CRA- Concrete Representational Abstract A Teaching Strategy -Shelby Bentley-

Background 0 First introduced in 1993 by S.P. Miller & C.D. Mercer 0 Was later supported by the National Council of Teachers of Mathematics (NCTM) because the results exceeded their expectations 0 It helps students view mathematical calculations concretely with the use of manipulatives to help retain and understand rules and calculations. 0 Can be used with all math concepts but we chose to focus on its results with students who have difficulties with fractions.

CRA 0 3 step process 1. Use of tangible materials to represent the math concept 2. Use of semi-concrete representations (pictoral) 3. Leading to the building of connections to ultimately form them into abstract ideas

Implementation 0 Fractions concept: “part of a whole” 0 Can essentially be implemented at any grade level where visuals can be of benefit 0 Teachers should question the student at every stage 0 One step to the next is a building block, which when all built up becomes an understanding as a whole 0 Use variety to keep students actively participating

Study 1 0 In 2009 Margaret Flores conducted a study on six students at a rural elementary school. 0 The students ranged from 8-10 years of age and all came from different ethnic backgrounds. 0 4 of the students had an identified learning disability and 2 did not. They all tested at a significantly low initial baseline. 0 Instruction was provided to the students 3 days a week for 30 minutes each session. 0 After CRA implementation the student were tested which showed that 5 of the 6 exceeded the criterion of writing twenty digits on three consecutive two-minute curriculum based measures. And of those students, 4 of the 5 maintained their performance 4 weeks after the end of instruction.

Study 2 0 A study by Miller and Kaffar attempted to determine the effectiveness of CRA on students with learning disabilities working with addition with regrouping. 0 The study included 15 males and 19 females, all which had diagnosed learning disabilities. 0 Over a six week program, 16 session of CRA were implemented. 0 The results of the study showed that the mean score of the group had increased from 10%. 0 It also proved that the students who were taught through CRA out performed students who learned basic mathematical skills in a traditional way.

Wrap up 0 This type of intervention blends conceptual and procedural understanding in structured way that aids student understanding of more abstract mathematical skills and can be implemented at any grade level 0 Research has shown that the use of the concrete- representational-abstract intervention helps students with or without disabilities learn basic mathematic concepts such as fractions 0 This intervention may also be used for other mathematic concepts