Mathematics Curriculum | North Cottesloe Primary School

Mathematics

North Cottesloe Primary School

Explicit Instruction in Mathematics

At North Cottesloe Primary School, our mathematics program is grounded in evidence-based, fully guided instruction. Decades of research have shown that when learning new content, explicit, structured teaching supported by modelling, guided practise, and feedback leads to stronger outcomes than discovery-based approaches (Clark, Kirschner & Sweller, 2012).

We know that all students—particularly novices—benefit from clear, direct teaching that gradually transfers responsibility as they develop mastery. This approach ensures that every learner builds confidence and proficiency through success and feedback at every stage of the learning process.

Building Conceptual Understanding Through Concreteness Fading

Young learners build abstract mathematical understanding through concrete experiences. Our teaching follows the Concrete–Pictorial–Abstract (CPA) model, allowing students to first explore concepts with physical materials, then move to visual representations, and finally to abstract symbols. Manipulatives are introduced in a guided context to strengthen understanding and are gradually replaced by symbolic reasoning.

This approach supports what cognitive scientists call concreteness fading—the gradual shift from tangible to abstract thinking (Deans for Impact; AERO, 2024). It reduces cognitive load, helping students connect new information to what they already know and retain it in long-term memory.

Developing Fluency to Support Problem Solving

Mathematical proficiency is built on five interrelated strands: conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. At North Cottesloe, we ensure all strands are nurtured through structured teaching, deliberate practise, and opportunities for application in real-world contexts.

Fluency in basic number facts—addition, subtraction, multiplication, and division—is essential for freeing cognitive space for higher-order thinking and multi-step problem solving. When basic facts are retrieved automatically from long-term memory, students have more capacity to reason, plan and apply strategies effectively in complex tasks.

Our Mathematics Block

Each daily mathematics session at North Cottesloe is designed around research-informed routines that optimise learning:

Daily Review and Mental Maths: Revisiting and retrieving prior learning to strengthen long-term memory.
Explicit Concept Development: Introducing new concepts through clear explanation, modelling and guided practise.
Independent Practise and Application: Opportunities for students to consolidate learning through structured and varied tasks.
Reflection and Feedback: Building metacognition and self-efficacy through discussion and checking for understanding.

This structure reflects the AERO model for how students learn best—sequencing content, managing cognitive load, and providing spaced and cumulative practise.

Early Mastery and Foundational Skills

Data from the Australian Early Development Census and AERO research highlight that early mastery of Language and Cognitive Skills—particularly number recognition, one-to-one correspondence, and counting—predicts later success in numeracy. These foundational skills provide the building blocks for reasoning, patterning, and problem-solving throughout the primary years.

Our early years teachers prioritise the development of these skills through structured play, mathematical talk, and explicit connections between language and mathematical ideas. This ensures students enter the middle years ready to engage confidently with abstract concepts.

Connecting Maths to the Real World

We believe that mathematics should feel purposeful and relevant. Teachers highlight the utility and beauty of maths—from identifying patterns in nature to applying measurement in design or data in environmental studies. Students learn to see themselves as capable mathematicians who can use maths to solve authentic problems and make sense of the world.