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Logic-mathematical skills combine with all the other intelligences to facilitate complex problem solving and creation such as environmental engineering and scientists (naturalist); symphonies (music); public sculptures (visual-spatial) and choreography/ movement analysis (kinesthetic).
In mathematics education, APOS Theory is a model of how mathematical concepts are learned. APOS Theory was developed by Ed Dubinsky and others and is based on Jean Piaget's notion of reflective abstraction. APOS stands for Actions, Processes, Objects, Schemas, the four main mental structures involved in the theory.
In mathematical logic, abstract model theory is a generalization of model theory that studies the general properties of extensions of first-order logic and their models. [ 1 ] Abstract model theory provides an approach that allows us to step back and study a wide range of logics and their relationships. [ 2 ]
In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the statements of the theory hold). [1]
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power.
Deductive reasoning plays a central role in formal logic and mathematics. [1] In mathematics, it is used to prove mathematical theorems based on a set of premises, usually called axioms. For example, Peano arithmetic is based on a small set of axioms from which all essential properties of natural numbers can be inferred using deductive reasoning.
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