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Transcript of Concrete-Representational-Abstract
students are actively drawing pictures to represent the concept
the pictures need to align with the concrete manipulatives
the simpler the picture, the easier for the student to see the concept
using colors may help students
the pictures need to be accurate representations of the skill
providing more than one option provides choice and can benefit students
teachers need to model extensively for students to bridge the gap
A "bridge" lesson is helpful -allow the students to use the manipulatives and draw the pictorial representation
Make explicit connections to the abstract concept
students are actively solving using numbers, symbols, and equations
the formulas need to align with the standard
the formula should include the components of the concrete and representational stage
the algorithm needs to conceptually 'make sense' to the student
showing more than one way to solve for the answer may benefit students
teachers need to model extensively
it is essential for teachers to encourage students to use other levels of understanding if they are struggling
A "bridge" lesson is helpful - allow student to use manipulatives and/or pictorial representations while working in the abstract.
within your class students may progress at different rates through the sequence
this is perfectly acceptable, but never fast forward a student until they demonstrate mastery at the given stage
always ensure that the manipulatives and pictures align with the given concept
don't choose a manipulative or picture technique because it's novel, cute, creative, or unique
choose a manipulative or picture technique because it is proven to be effective
This is a research based instructional technique. Studies have been done and suggest that this instructional technique is effective for a variety of mathematical skills and for students with varying disabilities.
One thing to consider however, is that all the studies utilized a direct instruction technique when implementing so this would be the best instructional method to follow when implementing.
students are actively using manipulatives
the manipulatives need to align and be appropriate for the objective being taught
manipulatives that are overstimulating will detract from the lesson
manipulatives that are not aligned will merely confuse students more
teachers need to model extensively in order for students to use the manipulatives appropriately
it is essential for teachers to refer to the abstract explicitly while modeling with the manipulatives
Concrete-Representational-Abstract Instructional Approach Summary Report—
The Access Center, American Institutes for Research, Washington, DC
Concrete-Representational-Abstract Sequence of Instruction. (n.d.).
Retrieved October 27, 2014, from www.fcit.usf.edu/mathvids/strategies/cra.html
Instruction/Mathematics/Teacher Tools/Concrete-to-Representational-to-Abstract Instruction | Special Connections. (n.d.). Retrieved October 27, 2014 from www.specialconnections.ku.edu/?q=instruction/mathematics/teacher_tools/concrete_to_representational_to_abstract_instruction
Maccini, P., Mulcahy, C., & Wilson, M. (2007). A Follow-Up of Mathematics Interventions for Secondary Students with Learning Disabilities. Learning Disabilities Research & Practice, 22(1), 58-74.
There are many synonyms for this instructional framework
Concrete Representational Abstract (CRA)
Concrete Pictorial Abstract (CPA)
Concrete Semi-concrete Abstract (CSA)
Graduated Instructional Sequence
Model (Explicitly show the skill)
Guided Practice (Do with the students)
Independent Practice (Provide opportunities for students to practice the skills independently)
Formative Assessment (Assess the students to make instructional decisions)
Formally conceptualized as a sequence of instruction
Now we think of it as a framework because we can work on multiple levels of understanding at once