Effective strategies for mental and written arithemtic calculation from the third to the fifth grade

ABSTRACT The strategies used to solve mental and written multidigit arithmetical addition, subtraction, multiplication and division were observed in 200 third, fourth and fifth grade children. A strategy was classified as effective if it resulted in the correct solution at least 75% of the time. For mental addition and subtraction, primitive strategies such as counting on fingers and counting on (mental counting from a specific point), and the more sophisticated strategy 1010 (solution of the calculation problem using tens and units separately) were more effective than the strategies learned at school. In written addition, subtraction and multipli-cation there was a shift from the CAR to the CAR- strategy (tabulating with, or without, a carried amount) from the third to the later grades. Results show that typical strategies taught at school progressively substitute every other strategy both in mental and written calculation, but without reaching the criterion of effectiveness. The implications for maths curricula are discussed. Although the mental and written execution of simple arithmetic operations is part of our daily activity, there have been relatively few studies related to the acquisition of strategies to solve them. The present study investigates the strategies necessary to arrive at a correct solution of multidigit arithmetical problems by schoolchildren of different ages. Several models of learning and development of arithmetic calculation problems have been proposed. Groen and Parkman (1972) hypothesised that the solution of a calculation problem is achieved with counting processes, using the bigger addendum a