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APOS Theory
In mathematics education, APOS Theory is a framework 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. APOS Theory takes a Constructivism (philosophy of education), constructivist view towards mathematical learning. Implementations of APOS Theory in classrooms typically use the ACE Teaching Cycle, a pedagogical strategy with three chronological components: activities, classroom discussion, and exercises. Implementations also often use mathematical programming languages, most commonly ISETL. Mental structures and mechanisms APOS Theory emphasizes four mental structures: Actions, Processes, Objects, and Schemas and its mental mechanisms: Interiorization, Encapsulation, Coordination, Reversal, among others. # ''Actions'' are specific manipulations or transformations ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Education
In contemporary education, mathematics education—known in Europe as the didactics or pedagogy of mathematics—is the practice of teaching, learning, and carrying out Scholarly method, scholarly research into the transfer of mathematical knowledge. Although research into mathematics education is primarily concerned with the tools, methods, and approaches that facilitate practice or the study of practice, it also covers an extensive field of study encompassing a variety of different concepts, theories and methods. List of mathematical societies, National and international organisations regularly hold conferences and List of mathematics education journals, publish literature in order to improve mathematics education. History Ancient Elementary mathematics were a core part of education in many ancient civilisations, including ancient Egypt, Babylonia, ancient Babylonia, ancient Greece, ancient Rome, and Vedic civilization, Vedic Ancient India, India. In most cases, formal edu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jean Piaget
Jean William Fritz Piaget (, ; ; 9 August 1896 – 16 September 1980) was a Swiss psychologist known for his work on child development. Piaget's theory of cognitive development and epistemological view are together called genetic epistemology. Piaget placed great importance on the education of children. As the Director of the International Bureau of Education, he declared in 1934 that "only education is capable of saving our societies from possible collapse, whether violent, or gradual". His theory of child development has been studied in pre-service education programs. Nowadays, educators and theorists working in the area of early childhood education persist in incorporating constructivist-based strategies. Piaget created the International Center for Genetic Epistemology in Geneva in 1955 while on the faculty of the University of Geneva, and directed the center until his death in 1980. The number of collaborations that its founding made possible, and their impact, ultimately le ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reflective Abstraction
Piaget's theory of cognitive development, or his genetic epistemology, is a comprehensive theory about the nature and development of human intelligence. It was originated by the Swiss developmental psychologist Jean Piaget (1896–1980). The theory deals with the nature of knowledge itself and how humans gradually come to acquire, construct, and use it. Piaget's theory is mainly known as a developmental stage theory. In 1919, while working at the Alfred Binet Laboratory School in Paris, Piaget "was intrigued by the fact that children of different ages made different kinds of mistakes while solving problems". His experience and observations at the Alfred Binet Laboratory were the beginnings of his theory of cognitive development. He believed that children of different ages made different mistakes because of the "quality rather than quantity" of their intelligence. Piaget proposed four stages to describe the development process of children: sensorimotor stage, pre-operational stag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constructivism (philosophy Of Education)
Constructivism in education is a theory that suggests that learners do not passively acquire knowledge through direct instruction. Instead, they ''construct'' their understanding through experiences and social interaction, integrating new information with their existing knowledge. This theory originates from Swiss developmental psychologist Jean Piaget's theory of cognitive development. Background Constructivism in education is rooted in epistemology, a theory of knowledge concerned with the logical categories of knowledge and its justification. It acknowledges that learners bring prior knowledge and experiences shaped by their social and cultural environment and that learning is a process of students "constructing" knowledge based on their experiences. While behaviorism focuses on understanding what students are doing, constructivism emphasizes the importance of understanding what students are thinking and how to enrich their thinking.Seifert, Kelvin & Sutton, Rosemary. Educ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Programming Language
A programming language is a system of notation for writing computer programs. Programming languages are described in terms of their Syntax (programming languages), syntax (form) and semantics (computer science), semantics (meaning), usually defined by a formal language. Languages usually provide features such as a type system, Variable (computer science), variables, and mechanisms for Exception handling (programming), error handling. An Programming language implementation, implementation of a programming language is required in order to Execution (computing), execute programs, namely an Interpreter (computing), interpreter or a compiler. An interpreter directly executes the source code, while a compiler produces an executable program. Computer architecture has strongly influenced the design of programming languages, with the most common type (imperative languages—which implement operations in a specified order) developed to perform well on the popular von Neumann architecture. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ISETL
