Concrete-Representational-Abstract (CRA)
Overview
CRA is a sequential instructional approach during which students move from working with concrete materials to creating representational drawings to using abstract symbols. Using this concrete-representational-abstract sequence helps students develop the thorough mental representations that are foundational for conceptual understanding.
Example: Use This Strategy in the Classroom
Watch how CRA can be used to teach difficult math concepts. By using n-boxes, the students begin to understand algebraic expressions.
Design It into Your Product
Learn how ST Math uses CRA to build mathematical understanding. All math concepts are first presented visually in games requiring digital manipulation of objects. As students progress, the math symbols are slowly introduced until a student sees the full equation represented in the game they are playing.
Videos are chosen as examples of strategies in action. These choices are not endorsements of the products or evidence of use of research to develop the feature.
Factors Supported by this Strategy
More Instructional Approaches Strategies
Providing math tasks with high cognitive demand conveys high expectations for all students by challenging them to engage in higher-order thinking.
Thinking of and about patterns encourages learners to look for and understand the rules and relationships that are critical components of mathematical reasoning.
Teaching students to recognize the structures of algebraic representations helps them transfer solution methods from familiar to unfamiliar problems.
Discussing strategies for solving mathematics problems after initially letting students attempt to problem solve on their own helps them understand how to organize their Algebraic Thinking and intentionally tackle problems.
The flipped classroom has two parts: cooperative group activities in class and digitally-based individual instruction out of class.
In guided inquiry, teachers help students use their own language for constructing knowledge by active listening and questioning.
Math centers with math games, manipulatives, and activities support learner interests and promote the development of more complex math skills and social interactions.
Through short but regular mindfulness activities, students develop their awareness and ability to focus.
Instruction in multiple formats allows students to activate different cognitive skills to understand and remember the steps they are to take in their math work.
Using multiple methods of assessment can help educators gain a comprehensive understanding of learner progress across a wide range of skills and content.
When teachers connect math to the students' world, students see how math is relevant and applicable to their daily lives.
A strengths-based approach is one where educators intentionally identify, communicate, and harness students' assets, across many aspects of the whole child, in order to empower them to flourish.
Untimed tests provide students the opportunity to flexibly and productively work with numbers, further developing their problem-solving abilities.
Writing that encourages students to articulate their understanding of math concepts or explain math ideas helps deepen students' mathematical understanding.
