South Australia's Bold Move on Maths.
Here's How I-CRAVE Maths® Makes It Possible.
By Esther White, CEO & Founder, Maths Australia
In May 2024, South Australia took a significant step by releasing the first subjects of the South Australian Curriculum for Public Education. Rather than simply using the Australian Curriculum as a generic national document - and similar to some other states - South Australia is adapting AC9 (Version 9 of the Australian Curriculum) into a state-specific framework for public schools - one designed to reflect local priorities, teacher feedback and the needs of South Australian students.
The language coming out of the Department for Education is striking. The emphasis, in the words of Chief Executive Professor Martin Westwell, must shift "from the passive reproduction of processes and facts to capabilities, both general and subject-specific, conceptual understanding, deep thinking and the ability to apply knowledge across various situations."
Read that again, because it matters. Another state education system is saying, out loud and in policy, that maths is not about memorising procedures. It is about understanding. It is about building capabilities and dispositions - resilience, confidence, the willingness to think deeply - and it is about being able to transfer what you know into the real world.
I want to say this plainly: this is the right move. It is a bold one. And it is exactly the future we have been building toward at Maths Australia for more than two decades.
But bold moves need a way to be delivered. A curriculum can name conceptual understanding, capabilities and dispositions. It cannot, on its own, produce them in a classroom on a Tuesday morning with thirty children of thirty different starting points - some ready to be extended, some needing targeted small-group support, and a few needing something more intensive again. That is the gap between an aspiration and a lesson. And closing that gap, for every one of those thirty children, is precisely what I-CRAVE Maths® was designed to do.
The trap hiding inside a good idea
Whenever a system moves toward "conceptual understanding" and "capabilities," there is a quiet danger. The language can be mistaken for an invitation to step back - to let children discover, explore and construct their understanding largely on their own. Decades of cognitive science, from Sweller's Cognitive Load Theory to Rosenshine's Principles of Instruction, tell us this is where many well-intentioned reforms come undone. Novices do not yet have the mental architecture to discover complex mathematics unaided. Ask them to, and working memory is quickly overloaded, and the understanding you were reaching for struggles to form. The risk is especially significant for students who are already behind, which is exactly why intervention teachers and learning support staff tend to be instinctively wary of "discovery" approaches - they see daily what happens when a vulnerable learner is asked to construct meaning from a gap rather than a foundation.
So conceptual understanding is the right destination. The question is how you get there. And the weight of the evidence tells us that deep understanding is not the opposite of explicit teaching - it is far more often the product of explicit teaching done with precision. That is the false binary I want to dissolve. You do not choose between "conceptual" and "explicit." You use the explicit to build the conceptual. I-CRAVE Maths® is the sequence that does exactly that.
How I-CRAVE Maths® delivers South Australia's ambition, step by step
I-CRAVE Maths® is not a philosophy to admire from a distance. It is a practical teaching sequence - Identify, Concrete, Representation, Abstract, Verbal, Explicit - and every stage maps directly onto what South Australia now says it wants.
I - Identify. SA's reform is underpinned by a Year 1 Numeracy Check, introduced after the state's own trial found that more than 60% of students were "mathematically vulnerable." You cannot build capabilities on foundations that aren't there. I-CRAVE Maths® starts in the same place, with a placement test that identifies mastery within the sequence of instruction - counting, then place value, then adding, subtracting, multiplying and dividing, and only then the operations of fractions, decimals and percentages. Maths is cumulative; each concept rests on the one before it. Identifying precisely where a student sits in that sequence is what lets teaching begin at the point of need rather than the point of assumption.
For most students, high-quality Tier 1 classroom instruction, delivered with this level of precision, is enough to close the gap. The stronger that Tier 1 teaching is, the fewer students go on to need Tier 2 or Tier 3 support - which is exactly why high-quality classroom instruction is the foundation of an effective multi-tiered system of supports. But not for all. Some students will need Tier 2 - targeted, small-group intervention - and a smaller number again will need Tier 3, more intensive and individualised support. This is where a multi-tiered system of supports earns its place alongside the curriculum, and it is why the same discipline of precise identification matters even more in the intervention room than in the whole class. A student referred to a learning support team rarely has a single, tidy gap; because maths is cumulative, the gaps tend to stack, one missing concept quietly undermining several that were built on top of it. Teaching solely to the year level, in that context, can mean teaching over the gap rather than through it. Teaching to the student's actual point of mastery - whatever year level that happens to sit in - is what gives intervention the best chance of closing the distance rather than simply keeping pace with it.
