Formal reasoning, Piaget
Formal reasoning skills (incomplete list)
1- Proportional reasoning - critical for algebra, chemistry
2- Identifying and controlling variables - critical for scientific investigation
3- Probabilistic reasoning - critical in biology and the social sciences
4- Combinatorial reasoning
5- Propositional logic - this one's less useful in science ( and easily misapplied)
6- Nonlinear reasoning - a step beyond proportional reasoning, critical for calculus
7- Suppositional reasoning - essential for exploring "hypothesis space"
8- Concrete reasoning about constructs - crucial for developing hypotheses
9- Multidimensional reasoning - critical for identifying variables
10- Suspending judgement - a key to creativity, crucial for understanding how others think
11- Self regulation (analyzing personal reasoning) - essential to get beyond "I just know it"
See Piaget's stages of intellectual development
A good site