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Thinking Deeply about Primary Education

Concreteness Fading: Bridging Procedural and Conceptual Understanding

Mar 1, 2025
John Jackson, a mathematics education expert, and Emma Lindley-Thompson, a primary education specialist, delve into the intricacies of bridging procedural and conceptual understanding in math. They discuss the challenges of blending concrete and abstract teaching methods, emphasizing the CPA framework and the significance of 'concreteness fading.' The duo also evaluates the effectiveness of manipulatives versus abstract symbols and stresses the importance of teacher professional development to enhance classroom practices, ultimately aiming to boost students' mathematical comprehension.
01:12:03

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Quick takeaways

  • Integrating procedural knowledge with conceptual understanding in math teaching enhances students' overall comprehension and flexible application of concepts.
  • Concreteness fading, which transitions from concrete to abstract representations, supports students in better understanding and transferring mathematical knowledge.

Deep dives

Understanding Procedural and Conceptual Knowledge

Procedural knowledge refers to the ability to perform specific mathematical operations, while conceptual understanding involves grasping the underlying principles behind those operations. For example, when calculating the area of a triangle, knowing the formula involves procedural knowledge, but understanding why the formula works requires conceptual insight. This spectrum indicates that students can possess varying depths of understanding, and the successful integration of both types of knowledge is crucial for flexible application of math concepts. It's essential to recognize that emphasizing one over the other in teaching can have significant implications on students' comprehension and performance.

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