Process- and object-based thinking in arithmetic
GilmoreCamilla
InglisMatthew
2011
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
childrenâ€™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.