Some of our students with learning disabilities have trouble with abstract reasoning. As such, they may have difficulty verbalizing what they have learned or observed, difficulty making the connection with symbolic representations and/or understanding the math concept that is being explained or shown.
The concrete-representational-abstract (CRA) approach is a framework that research suggests can enhance math understanding and performance for students with learning disabilities. CRA is a three-part instructional strategy, with each component building on the previous instruction to promote student learning, retention of concepts and conceptual understanding.
See below to move through the concrete-to-representational-to-abstract sequence of instruction for any mathematics concept.
Conduct a CRA assessment to differentiate instruction
Start by posting the problem/equation that the student needs to solve. Show the student one problem at a time to solve.
For example:
1. Abstract: 90-12 = ____ Ask the student to solve the problem the abstract way (just ask them to solve it and note the strategy).
2. Representational: 40-15 = ______ Ask the student to solve the problem using a representational tool provided (i.e., number line, 100 chart, grid paper, etc.)
3. Concrete: 20-9 = _____ Ask the student to solve the problem using manipulatives provided (i.e, two-colored counters, base 10 blocks, fraction bars, etc.)
The student must solve all three problems regardless of how he/she performs on each problem. The problems must go in reverse order of CRA (abstract-representational-concrete) because the end goal is for students to successfully solve an abstract problem.
Note on the data sheet if the student demonstrated:
- Mastery (highly proficient with the skill/prerequisites)
- Instructional (some knowledge of skills/prerequisites)
- Frustration (little/no knowledge of the skills/prerequisites)
After the assessment
Use the data to differentiate and specialize instruction. The data will help you determine
- which students need more support with the foundational concept/prerequisite skills using manipulatives
- which need support with the representational concept using pictures/diagrams
- which need support with the abstract concept using numbers only
Concluding tips
Practice is key. Provide students ample opportunities to practice after each stage. Be sure to create routines and create an organization system for manipulatives so students can always use them as needed.
Lastly, have fun exploring, creating and building conceptual knowledge using the CRA approach to putting the "special" into specially designed math instruction.
