The CRA approach consists of three main ideas: Concrete, Representational, and Abstract¹. The Concrete stage is the first stage of the CRA approach. It is known as the “doing” stage and involves physically manipulating objects to solve a problem, engage with a puzzle, or build an object. The Concrete stage helps students to understand abstract concepts better by providing them with a physical, touchable, movable object of the concept. This is where the concept of an “object lesson” comes from. Educators often engage the concrete stage when they represent mathematical concepts through concrete objects such as pattern blocks, base ten blocks, or relational rods. In other subjects such as the sciences or language arts students may explore objects related to their study such as pine cones, leaves, plants, or props related to a story. This is where the over-emphasis of two-dimensional “screened” representations of concepts too early in a child’s development is not only not beneficial but can become harmful. Almost all Edtech solutions are working within this realm, with the exception of a few (i.e. apps engaging students in the use of objects the move on a table to code characters on in iPad screen). We do a major disservice to the development of our students when we limit our technology to what’s convenient for companies to sell through a “screened” medium. We have to think beyond.

The Representational stage is the second stage of the CRA approach. It is known as the “seeing” stage and involves using visual aids to represent the concrete objects used in the first stage. The Representational stage helps students transfer the concrete explorations and exposure they have experienced into a visual (2D representation) of the concept. Students may draw a base ten block representation of number or draw a diagram to represent a scientific process.

The Abstract stage is the third and final stage of the CRA approach. It is known as the “symbolic” stage and involves using abstract symbols to represent the visual aids used in the second stage. Students here would represent mathematical ideas through only symbolic abstract numbers and symbols such as an equation.

Depending on the specific concept, students are often, throughout any developmental phase, moving through concrete, representational, and abstract stages.

Edtech companies must always consider how solutions are moving (or supporting the movement) of students through these stages as conceptual understanding grows.

Here are five key recommendations for Edtech companies in designing solutions that help children learn conceptually by engaging the CRA approach:

1. Use concrete materials to teach abstract concepts.

2. Use visual aids to help students understand abstract concepts.

3. Encourage pattern recognition in students.

4. Use appropriate concrete objects to teach particular math concepts/skills.

5. Foster deeper understanding of how manipulatives facilitate student learning of math concepts by emphasizing the connection between concrete and abstract⁵⁶.

Augmented reality technology can help with these key recommendations in several ways. For example, it can be used to create interactive and engaging learning experiences for students. Augmented reality can also be used to provide students with visual aids that help them understand abstract concepts better⁴. Here are some ways in which augmented reality technology can help with implementing the key recommendations:

1. Use augmented reality to create interactive and engaging learning experiences for students.

2. Use augmented reality to provide students with visual aids that help them understand abstract concepts better.

3. Use augmented reality to provide students with appropriate concrete objects to teach particular math concepts/skills⁴.
   

Sources:

(1) What Is The Concrete Representational Abstract (CRA) Approach And How to Use It. https://thirdspacelearning.com/us/blog/concrete-representational-abstract-math-cpa/ Accessed 3/15/2023.

(2) The CRA Approach - LD@school. https://www.ldatschool.ca/learning-modules/cra-strategies/the-cra-strategy/ Accessed 3/15/2023.

(3) How to Teach Math Effectively Using the Concrete Representational .... https://shelleygrayteaching.com/concrete-representational-abstract-model/ Accessed 3/15/2023.

(4)Augmented Reality in Education: Use Cases, Benefits & Examples. https://program-ace.com/blog/augmented-reality-in-education/ Accessed 3/15/2023.

(5) What Is Visual-Spatial Learning? (With Characteristics). https://www.indeed.com/career-advice/career-development/what-is-visual-spatial-learning Accessed 3/15/2023.

(6) Why spatial is special in education, learning, and everyday activities .... https://cognitiveresearchjournal.springeropen.com/articles/10.1186/s41235-021-00274-5 Accessed 3/15/2023.

(7) Augmented Reality in Education: Interactive Classrooms. https://online.maryville.edu/blog/augmented-reality-in-education/ Accessed 3/15/2023.

(8) 10 Best Examples Of VR And AR In Education - Forbes. https://www.forbes.com/sites/bernardmarr/2021/07/23/10-best-examples-of-vr-and-ar-in-education/ Accessed 3/15/2023.

(9) Use of Augmented Reality in Education: tools, apps and tips - 2023. https://thinkmobiles.com/blog/augmented-reality-education/ Accessed 3/15/2023.

(10) Augmented Reality In Education - eLearning Industry. https://elearningindustry.com/augmented-reality-in-education-staggering-insight-into-future Accessed 3/15/2023.