Early understandings of numbers: paths or barriers to the construction of new understandings?

We propose that concept development is facilitated when existing conceptual structures overlaps with the structure of the to-be-learned data. When the new inputs do not map readily or are inconsistent with available mental structures, the risk is high that the data will be misinterpreted as examples of what is known. Results of two kinds of studies with children aged 5 to 7 years provide support for these predictions. Childrenʹs knowledge of counting and addition facilitated their acquisition of a concept that is not taught in school, the Successor Principle, that is that every natural number has a successor. In contrast, even the eldest children could not rank order correctly numbers that contained fractional notations. The several kinds of solutions invented by the children were based either on classification strategies or a natural number ordering rule.