CRA (Concrete – Representational – Abstract) VRA (Virtual-Representational -Abstract)
Table of Contents
Bloom's Level
Use
Setting
Activity
Technology
Related Strategies
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Description
Concrete-Representational-Abstract (CRA) is a three-stage instructional strategy that supports conceptual understanding and procedural learning, particularly in mathematics. Students learn by manipulating concrete materials, followed by pictorial representations of the concrete materials, and then solve problems using abstract symbols. When teachers use CRA, they model each stage explicitly and provide many opportunities for students to practice during each stage. Students make connections between each stage and should not move on to the next stage until they have mastered the previous stage. CRA is a gradual, systematic process and should be implemented in order because each stage builds on the next. While CRA was specifically designed as a math strategy, it can also be used in other STEM subjects where students would benefit from developing conceptual understanding through these distinct stages. VRA is similar with the exception that instead of concrete manipulatives, students use virtual manipulatives.
When To Use It
As a learning strategy, use CRA/VRA when you want students to:
- use manipulatives to develop conceptual understanding of abstract concepts
- connect concrete understanding to abstract processes
- practice solving problems using a multisensory approach
As an instructional strategy, use CRA/VRA when you want to:
- apply a structured approach to teaching conceptual and procedural information
- make learning accessible to diverse learners
- apply a multisensory approach to teaching concepts and skills
How To Use It
Advance Prep
- Determine which manipulatives or concrete materials are most appropriate for teaching a particular concept/skill.
- Determine the appropriate drawing techniques or pictorial representations of the concrete objects.
- Based on the particular concept/skill you are teaching, identify appropriate strategies for supporting students with making connections between the concrete and representational stages, and the representational stage and the abstract stage.
- Plan to model each stage explicitly and provide ample opportunities for students to practice and demonstrate mastery before moving on to the next stage. As you move through each stage, the abstract symbols should be presented in conjunction with the concrete materials and representations so that students can associate the abstract symbols with their concrete and representational understanding.
Implementation
- Introduce the concept or skill using concrete materials (e.g. cubes, counters, geoboards, blocks, alpha tiles, molecular models, etc.) Model how to use the manipulatives to demonstrate the concept or solve a problem.
- Allow students many opportunities to practice the concept using the concrete materials and assess their understanding. Ensure that students have mastered the concept at the concrete level before moving on to the representational stage.
- Introduce pictorial representations of the concrete materials. Model how to use pictorial representations to demonstrate the concept or solve a problem.
- Give students ample opportunities to practice the concepts using pictures, drawings, or digital images. Assess student understanding and do not move on to the abstract stage until students have mastered the concept at the representational level.
- Now, teach students the concept using numbers, symbols, notations, etc. Model the concept using abstract symbols and include concrete and pictorial representations to help students connect their concrete understanding to the abstract.
- Provide many opportunities for students to practice the concept/skill using abstract symbols. Assess student understanding, and a
Pros
- Aligns with principles of Universal Design for Learning
- Promotes a deep understanding of concepts before rules
- Builds conceptual as well as procedural understanding
- Meets the needs of diverse learners
- Provides a structured approach for students to learn STEM concepts
- Helps to build confidence in conceptual and procedural understanding
Cons
- Teachers must take care to choose appropriate manipulatives to represent concepts.
- Students must achieve mastery at each stage before moving on to the next, which may be time-consuming and require increased differentiation.
- Physical materials are required for students to develop their concrete understanding.
Culturally Responsive Application
Concrete-Representational-Abstract is a multisensory approach to developing conceptual and procedural understanding. Multisensory learning is effective for meeting the needs of diverse learners and is one of many cultural learning tools that utilize the brain’s memory systems. Using concrete representations not only engages students but it makes learning accessible. Because this three-stage strategy emphasizes mastery before moving on to the next stage, all students are accountable to the same high standards of learning. CRA promotes equity in the learning process and aligns with the tenets of culturally responsive pedagogy.
Emerging English Language Support
Modeling the concept and provide lots of opportunities to practice at all three levels.
Students with Disabilities Support
CRA instructional framework is effective in mathematics for students with learning disabilities relative to computational instruction
Subjects
2.1 K-8 mathematics, 2.2 High school number & quantity, 2.3 High school algebra, 2.4 High school functions, 2.5 High school geometry, 2.6 High school statistics & probability, 3.1 Earth and space science, 3.2 Life science, 3.3 Physical science, 5.1 Computing systems, 5.2 Networks & the internet, 5.3 Data & analysis, 5.4 Algorithms & programming
Why It Works
CRA and VRA research has largely focused on investigating the effect of the approach for learners with disabilities in inclusive settings. The gradual release from concrete to representational has 4 known steps: demonstration, modeling, guided practice followed by independent practice, and immediate feedback (REF88). CRA/VRA can be used with students of low, medium, or high ability (REF89). Students using the CRA/VRA method may develop and remember procedural steps more accurately and help make fewer basic computational mistakes than if taught abstract-only(REF94). Virtual manipulatives have evidence of being effective for content acquisition and maintenance for both with students with disabilities (REF92) and in elementary math classrooms (REF93).