How does TouchMath use the Concrete Representational Abstract (CRA) Continuum?

CRA is a three-stage learning process where students learn through the physical manipulation of concrete objects, then through pictorial representations, and finally by solving problems using abstract notation.

The Concrete-Representational-Abstract (CRA) continuum is one foundation of the TouchMath program. CRA provides a structure for students to grasp mathematical concepts, and you’ll see it referenced in each

The CRA continuum ensures that learning progresses through three stages:

Concrete

Students use real-life physical objects to explore concepts.

• TouchNumerals
• TouchPoints
• Finger Counting
• Manipulatives

Representational

Students draw or use visual aids.

• Modeling and Drawing
• Number Lines
• Descriptive Model: describing a math happening
• Predictive Model: making a prediction
• Optimizing Model: finding the best
• Statistics and Probability Model: using data and chance
• Rating and Ranking Model: making decisions

Abstract

Students work with symbols and numbers.

• Concepts (Properties)
• Numbers
• Operations
• Calculator

This scaffolded approach:

• Solidifies understanding between different stages of learning
• Allows students to gain confidence and proficiency in math at their own pace
• Enables students to apply their knowledge to more complex mathematical problems effectively