The Classroom Problem Many Teachers Recognise.
A teacher explains a maths concept clearly. Students nod along. Some even complete the first example correctly.
Then independent work begins.
Suddenly hands go up. A student who seemed confident moments ago is unsure where to start. Another applies the wrong method entirely. A few simply stare at the page.
By the end of the lesson, it’s clear that only a small group has truly understood the concept.
For many educators, this pattern repeats daily. The explanation felt clear. The lesson was carefully planned. Yet understanding did not hold.
This is the moment where many teachers begin searching for evidence based maths teaching - approaches grounded not in trends, but in how students actually learn.
Reframing the Problem
It is tempting to assume the issue lies in student ability, motivation, or attention.
But in many cases the problem sits elsewhere.
Students often struggle not because maths is inherently difficult, but because the path from new idea to deep understanding has too many invisible steps.
Experts see patterns instantly. Students do not.
A teacher may move smoothly from explanation to symbolic notation because the concept is already secure in their mind. For a learner, however, that leap can be enormous.
What appears simple to the teacher may still be abstract to the student.
When this gap is not carefully bridged, confusion accumulates quietly.
Students memorise procedures without meaning.
They forget methods between lessons.
Confidence begins to erode.
The science of learning points to a different way of thinking about the problem. The goal is not simply to explain maths clearly, but to build understanding in stages that align with how the brain processes new information.
This is the foundation of effective evidence based maths teaching.
The Core Teaching Insight
One consistent finding from the science of learning is that students learn complex ideas best when instruction moves carefully from the concrete to the abstract.
New knowledge cannot float freely. It needs anchors.
When a concept begins with symbols alone, many students attempt to memorise rules without understanding what those symbols represent. Working memory becomes overloaded, and errors multiply.
But when instruction begins with tangible examples and gradually builds toward representation and abstraction, the structure of the idea becomes visible.
Students are not simply copying a process. They are seeing how the mathematics works.
This progression is central to the I-CRAVE Maths™ methodology, which structures instruction so that each stage of understanding supports the next.
Building Understanding Through I-CRAVE Maths™
In practice, effective evidence-based maths teaching follows a predictable sequence.
The first step is Identify.
Before new learning begins, the teacher clarifies the exact concept students must understand. Not the entire unit, but the specific idea that unlocks the skill.
Next comes the Concrete stage.
Students work with materials, visual contexts, or real situations that make the concept visible. Counters, number lines, fraction bars, or simple drawings help students see relationships that symbols alone cannot show.
Once the idea is grounded, it moves to Representation.
Students begin translating what they see into structured models: diagrams, area models, arrays, or visual strategies. These representations act as bridges between concrete experience and formal mathematics.
Only then do students reach the Abstract stage.
Symbols now make sense because they represent something the learner has already explored.
The Verbal component is equally important.
Students explain what they are doing and why. Language clarifies thinking and helps concepts settle into long-term memory.
Finally, instruction remains Explicit.
The teacher models thinking clearly, highlights key steps, and gradually releases responsibility to students as understanding strengthens.
This sequence does not slow learning. It strengthens it.
What This Looks Like in Practice
Consider a common example: teaching multiplication.
In many classrooms, students first encounter multiplication through memorisation of times tables or symbolic equations such as 4 × 6.
Some students succeed quickly.
Others struggle because the meaning behind the numbers is unclear.
An evidence-based approach begins differently.
Students might first build equal groups using counters. Four groups of six becomes something they can physically see and organise.
Next, those groups are represented as arrays. The same structure now appears visually as rows and columns.
Students begin to notice patterns. Four rows of six is also six columns of four.
When the symbolic form 4 × 6 is introduced, it no longer appears arbitrary. It simply describes a structure they already understand.
Later, when they encounter larger numbers or algebraic expressions, the underlying concept of multiplication as equal groups or areas remains intact.
Teachers often observe a subtle but important shift.
Students explain their thinking more confidently.Errors decrease because procedures have meaning.Independent work becomes more productive.
The lesson itself may look calmer, but the cognitive work happening underneath is far stronger.
Why This Works
The science behind these changes is well established.
Cognitive Load Theory shows that working memory has limited capacity. When students face unfamiliar symbols and procedures simultaneously, that capacity is quickly overwhelmed.
Concrete and representational stages reduce this load. They allow students to process one layer of complexity at a time.
Explicit instruction further supports this process by making thinking visible. Instead of guessing how to approach a problem, students observe the reasoning behind each step.
The Science of Learning also highlights the importance of building secure knowledge in long-term memory. When foundational concepts are deeply understood, new learning connects more easily.
Within a Response to Intervention (RTI) framework, this clarity becomes even more valuable. Strong Tier 1 instruction reduces the number of students who later require intensive intervention.
In other words, when everyday teaching aligns with cognitive science, learning difficulties often decrease before they fully develop.
This is the practical heart of evidence-based maths teaching.
What Changes for Teachers
When instruction follows a clear structure, teaching itself becomes more predictable.
Lesson planning requires less guesswork. Teachers know where to begin and how to move students toward abstraction.
Explanations become shorter because they build on visible structures rather than lengthy verbal descriptions.
Assessment also becomes clearer. When a student struggles, the teacher can identify which stage of understanding is missing.
Perhaps the concept was introduced abstractly before students had concrete experience.Perhaps the representation stage was skipped.
Instead of reteaching the entire topic, instruction can return to the exact point where understanding broke down.
Many educators report that this clarity brings renewed confidence to their practice.
Maths lessons become less about managing confusion and more about guiding understanding.
When Maths Begins to Make Sense
For students, the difference is significant.
When mathematical ideas are introduced in a sequence that reflects how the brain learns, the subject begins to feel logical rather than mysterious.
Procedures no longer appear as isolated rules. They emerge naturally from patterns students have already seen.
Over time, this builds something more important than correct answers.
It builds trust.
Students begin to trust that maths is something they can understand. Teachers trust that their instruction is working.
This is ultimately what the science of learning points us toward: teaching that makes mathematical structure visible, step by step.
Because when maths makes sense, learning becomes far more powerful.
Maths Australia provides practical, research-informed training that shows educators exactly how to teach maths with clarity and confidence using the I-CRAVE Maths™ Methodology.
If you're working with students who are unmotivated, stuck, or missing foundations, explore our educator training and accreditation pathways.
Explore training options at mathsaustralia.com.au/training or have your student undertake the free placement test before progressing to the Brighter Maths program.
Warmly,
The Maths Australia Team