The inappropriate application of natural number properties in rational number tasks: Characterizing the development through primary and secondary education

The natural number bias is known to explain many difficulties learners have with understanding rational numbers. The research field distinguishes three aspects where natural number properties are inappropriately applied in rational number tasks: density, size, and operations. A comprehensive test was constructed to characterize the development of 4th to 12th graders’ natural number bias. This test was administered to 1343 elementary and secondary school students. Results showed an overall natural number bias that was weakest in size tasks, somewhat stronger in operations tasks, and by far the strongest in density tasks. An overall decrease of the strength of the natural number bias – but no disappearance except for size tasks – could be found with grade.status: publishe