Use of invented algorithms by second graders in a reform mathematics curriculum

Abstract Second-grade students in three schools were individually tested on multidigit addition and subtraction problems and solution procedures observed. The schools were all using a reform mathematics curriculum (UCSMP) with an emphasis on problem solving in broader mathematical contexts. Both contextualized and bare computation problems were included in these interviews. On all but one problem, more students used a mental procedure than used the standard written algorithms, and both methods were used with about the same degree of accuracy. Although the standard school algorithm was the only written algorithm used, a number of different mental procedures were employed by students, and choice appeared to be influenced by characteristics of the problems (magnitude of the numbers or the need for regrouping). Major differences between the three schools were found, which are linked to instruction.