Parity influences the difficulty of simple addition and subtraction but not multiplication problems in children.

In the present paper, the results of early 20th century studies of children's difficulties with basic addition, subtraction, and multiplication problems are analyzed for parity effects. Parity influenced the difficulty of addition and subtraction problems, tasks in which any parity influence must be implicit, but did not influence difficulty of multiplication problems. Solution of multiplication problems relies to a greater extent on retrieval of rote-memorized answers. Addition and subtraction problems rely more on non-retrieval strategies. It is these latter strategies that depend on internal representations sensitive to the parity status of the numbers being processed. That parity affected responding in tasks where parity was irrelevant and no overt motor responses were made poses problems for the Markedness of Response Codes (MARC) and polarity explanations of parity effects in reaction time. Both these explanations require that an explicit parity judgment indicated by a binary motor response be made for a parity effect to be seen.