Students don’t struggle with maths because they’re incapable.
They struggle because something foundational was never properly built.
A concept was rushed.
A step was assumed.
Symbols were introduced before meaning existed.
Once that happens, maths stops feeling logical. Students begin memorising without understanding, guessing instead of reasoning, and avoiding tasks that expose what they don’t know.
The I-CRAVE Maths™ methodology was developed to address this exact problem – not by adding more content, but by changing how maths is taught.
Why we needed a clear methodology
For many years, I watched well-intentioned teachers work incredibly hard using a wide range of resources, yet still see students fall behind.
The issue wasn’t a lack of commitment or care.
It wasn’t a lack of effort.
And it certainly wasn’t a lack of curriculum knowledge.
The issue was inconsistency in teaching practice.
Maths is a language. Like any language, it must be taught in a precise and logical order if learners are going to understand, use, and retain it.
It must be:
multi-sensory
mastery-based
student-paced
sequential so foundations are established before progression
relevant and applicable to everyday life
The I-CRAVE Maths™ methodology was developed to systematise what research has been telling us for decades – and to bridge the gap between educational theory and everyday teaching practice.
What I-CRAVE Maths™ actually stands for.
I-CRAVE Maths™ is not a philosophy. It is a practical teaching sequence.
It ensures concepts are built accurately and securely before students move on.
Each stage plays a distinct role.
Each stage contains subtleties that make the difference between memorisation and understanding.
(I) Identify
Effective instruction begins with knowing where the student actually is.
Through structured assessments, teachers identify which foundations are secure and which are missing. This ensures teaching begins at the correct starting point.
Guessing disappears.
Teaching becomes targeted.
Students become engaged.
(C) Concrete
Every new concept begins with carefully designed hands-on materials, such as colour-consistent base ten blocks and structured maths kits.
Students physically build maths.
They see quantity.
They feel structure.
They connect maths to real experience.
This is where understanding begins.
(R) Representation
Students then draw proportionally accurate representations of what they have built.
This step is often overlooked, but it is critical.
Representation connects the concrete experience to abstract thinking.
If representations are inaccurate, understanding becomes distorted. Confusion grows. Anxiety develops.
Accuracy at this stage matters.
(A) Abstract
Only once meaning is secure are symbols introduced.
Students learn the language of maths with confidence because the symbols now represent something real and meaningful.
They are no longer memorising steps.
They are understanding the language of mathematics.
(V) Verbal
Students are actively engaged in discussion.
They explain their thinking.
They teach the concept back.
They articulate their reasoning.
This allows teachers to immediately check understanding and correct misconceptions.
Language strengthens learning.
(E) Explicit
Explicit instruction underpins every stage of the process.
Models, representations, symbols, and language must all align.
Nothing contradicts.
Nothing is vague.
Nothing is left to chance.
This clarity ensures learning becomes transferable beyond the lesson.
Why this works for all learners
Since 2000, this methodology has been tested and refined with both neurotypical and neurodivergent learners.
The reason it works so consistently is simple:
Understanding is built, not assumed.
Students are never asked to operate at an abstract level without the foundations in place.
Gaps are identified early.
Confusion is addressed before it compounds.
When maths makes sense, something powerful happens.
Students begin to enjoy it.
What changes for teachers
When educators learn and apply the I-CRAVE Maths™ methodology, the shift is immediate.
Teaching becomes calmer.
Decision-making becomes clearer.
Intervention becomes precise rather than reactive.
Most importantly, confidence grows – for both teachers and students.
Maths stops being the subject everyone braces for.
Turning pedagogy into practice
At Maths Australia, our focus has always been to equip educators with the tools to teach maths clearly and confidently.
I-CRAVE Maths™ is how we turn pedagogy into everyday teaching practice.
It informs everything we do – from educator training and accreditation to our fully integrated numeracy programs.
Because good teaching doesn’t need to be complicated.
It needs to be clear.
Maths Australia provides practical training for educators to learn how to teach maths using the I-CRAVE Maths™ methodology. The training is step-by-step, online, hands-on, and grounded in research.
Learn more at mathsaustralia.com.au/training.
Warmly,
The Maths Australia Team