model when used with Tier 2 students in a Response to Intervention Model on students' computational fluency and mathematical achievement.