But don’t push the child to dispense with her manipulatives until she’s ready. Children’s minds mature at different rates; if you require a child to do addition with numerals alone (no objects) before she’s ready, the result will be math frustration. Children aged 5 through 7 usually need concrete objects; children aged 8 through 10 begin to shift into “mental image” mode (but will still need manipulatives when new concepts are introduced).
