In math instruction, what is the relationship between concrete representation and abstract concepts?

Concrete representation serves as the foundation for understanding abstract concepts because it allows learners to grasp mathematical ideas through tangible experiences before moving on to more theoretical understandings. When students manipulate physical objects, such as counting blocks or geometric shapes, they develop a concrete understanding of quantities, operations, or properties. This hands-on experience aids in building a mental connection to the more abstract concepts of mathematics, such as numbers and operations, which may be difficult to visualize without a physical representation.

For instance, when children learn addition through counting blocks, they can see and physically manipulate the blocks to understand what it means to combine quantities. Once they have a solid grasp of this concrete representation, they can transition to abstract notation and problems involving numbers, leading to a deeper comprehension of mathematical principles. In this way, concrete experiences enhance the ability to engage with and understand abstract mathematical concepts effectively.