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