Mathematical reasoning is the ability to analyze and calculate with abstract patterns, according to statisticians Dani Ben-Zvi et al. Being able to mentally work with numbers, symbols and mathematical relationships is all part of the skill of mathematical reasoning. Like language, mathematics is essentially a set of abstract concepts, and some researchers believe that the same intellectual skills are needed for both disciplines. Even so, an ability with either does not directly lead to an ability with the other.
An ability to describe things is a skill that humans begin to master in infancy when they learn concepts like color, shape and size. In later life, people often describe things to convey information to others, like telling a mechanic the kind of noise their car engine is making. Even Plato referred to the ability to describe, in his "Theory of Knowledge," according to former Oxford don I. M. Crombie. However, interestingly, the eminent Greek philosopher did not necessarily link ability to describe with knowledge.
Closely allied to an ability to describe is an ability with vocabulary. Our vocabulary tends to expand with experience, so that as adults, we can correctly use words like "ultramarine," "octagonal" and "miniscule" where, as children, we may have used "blue," "round" and "little." Being able to recognize the difference between two words with similar meanings, like "occasional" and "erratic," is also a mark of increasing ability with vocabulary.
Associate Professor of Psychology Bob Rehder refers to inductive reasoning as "reasoning to uncertain conclusions," in other words, reaching tentative inferences about things, or generalizations. Inductive reasoning is associated with deduction, although psychologists disagree about whether the two are different intellectual skills or two aspects of the same skill. Inductive reasoning may require a dual process of fast and slow thinking, the former to make associations and the latter to manipulate symbolic concepts.