Introduction
Teaching maths isn’t just about presenting formulas – it’s about helping students develop a deep, lasting understanding of the maths concepts through a clear, structured approach: an approach that is informed by research and proven by implementation.
That’s exactly what our I-CRAVE Maths® Methodology achieves.
Designed to provide explicit, step-by-step instruction, our I-CRAVE Maths® Methodology guides educators in teaching maths as the language it is, bridging the gap between abstract theory and practical application. Here’s a breakdown of how our I-CRAVE Maths® Methodology works and why it’s transforming numeracy outcomes in classrooms all across Australia and Internationally.
Our I-CRAVE Maths® Methodology acronym stands for:
I: Identify Their Level
Effective instruction begins with knowing exactly where a student is in their learning journey.
Using sequential, simple-to-administer assessments, teachers first identify the student’s current level of mastery. This ensures that instruction starts at a point where the learner is both capable and ready to progress. From this starting point, the teacher follows the I-CRAVE Maths® framework and a mastery-based approach, ensuring students gain full command and understanding of each concept before moving on.
The instructional process is grounded in the “Build, Draw, Write, Say” cycle, which reinforces concepts through multiple sensory pathways.
C: Build in the Concrete
Concrete teaching and learning forms the foundation of the I-CRAVE Maths® Methodology. Each lesson begins with accurate demonstrations using hands-on manipulatives, such as integer blocks or an advanced kit. The focus is on building rectangles, a visual and tactile method that helps students understand complex ideas from addition, subtraction, multiplication and division of whole numbers to that of fractions, decimals and percents and algebra in a concrete, physical way.
By starting every lesson with manipulatives, students engage their tactile and visual senses, making abstract concepts tangible and simple to grasp.
R: Draw a Representation
After building a concrete model, the next step is to draw a proportionately accurate representation of what has just been built. This stage transitions students from a physical to a visual understanding of the concept.
For example, if a student has built a rectangle to represent a multiplication problem, they’ll now draw that rectangle on paper, ensuring the proportions remain consistent with what they have built, based on the unit of measure. This step is crucial because it bridges the gap between what the student can see and touch and what they will eventually represent symbolically (abstractly).
A: Write in the Abstract
With a clear visual model in place, students are now ready to move to the abstract stage.
Here, they learn to write the symbols that represent the maths problem, such as equations or expressions. At this point, the teacher emphasises that maths is a language, and symbols are a way of communicating ideas clearly and concisely.
By gradually introducing abstract notation after concrete and representational learning, students develop a deep understanding of the symbols, rather than memorising formulas by rote.
V: Say It to Be Heard Verbally
Dialogue plays a critical role in deepening understanding. In this stage, the teacher engages students in verbalising their thought process, encouraging them to explain what they’ve learned and how they arrived at their answers.
This process not only enhances retention but also allows the teacher to check for comprehension. Asking open-ended questions and encouraging students to articulate their reasoning helps reinforce learning and builds confidence in using maths language. Research also emphasises the importance of the student verbalising their findings and hearing their own voice, to support their learning and mastery of the concepts.
E: Be Explicit
The final step of I-CRAVE Maths® focuses on explicit instruction, ensuring that everything taught is clear, accurate, precise, and transferable.
Explicit Instruction means:
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- Ensuring congruency between the models used, the representations drawn, the symbols written, and the verbal instructions given and said.
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- Avoiding ambiguity by being direct and clear in teaching.
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- Using scripted teaching where appropriate to ensure precision, while avoiding the mere memorisation of formulas or maths facts without understanding.
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- Ensuring that all instruction and all learning lays a foundation for more advanced maths workings.
This step is vital because students need consistency and clarity to apply what they’ve learned in real-world situations. By maintaining congruency across all stages, the I-CRAVE Maths® framework ensures that students not only understand the concept but can also use it confidently outside the classroom, and in every-day, real life situations.
Why I-CRAVE Maths® Methodology Works
The I-CRAVE Maths® Methodology works because it is rooted in multi-sensory learning – engaging sight, touch, hearing, and verbal interaction to reinforce understanding. It ensures:
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- No step is skipped: Each phase builds on the previous one, providing a complete, scaffolded learning experience.
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- Mastery before progression: Students only move forward once they’ve fully understood a concept, minimising gaps in learning.
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- Real-world application: The explicit instruction and dialogue stages help students transfer their learning to real-world scenarios, improving problem-solving skills and confidence.
Conclusion
I-CRAVE Maths® Methodology provides educators with a structured, sequential, and mastery-based framework that transforms how students learn maths effectively. By starting with hands-on manipulation, moving through visual representation, and gradually introducing abstract symbols, students gain a solid conceptual foundation of maths. The addition of explicit instruction and dialogue ensures that no concept is left vague or ambiguous.
For educators looking to improve numeracy outcomes, especially for struggling learners, students with Dyscalculia and other learning differences, I-CRAVE Maths® offers a proven path from confusion to clarity – one step at a time.
Join our leading multi-sensory maths specialist and Dyscalculia Specialist (DUK), Esther White, at our next training to learn the subtleties of her I-CRAVE Maths® Methodology that makes all the difference; the subtleties that you need to embed into your maths instruction to absolutely transform your student’s numeracy outcomes.
Register for Training Today and start making maths make sense.