C - Concrete. This is where conceptual understanding is actually born. Using purpose-built manipulatives, the child builds the mathematics before they ever meet a symbol - and two subtleties do the heavy lifting: colour consistency and model consistency. The same mathematical idea always looks the same, and every concept is built the same way (building rectangles), so working memory is freed for understanding rather than spent decoding a new picture each lesson. When a student constructs a concept with their own hands, the understanding is theirs. It is not borrowed from a worksheet. This is the concrete root of the "deep thinking" the curriculum is calling for - and it holds whether the building is happening at a table of thirty or in a small-group intervention session built around exactly this need.
R - Representation. The child then draws their own representation of what they built - and it must be proportionally accurate, because this is the bridge from the 3D concrete to the abstract. This is a subtlety most approaches miss, and we treat it as essential. No bundles, no ten frames, no dots. If the representation isn't proportionally accurate, the mental model is compromised, and transfer is more likely to break down later. Getting this bridge right is what allows a student to apply their knowledge across contexts - the exact capability SA is asking for.
A - Abstract. Only now, with the understanding already secure, do we bring in the symbols - the code, the written language of maths, used as a communication tool for something the child already comprehends. Because the meaning came first, the child can encode and decode the abstract with confidence rather than fear. The "squiggles" finally mean something.
V - Verbal. Here is where dispositions are forged, through genuine student engagement and feedback. We keep the student in dialogue and have them teach the concept back - which does two things at once. Hearing their own voice explain their reasoning embeds the knowledge, and it gives the teacher immediate feedback on whether the instruction has actually landed. It also builds the confidence, the mathematical language and the willingness to reason out loud that a capabilities-based curriculum depends on. This is metacognition made routine, and for a student who has spent years going quiet in maths lessons, it is often the first sign that something has genuinely shifted.
E - Explicit. Everything holds together through congruency: close alignment between the model built, the representation drawn, the symbols written and the words spoken - clear, accurate and consistent across all parts. That congruency is what makes learning transferable and portable into everyday life. It is also what strips out the extraneous clutter that steals teaching time and adds to cognitive load.
The difference is in the subtleties
Here is what I most want South Australia's teachers and leaders to hear. You have almost certainly encountered these ideas before - hands-on learning, explicit instruction, cumulative review, mastery before progression. They are not new. What makes the difference is not the list; it is the subtlety in the application.
It is insisting that a representation be proportionally accurate, not roughly indicative. It is using colour-consistent manipulatives so that the same idea looks the same every time, aiming to reduce cognitive load rather than add to it. It is working toward true congruency across all four modes - build it, draw it, write it, say it - so nothing the child sees contradicts anything else the child sees. It is mastering whole numbers deeply before moving on, rather than racing across the surface of a crowded curriculum. It is the same precision, applied consistently, whether a child is meeting a concept for the first time in the whole class or meeting it again, more carefully, in a Tier 2 or Tier 3 room.
South Australia is deliberately "decluttering" its curriculum so teachers can teach fewer things in more depth. That instinct is precisely correct, and it is the instinct I-CRAVE Maths® was built around. Depth is not achieved by covering less carelessly; it is achieved by teaching each concept with enough precision that it rarely needs to be re-taught - a standard that matters in every classroom and is especially important for students receiving Tier 2 and Tier 3 intervention, where every opportunity to build secure mathematical understanding matters.
Capabilities and dispositions are outcomes, not add-ons
The part of SA's reform I find most exciting is its honesty about dispositions: resilience, confidence, the disposition to persist and think. For too long these have been treated as things you hope for, or bolt on at the end.
In a multi-sensory mastery classroom, they are not bolted on. They are built by the method itself. When a child builds understanding with their own hands, draws it accurately, and then teaches it back in their own voice, confidence is not a slogan on the wall. It is the felt experience of "I can do this." Success builds success. That is how you grow a mathematician's disposition - and it matters most for the mathematically vulnerable student who has come to expect failure in a maths lesson before it has even begun. It is measurable, lesson by lesson, in a way that aspiration alone rarely is.
An invitation to South Australia
To the teachers, leaders, intervention specialists and families of South Australia: your state has set a genuinely ambitious direction for mathematics - conceptual, capable, deep and applied. We are cheering it on. And we would love to help you deliver it, whether in the core classroom or the intervention room, because the how already exists, it is evidence-informed, and it is ready for your classroom now.
Maths is a language. When we teach it as one - concretely, accurately, explicitly, and with attention to every subtlety - capabilities, conceptual understanding and confident dispositions stop being goals we reach for and become results we can see. That is the promise of I-CRAVE Maths®. And it is exactly the bold move South Australia has just made possible.
Want to see how I-CRAVE Maths® Methodology could support your school's move toward conceptual, capabilities-based mathematics? Start with our free placement tests to see exactly where your students stand, explore our specialist educator training, or book a call with me, Esther White.