
Webster's says "a poem is concrete; poetry is abstract." Though we have understood the value and used Piaget's concrete stage for decades, we often do not recognize that a large part of the value in making an approach concrete is to assist students in moving to higher level thinking. The ConcreteRepresentationalAbstract Strategy (CRA Strategy) provides an organizational structure within which lessons can be designed to effectively help students reach an abstract level of thinking around difficult concepts and content. The ConcreteRepresentationalAbstract Strategy focuses on helping students move in sequence through the following phases. concrete: When introducing new concepts to students, describe and model the concept using concrete materials. The concrete level of understanding is the most basic level of cognitive skill. When students have mastered this level of concrete understanding by modeling and describing the concept concretely themselves, instruction moves to the next step. In math, this could involve using manipulatives to count, measure, or sort. Representational: When students have mastered understanding on the concrete level, describe and model the concept by drawing or using other pictures that represent the concrete objects. The ability to represent concepts is the next level of cognitive skill. When students are able to demonstrate the concept representationally themselves, instruction moves to the next step. In math, this could involve using tally marks or dots to count, measure, or sort. Abstract: When students have mastered the representational level, describe and model the concept in an abstract manner, using the typical form in which problems are presented. The ability to work abstractly is the most advanced cognitive level. In math, this could involve using numbers to count, measure, or sort.
Note: CRA is dependent on the number of times a student gets to successfully demonstrate a skill at each cognitive level before moving to a higher level. This strategy is especially effective for mathematics, science, and social studies, where students learn abstract concepts that are readily adaptable to concrete materials. It is important that each step is modeled and described by the instructor, and that students get immediate feedback at each step to correct any misconceptions along the way.
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