Constructivism is a theory of knowledge that argues that humans generate knowledge and meaning from an interaction between their experiences and their ideas. It has influenced a number of disciplines, including psychology, sociology, education and the history of science. During its infancy, constructivism examined the interaction between human experiences and their reflexes or behavior-patterns. Jean Piaget called these systems of knowledge schemata. Constructivism is not a specific pedagogy, although it is often confused with constructionism, an educational theory developed by Seymour Papert, inspired by constructivist and experiential learning ideas of Piaget. Piaget's theory of constructivist learning has had wide ranging impact on learning theories and teaching methods in education and is an underlying theme of many education reform movements. Research support for constructivist teaching techniques has been mixed, with some research supporting these techniques and other research contradicting those results.
The goal of learning is prediction. Learning falls into many
categories, including supervised learning, unsupervised learning,
online learning, and reinforcement learning. From the perspective of
statistical learning theory, supervised learning is best understood.
Supervised learning involves learning from a training set of data.
Every point in the training is an input-output pair, where the input
maps to an output. The learning problem consists of inferring the
function that maps between the input and the output in a predictive fashion,
such that the learned function can be used to predict output from
future input.
Learning theories are conceptual frameworks describing how information is absorbed, processed, and retained during learning. Cognitive, emotional, and environmental influences, as well as prior experience, all play a part in how understanding, or a world view, is acquired or changed and knowledge and skills retained.
Behaviorists look at learning as an aspect of conditioning and will advocate a system of rewards and targets in education. Educators who embrace cognitive theory believe that the definition of learning as a change in behavior is too narrow and prefer to study the learner rather than their environment and in particular the complexities of human memory. Those who advocate constructivism believe that a learner's ability to learn relies to a large extent on what he already knows and understands, and the acquisition of knowledge should be an individually tailored process of construction. Transformative learning theory focuses upon the often-necessary change that is required in a learner's preconceptions and world view.
Theory is a contemplative and rational type of abstract or generalizing thinking, or the results of such thinking. Depending on the context, the results might for example include generalized explanations of how nature works. The word has its roots in ancient Greek, but in modern use it has taken on several different related meanings. A theory is not the same as a hypothesis. A theory provides an explanatory framework for some observation, and from the assumptions of the explanation follows a number of possible hypotheses that can be tested in order to provide support for, or challenge, the theory.
A theory can be normative (or prescriptive), meaning a postulation about what ought to be. It provides "goals, norms, and standards". A theory can be a body of knowledge, which may or may not be associated with particular explanatory models. To theorize is to develop this body of knowledge.
As already in Aristotle's definitions, theory is very often contrasted to "practice" (from Greek praxis, πρᾶξις) a Greek term for "doing", which is opposed to theory because pure theory involves no doing apart from itself. A classical example of the distinction between "theoretical" and "practical" uses the discipline of medicine: medical theory involves trying to understand the causes and nature of health and sickness, while the practical side of medicine is trying to make people healthy. These two things are related but can be independent, because it is possible to research health and sickness without curing specific patients, and it is possible to cure a patient without knowing how the cure worked.
The game of chess is commonly divided into three phases: the opening, middlegame, and endgame. There is a large body of theory regarding how the game should be played in each of these phases, especially the opening and endgame. Those who write about chess theory, who are often but not necessarily also eminent players, are referred to as "theorists" or "theoreticians".
"Opening theory" commonly refers to consensus, broadly represented by current literature on the openings. "Endgame theory" consists of statements regarding specific positions, or positions of a similar type, though there are few universally applicable principles. "Middlegame theory" often refers to maxims or principles applicable to the middlegame. The modern trend, however, is to assign paramount importance to analysis of the specific position at hand rather than to general principles.
The development of theory in all of these areas has been assisted by the vast literature on the game. In 1913, preeminent chess historian H. J. R. Murray wrote in his 900-page magnum opus A History of Chess
that, "The game possesses a literature which in contents probably exceeds that of all other games combined." He estimated that at that time the "total number of books on chess, chess magazines, and newspapers devoting space regularly to the game probably exceeds 5,000". In 1949, B. H. Wood opined that the number had increased to about 20,000.David Hooper and Kenneth Whyld wrote in 1992 that, "Since then there has been a steady increase year by year of the number of new chess publications. No one knows how many have been printed..." The world's largest chess library, the John G. White Collection at the Cleveland Public Library, contains over 32,000 chess books and serials, including over 6,000 bound volumes of chess periodicals. Chess players today also avail themselves of computer-based sources of information.
In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. Usually a deductive system is understood from context. An element of a theory is then called an axiom of the theory, and any sentence that follows from the axioms () is called a theorem of the theory. Every axiom is also a theorem. A first-order theory is a set of first-order sentences.
Theories expressed in formal language generally
When defining theories for foundational purposes, additional care must be taken and normal set-theoretic language may not be appropriate.
The construction of a theory begins by specifying a definite non-empty conceptual class, the elements of which are called statements. These initial statements are often called the primitive elements or elementary statements of the theory, to distinguish them from other statements which may be derived from them.
A theory is a conceptual class consisting of certain of these elementary statements. The elementary statements which belong to are called the elementary theorems of and said to be true. In this way, a theory is a way of designating a subset of which consists entirely of true statements.
... to curriculum and instruction (the “classical” approach, as it’s known today) in favor of an increasingly popular and incredibly harmful learning theory called “constructivism.” ....
Piaget’s theory of constructivism is a theory of learning, not a theory of pedagogy, but as a teacher I was required to use “student-centred” teaching methods in order to meet the requirements of a “good lesson” as determined by senior managers.
Constructivist learning theories propose that learners actively construct knowledge through their experiences and interactions with the world ... Collaborative learning theory is also relevant when considering educational scaffolding.
As explained in the brilliant “Deconstructing Constructivism” by Jon Gustafson, the most persistent flaw in constructivism is that “it was created as a theory to explain how an individual learns, and ...
of a theory 
is then called an 
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, the elements of which are called statements. These initial statements are often called the primitive elements or elementary statements of the theory, to distinguish them from other statements which may be derived from them.
is a conceptual class consisting of certain of these elementary statements. The elementary statements which belong to 