Process- and object-based thinking in arithmetic

Many influential theorists have proposed that learners construct mathematical objects via the encapsulation (or reification) of processes into objects. These processto- object theories posit that object-based thinking comes later in the developmental path than process-based thinking. In this paper we directly test this hypothesis in the field of early arithmetic. An experiment is reported which studied 8 and 9 year-old children’s use of the inverse relationship between addition and subtraction. We demonstrate that a subset of children were unable to solve arithmetic problems using process-based thinking, but that, nevertheless, they were able to use the inverse relationship between addition and subtraction to solve problems where appropriate. The implications of these findings for process-to-object theories are discussed.