Math Made Visible: CRA Process

Concrete, Representational and Abstract Models

What is CRA?

The CRA sequence of instruction provides a framework for students which moves learners through three levels of understanding: Concrete, Representational and then Abstract.

Students make multiple representations while they solve problems, which progress from concrete to abstract as they make sense of a contextual problem (Gravemeijer et al., 2002; Stylianou, 2011).

CRA process and Instruction

First, manipulative objects are used to promote conceptual understanding. Concrete-level instruction proceeds as follows: The instructor demonstrates the mathematical skill/process with manipulatives; the instructor then guides the students by participating in the use of manipulatives with the students, providing prompts and cues; and the students independently use manipulatives to demonstrate the skill/process.

Instruction at the representational level follows the same steps, but the manipulative objects are replaced by pictures and/or drawings. This serves as a transition from the use of pictures or drawings to the use of numbers only—that is, the abstract phase.

During this final phase (abstract), students use numbers only in completing a mathematical task, and instruction focuses on fluency.(Flores, 2009, p.185)

CRA Process: Topic and Dates

CRA Process for Addition, Subtraction, Multiplication and Division: One Day Session

During the morning part of our day we will visit three areas of mathematics. We will begin with place value and then move into the process of addition and subtraction. The process will proceed from using manipulatives to the abstract notations. In the afternoon, we will continue our math journey and work our way through the process of multiplication and division. At all stages we will practice the language of mathematics while using the three stages of the CRA instructional process.

Click to Register: BLaST Williamsport Office - March 24