arranging a group of items (objects or ideas) into multi-level hierarchy according to observable or intangible properties (classifying members of the UN. according to forms of government; economic system; standard of living)

f / 2 conservation

realizing that certain properties of a system remain the same if nothing is added/taken away, but that this reasoning cannot be applied to all properties (total angular momentum of an isolated system is constant; some students can gain knowledge without depriving others of knowledge)

f / 3 theoretical reasoning

applying multiple classification, conservation logic, serial ordering, and other reasoning patterns to relationships and properties that are not directly observable (distinguish between oxidation and reduction reactions; using the energy conservation principle; arranging lower and higher plants in an evolutionary sequence; making inferences from the theory according to which the earth's crust consists of rigid plates; accepts assumptions /hypotheses for the sake of discussion; 'what if' statements are a springboard to thought)

f / 4 combinatorial reasoning

considering all conceivable combinations of tangible or abstract items (systematically enumerating the genotypes and phenotypes with respect to characteristics governed by two or more genes)

f / 5 proportional reasoning

making inference from data under conditions of constant ratio; truly understands fractions and ratios (the rate of diffusion of a molecule is inversely proportional to the square root of its molecular weight)

f / 6 functional reasoning

making inferences from data that give information about the relation between two continuous variables (as a pendulum gets shorter its frequency increases)

f / 7 control of variables

recognizing the necessity of an experimental design that controls all variables but the one being investigated (see the Mealworm Puzzle; suggesting the usefulness of a set-up without any light)

f / 8 analogic reasoning

establishing correspondence between objects and/or ideas that share the same relationship (the length of a soda straw "flute" determines pitch or frequency ... just like the length of a pendulum)

f / 9 prepositional reasoning

using postulates or axioms of a theory to derive consequences without regard to the factual basis of the postulates (making inferences from the theory that says the earth's crust consists of rigid plates moving in relation to one another; can handle such statements (propositions) as ... it is this (OR) that; it is this AND that; it is this BUT NOT that; it is NEITHER this or that)

f / l0 correctional reasoning

recognizing relationships among variables in spite of random fluctuations that mask them (in the Mealworm Puzzle, recognizing that a small number of specimens showing exceptional behavior need not invalidated the principal conclusion; recognizing interdependence between mathematical variables; especially statistics)

f / 11 probabilistic reasoning

interpreting observations that show unpredictable variability in spite of random fluctuations that hide them; understanding of probability and its implications

f / 12 abstract reasoning

has 'mental holding power' that is needed to mentally operate on many pieces of data at once

f / l3 reflexive thinking

can reflect over a series of operations and identify their functions; reflection brings about critical judgments to the thought process; rids the student of; they can admit that a previous hypothesis they had was invalid)

f / l4 comprehends allegory

grasps double meaning in literature; considers the context of the whole story

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