| A | B |
| conservation | understanding that rearranging materials does not change quantity |
| centering | focusing on one aspect of a physical relationship at a time |
| reversibility argument | maintaining that objects can be returned to their original positions |
| identity argument | claiming that no objects have been added or taken away |
| compensation argument | contending that an abundance of one dimension of a configuration makes up for an abundance of a different dimension in another |
| class-inclusion | considering a subgroup as part of a superordinate group |
| egocentric | erroneously believing that others see world and environment as you do |
| artificialism | tendency to see natural objects as existing to serve our purposes |
| sequencing error | using unconventional ways of counting |
| coordination error | not linking the number word sequence with pointing at the objects |
| partitioning error | losing track of objects that have and have not been counted |
| tags | terms that refer to number words used in counting |
| representational theory of mind | knowledge that thoughts can misrepresent reality |
| realism | confusion between thoughts and the material world |
| animistic | thinking in which nonliving objects are considered alive |
| preoperational | thinking that is inflexible, illogical, fragmented, and tied to specific contexts |
| topological | thinking in terms of the surface structure and arrangement of objects |
| consciousness | state of having thoughts and feelings |