The Addition Methods of First- and Second-Grade Children.

This study is concerned with the procedures used by firstand second-grade children in solving addition problems. First, consider the precursors of such procedures that emerge even before the onset of schooling. Hebbeler (1978) has shown that children of preschool age can use counting methods to solve addition problems involving concrete objects. Cross-cultural research (Posner, 1978; Ginsburg, 1978) has shown that in the Ivory Coast both preschool children and older children not attending school are capable of solving such concrete addition problems. Zaslavsky (1974) describes many nonliterate African cultures displaying fairly sophisticated methods for solving various mathematical tasks. In brief, techniques for dealing with addition develop before the onset of schooling or without the benefit of schooling in nonliterate cultures. These informal procedures then have effects on what is learned in school. According to Ginsburg (1977), children assimilate school arithmetic into existing cognitive structures, in this case the counting strategies developed in the preschool years. The results are often "invented strategies." He reports various case studies showing that in the first several grades addition is usually accomplished by means of some form of counting, even when this is not the method taught in school. These invented strategies are often combinations of remembered addition facts and counting procedures. Thus, a child might say that "6 and 6 is 12 because I remembered that 5 and 5 is 10, and then I go 11, 12." Groen and Resnick (1977) also describe "invented" addition algorithms in preschool children. There are few systematic studies that deal with addition strategies in young children. Groen and Parkman (1972) and Suppes and Groen (1967) investigated several different procedures which might be used by first graders on problems with two single-digit addends. Suppes and Groen (1967)