separating a group of objects into several groups according to an observable property (they distinguish consistently between acids/bases by the litmus test)

c / 2 conservation

realizing that an observable quantity remains the same if nothing is added or taken away, even tho it may appear different (a clay pancake made from a ball has as much material as the ball)

c / 3 serial ordering

arranging a set of objects according to an observable property and possibly establishing a l-to-l correspondence between two observable sets (small animals = fast heartbeat and large animals = slow heartbeat)

c / 4 reversibility

mentally inverting a sequence of steps to return from the final condition of a certain procedure to its initial conditions (in c/3 the child mentally 'reversed' the squashing process to remake the ball from the pancake)

c / 5 proportional reasoning

making inference from data under conditions of a constant ratio equal to a small whole number (if 2 pieces of candy costs $l, the 4 pieces would cost $2)

c / 6 interactional reasoning

attributing a simple observable change to interaction among a set of objects (magnets picking up a nail; rubber band stretching when it is pulled)

c / 7 additive reasoning

making an inference from data under conditions of constant difference or constant sum (when mary is 5, joan is l0; when joan is l5, mary is l0)

c / 8 direct observation

understanding concepts defined in terms of familiar actions and examples that can be directly observed

"analysis of concepts in an 8th grade sci textbook"