The Concrete-Representational-Abstract sequence of mathematics instruction allows students to move meaningfully through less complex math concepts and procedures to more abstract, complex ones. Research indicates that the CRA sequence has been effective for students with and without disabilities. Teaches provide explicit teacher modeling and scaffolding, and also conduct ongoing assessment to determine what level of instruction is needed by various students.
CONCRETE The “Concrete” level is the most basic and crucial. Using concrete objects, students can have a sensory experience of mathematical concepts. They can see, touch, and feel math! Teachers can facilitate learning at this level by getting students to think about and verbalize how the objects reflect the mathematics.Use chips, straws, interlocking cubes, base-10 blocks, beans and bean sticks, pattern blocks, geometric prisms, paper plates, fraction barsMastery to move to Representational Level: Performs skill correctly 3/3 times, 3 consecutive days. REPRESENTATIONAL When students are able to “see” concepts and are proficient with the concrete, the concept can be modeled at the “Representational” level using drawings that represent the concrete items. When students begin to draw, their understanding of the concept can become apparent. Teachers can facilitate learning by explicitly relating the drawings to the concrete materials that were used earlier. Replicating the movements used while using the concrete items can assist struggling learners.Use tallies, dots, circles, stamps, number lines, graphs, pictograms, etc.Mastery to move to Abstract Level: Performs skill correctly 5/5 times, 3 consecutive days. ABSTRACT When students are proficient at drawing representations of math solutions, they are ready for the “Abstract” level. By connecting what students did at the earlier “representational” and “concrete” levels of learning, teachers can promote conceptual understanding and allow students to internalize their learning. Linking the abstract symbols to the concrete items and drawings that students used to progress through earlier stages, can assist in this process.Use number sentences and algorithms.Mastery of Skill at Abstract Level: Performs skill correctly 10/10 times, 3 consecutive days.
Allsopp, D., Kyger, M., & Lovin, L. (2007). Teaching mathematics meaningfully: Solutions for reaching struggling learners. Baltimore: Brookes.