CRA- Concrete Representational Abstract

A Teaching Strategy-Shelby Bentley-

Background

0First introduced in 1993 by S.P. Miller & C.D. Mercer0Was later supported by the National Council of

Teachers of Mathematics (NCTM) because the results exceeded their expectations

0It helps students view mathematical calculations concretely with the use of manipulatives to help retain and understand rules and calculations.

0Can be used with all math concepts but we chose to focus on its results with students who have difficulties with fractions.

CRA03 step process 1. Use of tangible materials to represent the

math concept2. Use of semi-concrete representations

(pictoral)3. Leading to the building of connections to

ultimately form them into abstract ideas

Implementation0Fractions concept: “part of a whole”0Can 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

0This 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

0This intervention may also be used for other mathematic concepts