What is CPA (Concrete-Pictorial-Abstract)?

What is CPA (Concrete-Pictorial-Abstract)?

“I’ve already taught them that – they should know it!”

One of the biggest misconceptions in Mathematics education is that “teaching” automatically equals “learning.” As teachers, we carefully plan lessons, model strategies, provide guided practice and create engaging activities — yet many students still struggle to retain or transfer what they have supposedly “already learned”.

Research continues to show that high-quality teaching resources have a significant impact on both teacher effectiveness and student learning outcomes. The Grattan Institute report (2023) highlighted that teachers can achieve the best results when they are supported with a strong bank of quality curriculum resources that reduce workload while strengthening instructional consistency. This is particularly important in Mathematics, where carefully sequenced learning experiences are essential for building deep conceptual understanding.

PR1ME Mathematics Australia is grounded in research-based pedagogy that supports all learners in developing strong mathematical understanding. Central to the program is the CPA approach — Concrete, Pictorial and Abstract — alongside Explicit Instruction delivered through the Gradual Release of Responsibility model.

CPA is far more than a simple three-step process. It is an integrated approach to learning that intentionally connects physical experiences with visual representations before moving students towards abstract mathematical symbols and procedures. Through this process, students are supported to build meaning and understanding rather than simply memorising rules or algorithms.

The approach originates from the work of Jerome Bruner, whose research in the 1960s proposed that children learn through three stages: enactive, iconic and symbolic representation. Over time, these stages became more commonly known as concrete, pictorial and abstract. Bruner’s work emphasised that learners construct understanding by moving between experiences, images and symbols in meaningful ways.

Within PR1ME Maths, teachers are supported through detailed lesson notes and scripted guidance aligned to the CPA pedagogy. The program also includes helpful instructional videos that model how teachers can effectively implement CPA strategies within individual lessons. This support assists teachers in delivering consistent, high-quality Mathematics instruction while also building confidence in applying the pedagogy effectively in the classroom.

Importantly, the CPA approach also provides strong opportunities for differentiation. By adjusting the level of concrete materials, visual scaffolds or abstract representation required, teachers can respond to the diverse needs of learners while students continue developing conceptual understanding. Some students may require extended time using hands-on materials, while others may move flexibly between pictorial and abstract representations. This responsiveness helps ensure all students can access and engage successfully with mathematical concepts.