# Concrete-Representational-Abstract Instructional Approach

What is it?

Concrete-Representational-Abstract-Approach or CRA for short “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.” (The Access Center, 2004).

The purpose of teaching through a concrete to representational to abstract approach is to make sure students completely understand the skill or concept they are learning before executing the problem on their own. The three steps of CRA include: Concrete, Representational and Abstract. The Concrete stage is the “doing” stage, the Representational is the “seeing” stage and the Abstract is the “symbolic” stage.

1.     Concrete

In this step, the teacher introduces a math concept by modeling examples using manipulatives such as unifix cubes, pattern blocks, beans, base ten blocks etc. Students are able to manipulate the objects by using their visual, tactile and kinesthetic senses. Students are given many opportunities to use these objects to problem solve.

Research-based studies show “that students who use concrete materials develop more precise and more comprehensive mental representations, often show more motivation and on-task behavior, understand mathematical ideas, and better apply these to life situations.” (Anstrom, 2006).

A teacher could model how to multiply by using marbles as manipulatives. The teacher would display three groups of three marbles each and ask the students how many marbles there are.  The teacher would allow students to touch and count the marbles.

Once students have demonstrated mastery using concrete materials, they are ready to move onto the Representational step.

2.     Representational

In this step, the student would draw pictures that represent the concrete objects previously used. These pictures help the student visualize the math operations during problem solving. The teacher must explain the relationship between the pictures and the concrete objects and allow the student numerous opportunities to practice until they solve the problems independently. After students are successful with the representational step, they would move on to the abstract step.

3.     Abstract

During this final step teacher models the concept at a symbolic level and uses math symbols to represent addition, subtraction, multiplication and division.  It is often referred to as “doing math in your head.” After students have handled multiplication manipulatives and made pictorial representations, the teacher would show the abstract form, which is “3 x 3.”

This is an example of what CRA would look like.

This instructional approach “benefits all students but has been shown to be particularly effective with students who have mathematics difficulties, mainly because it moves gradually from actual objects through pictures and then to symbols. (Sousa, 2007).

While this video is a little lengthy, it gives a great overview of the CRA approach.

Connection to Multiple Intelligences

Students with strengths in tactile and kinesthetic learning styles learn best with hands-on experiences. These students might even prefer to act out the concepts. Visual learners can easily visualize counters and auditory learners can repeat the concepts in their heads.

My thoughts…

I believe this is a great approach to use with learning disabled students as well as non-disabled students.  It is especially beneficial to students with learning disabilities because they have a harder time with abstract concepts. The CRA  approach can help students connect ideas so the gain a deep understanding of the math concept. As a result, students are more likely retain the information .

CRA allows the teacher to differentiate instruction and meet the needs of all students.

Resources

Anstrom, T. (2006). Supporting Students in Mathematics Through the Use of Manipulatives. Retrieved from Center of Implementing Technology in Education : http://www.cited.org/library/resourcedocs/Supporting%20Students%20in%20Mathematics%20Through%20the%20Use%20of%20Manipulatives.pdf

Kurczodyna, V., Cavanagh, C. & Curiel, J. (n. d.) Math Instrucitonal Strategies. Retrieved from http://www.eiu.edu/~speebp/ppt/Math–_CRA_PPT.ppt