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Concrete vs. abstract
Children first learn through concrete materials that they will later be able to transfer to abstract ideas. Concretely seeing what 1,000 beads looks and feels like will give more significance to the abstract symbol (the number 1,000). 

Concrete: Developmentally, a child understands the world through real concrete experiences. Learning how to make tea using a kettle, tea bags and ceramic mugs will give the child the opportunity to use new skills. Pouring hot water from a kettle requires the child to concentrate in order not to burn the skin or spill water. Also, using real ceramic mugs will teach the child that dishes can be breakable. If the child accidentally drops the mug and it shatters then a life lesson will be taught, be careful with breakable items! Academically, the child will be able to work with materials that are manipulated with the hands. To understand different shapes the child will be able to use different senses (touch, smell). This would not be possible if the child was learning using a sheet of paper. Children at a young age learn through the hands which allows the child to retain new information. Working with real materials also provides real consequences. This prepares the child for real life scenarios. 

Abstract: One of the goals for a child in a Montessori environment is to be able to apply concrete concepts to an abstract world. Once the child understands lessons by using materials then the child can start to understand the environment on a deeper level. For example, when a child learns a shape by manipulating it with the hands then the child can start to name different shapes in an abstract environment. Touching, and feeling the weight of 100 items compared to 10 items will abstractly teach the child that 100 is more than 10. 

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