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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.
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).
If the learning style hypothesis is correct, then, for example, visual learners should learn better with the visual method, whereas auditory learners should learn better with the auditory method. As disclosed in the report, the panel found that studies utilizing this essential research design were virtually absent from the learning styles ...
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.
Logical Intuition, or mathematical intuition or rational intuition, is a series of instinctive foresight, know-how, and savviness often associated with the ability to perceive logical or mathematical truth—and the ability to solve mathematical challenges efficiently. [1]
Sometimes it's not obvious what mathematics children learn by "just playing," but basic spatial and numerical skills gained in free play help with mathematical concepts. [11] Some abstract games such as chess can benefit learning mathematics by developing systems thinking, logic, and reasoning.
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.
In proof theory and mathematical logic, sequent calculus is a family of formal systems sharing a certain style of inference and certain formal properties. The first sequent calculi systems, LK and LJ, were introduced in 1934/1935 by Gerhard Gentzen [1] as a tool for studying natural deduction in first-order logic (in classical and intuitionistic versions, respectively).
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