math materials used in the concrete, representational, abstract tutoring method

Mindguide uses the Concrete Representational Abstract (CRA) method to demystify algorithms.

At Mindguide Learning, we use the Concrete-Representational-Abstract (CRA) teaching method to explicitly illustrate what can seem like meaningless symbols and procedures to students who need a different, non-traditional method of instruction. Aligned with the National Mathematics Advisory Panel, our method supports the development of conceptual understanding before expecting accurate use of algorithms.

The CRA method, developed by American psychologist Jerome Bruner, is the core of our instructional philosophy and provides students with an engaging, dynamic and comprehensive learning experience.

In the concrete phase, students use hands-on tangible objects to demonstrate concepts.

In the representational phase, they draw or use digital models, bridging the physical and the abstract.

The abstract phase is purely symbolic. Students use only numbers and symbols to model problems or concepts - only after demonstrating proficiency in the previous phases, so they move forward with deep understanding and confidence.

We adapt CRA for all kinds of students. Our concrete manipulatives - base ten materials, fraction tiles, bead strings and analog clocks - were carefully chosen. We tailor our approach to meet each student's conceptual understanding, providing a personalized and immersive learning experience. Our experienced educators create plenty of opportunities for practice using fun and engaging games with playing cards, dominoes, and dice. The combination of explicit instruction, immediate feedback and repetition creates deep and lasting learning.

CRA is more than just a teaching method – it's a bridge that spans the gap between conceptual understanding and procedural knowledge. This approach aligns with the National Council of Teachers of Mathematics' emphasis on problem-solving and sets the stage for a transformative learning experience that can undo a student's resistance to math.