Children move from concrete to abstract thinking. With math, they must first see and touch what they are counting—three cookies. Next they understand that the number 3 represents three cookies. After many experiences with concrete objects, and time for brain maturation, they start to move to abstract thought, e.g., x=3. (Your Child’s Growing Mind by Jane Healy.)
Manipulatives enable children to visualize a problem concretely. Allow them to work with manipulatives as long as they need to. Once they begin to see the manipulative in their minds’ eye, they can stop using it. Do not hurry them away from the manipulative. As you introduce new concepts, encourage your child to use a manipulative to explore the concept. Even engineers use manipulatives!