What is the Concrete-Representational-Abstract Model?
Concrete-Representational-Abstract (CRA) is an intervention for mathematics instruction that research suggests can enhance the mathematics performance of students with learning disabilities. It is a three-part instructional strategy, with each part building on the previous instruction to promote student learning and retention and to address conceptual knowledge (American Institute for Research, 2016). The CRA instructional sequence consists of three stages: concrete, representation, and abstract:
- Concrete: The teacher begins instruction by modeling each mathematical concept with concrete materials (e.g., red and yellow chips, cubes, base-ten blocks, pattern blocks, fraction bars, and geometric figures). Students manipulate the hands on concrete objects to model the math concept/skill.
- Representational: The teacher transforms the concrete model into a representational (semi-concrete) level, which may involve drawing pictures; using circles, dots, and tallies; or using stamps to imprint pictures for counting. Students draw pictures that represent the concrete objects previously used.
- Abstract: The teacher models the mathematics concept at a symbolic level, using only numbers, notation, and mathematical symbols to represent the number of circles or groups of circles. The teacher and students use operation symbols (+, -) to indicate addition, multiplication, or division.
As the teacher moves through the concrete-to-representational-to-abstract sequence of instruction, the abstract numbers and/or symbols should be used in conjunction with the concrete materials and the representational drawings.
An informative self-paced training that provides greater insights on the CRA model may be viewed by visiting the CPALMS website, at the following link: http://www.cpalms.org/Public/PreviewProfessionalDevelopment/Preview/244