Research-Based Concrete-Representational-Abstract Instruction
According to Jean Piaget’s research, most students do not become Abstract learners until between the ages of 12-14.
Manipulatives have been described as the “missing link” to help students become abstract learners and successful at math.
Manipulatives have been described as the “missing link” to help students become abstract learners and successful at math.
This llustration shows the three theoretical stages of learning that children move through according to Jean Piaget and other cognitive psychologists. Moving with Math® lessons are carefully crafted using the research-based Concrete-Representational-Abstract (CRA) instructional model.
CRA Sequence of Experiences Builds a Strong Foundation
In CRA instruction every math concept is explicitly introduced
with a concrete manipulative and a hands-on activity. This allows students to physically interact with concrete representations of abstract mathematical concepts, which helps them build a
deeper understanding and improve engagement.
As students move to the representational stage they are asked to visually describe and communicate the concept by writing or drawing pictures. This step is crucial because it acts as a bridge between concrete manipulation of objects and the abstract symbolic level.
This sequence of experiences in CRA instruction provides an access point and a firm, memorable foundation for the abstract, symbolic operations needed for success in math.
As students move to the representational stage they are asked to visually describe and communicate the concept by writing or drawing pictures. This step is crucial because it acts as a bridge between concrete manipulation of objects and the abstract symbolic level.
This sequence of experiences in CRA instruction provides an access point and a firm, memorable foundation for the abstract, symbolic operations needed for success in math.
Benefits of Using Manipulatives
As students are involved in CRA learning, they engage each of the three learning styles – visual, auditory and kinesthetic as they Explore, Discover and Describe the patterns of mathematics. Students
communicate the patterns they have discovered in several ways.
CRA lessons ask students to communicate verbally, by drawing pictures and by writing with pencil and paper. These activities reach out to students with various learning styles and assist them in their movement to the abstract stage of learning.
CRA lessons ask students to communicate verbally, by drawing pictures and by writing with pencil and paper. These activities reach out to students with various learning styles and assist them in their movement to the abstract stage of learning.
The kinesthetic and visual experiences that are offered when students use manipulatives supports students’ retention and recall of important mathematical procedures, facts, and understanding.