Many educators begin their planning by turning directly to the curriculum documents provided by their school, district, or national guidelines. These documents often outline standards and content goals that feel urgent to cover. So we move quickly into teaching the facts and following the sequence, and then we wonder why learners struggle to recall the information even shortly after an assessment.
This is not a sign of ineffective teaching. Rather, it shows how the system tends to prioritize content coverage over meaningful engagement. When the focus remains solely on the content, the learner’s experience fades into the background. And when we do not center the learner’s experience, understanding becomes shallow, and transfer becomes rare. Learners might memorize content for a test, but they are less likely to make lasting connections or apply what they have learned in real-world situations.
If we want to make a deeper and more lasting impact, we need to rethink how learning unfolds. One powerful approach is Concrete, Representational, Abstract coined by Jerome Bruner based on the work of Jean Piaget. Singapore Maths decided to change it to CPA or Concrete, Pictorial, Abtract. Regardless of name, this method honors how learners naturally make sense of new ideas. We begin with concrete materials they can touch and manipulate. We then move to pictorial representations that help make thinking visible. Only after that do we guide learners toward abstract concepts, symbols, and formulas. It is a developmental process that supports deeper understanding.
Although CRA/CPA is used predominately in mathematics, it can be easily applied to other subjects as well. It's about setting the stage for our learners to think differently, so they can break down big ideas.
This is not a sign of ineffective teaching. Rather, it shows how the system tends to prioritize content coverage over meaningful engagement. When the focus remains solely on the content, the learner’s experience fades into the background. And when we do not center the learner’s experience, understanding becomes shallow, and transfer becomes rare. Learners might memorize content for a test, but they are less likely to make lasting connections or apply what they have learned in real-world situations.
If we want to make a deeper and more lasting impact, we need to rethink how learning unfolds. One powerful approach is Concrete, Representational, Abstract coined by Jerome Bruner based on the work of Jean Piaget. Singapore Maths decided to change it to CPA or Concrete, Pictorial, Abtract. Regardless of name, this method honors how learners naturally make sense of new ideas. We begin with concrete materials they can touch and manipulate. We then move to pictorial representations that help make thinking visible. Only after that do we guide learners toward abstract concepts, symbols, and formulas. It is a developmental process that supports deeper understanding.
Although CRA/CPA is used predominately in mathematics, it can be easily applied to other subjects as well. It's about setting the stage for our learners to think differently, so they can break down big ideas.
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Concrete - Representational - Abstract
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