SETL (SET Language) is a very high-level programming language based on the mathematical Set theory, theory of sets. It was originally developed at the New York University (NYU) Courant Institute of Mathematical Sciences in the late 1960s, by a group containing (Jack) Jacob T. Schwartz, R.B.K. Dewar, and E. Schonberg. Schwartz is credited with designing the language. Design SETL provides two basic aggregate data types: (unordered) ''sets'', and ''tuples''. The elements of sets and tuples can be of any arbitrary type, including sets and tuples themselves, except the undefined value om (sometimes capitalized: OM). ''Maps'' are provided as sets of ''pairs'' (i.e., tuples of length 2) and can have arbitrary domain and range types. Primitive operations in SETL include set membership, union, intersection, and power set construction, among others. SETL provides quantified boolean expressions constructed using the universal quantifier, universal and existential quantifiers of first-ord ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mental Structure
Mental may refer to: * of or relating to the mind Films * ''Mental'' (2012 film), an Australian comedy-drama film starring Toni Collette * ''Mental'' (2016 film), a Bangladeshi romantic-action film starring Shakib Khan * ''Mental'', a 2008 documentary by Kazuhiro Soda * ''Mental'', a 2014 Odia language remake of the 2010 Telugu film ''Seeta Ramula Kalyanam'' * ''Jai Ho'', a 2014 Indian action drama film originally titled ''Mental'' Other uses * ''Mental'' (TV series), a 2009 TV series produced by Fox Telecolombia * ''Mental'' (album), a 2014 album by KJ-52 *"Mental", a song by Eels from their 1996 album ''Beautiful Freak'' *Mental (Sri Aurobindo), a term in the philosophy of Sri Aurobindo See also * * Mental disability (other) * Mental foramen, an opening on the anterior surface of the mandible * Mental health Mental health is often mistakenly equated with the absence of mental illness. However, mental health refers to a person's overall emotional, psycholog ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Object
A mathematical object is an abstract concept arising in mathematics. Typically, a mathematical object can be a value that can be assigned to a Glossary of mathematical symbols, symbol, and therefore can be involved in formulas. Commonly encountered mathematical objects include numbers, Expression (mathematics), expressions, shapes, function (mathematics), functions, and set (mathematics), sets. Mathematical objects can be very complex; for example, theorems, proof (mathematics), proofs, and even theory (mathematical logic), formal theories are considered as mathematical objects in proof theory. In Philosophy of mathematics, the concept of "mathematical objects" touches on topics of existence, Identity (philosophy), identity, and the Nature (philosophy), nature of reality. In metaphysics, objects are often considered Entity, entities that possess Property (philosophy), properties and can stand in various Relation (philosophy), relations to one another. Philosophers debate whether m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function (mathematics)
In mathematics, a function from a set (mathematics), set to a set assigns to each element of exactly one element of .; the words ''map'', ''mapping'', ''transformation'', ''correspondence'', and ''operator'' are sometimes used synonymously. The set is called the Domain of a function, domain of the function and the set is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a ''function'' of time. History of the function concept, Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable function, differentiable (that is, they had a high degree of regularity). The concept of a function was formalized at the end of the 19th century in terms of set theory, and this greatly increased the possible applications of the concept. A f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
N-tuple
In mathematics, a tuple is a finite sequence or ''ordered list'' of numbers or, more generally, mathematical objects, which are called the ''elements'' of the tuple. An -tuple is a tuple of elements, where is a non-negative integer. There is only one 0-tuple, called the ''empty tuple''. A 1-tuple and a 2-tuple are commonly called a singleton and an ordered pair, respectively. The term ''"infinite tuple"'' is occasionally used for ''"infinite sequences"''. Tuples are usually written by listing the elements within parentheses "" and separated by commas; for example, denotes a 5-tuple. Other types of brackets are sometimes used, although they may have a different meaning. An -tuple can be formally defined as the image of a function that has the set of the first natural numbers as its domain. Tuples may be also defined from ordered pairs by a recurrence starting from an ordered pair; indeed, an -tuple can be identified with the ordered pair of its first elements and its th e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological Space
In mathematics, a topological space is, roughly speaking, a Geometry, geometrical space in which Closeness (mathematics), closeness is defined but cannot necessarily be measured by a numeric Distance (mathematics), distance. More specifically, a topological space is a Set (mathematics), set whose elements are called Point (geometry), points, along with an additional structure called a topology, which can be defined as a set of Neighbourhood (mathematics), neighbourhoods for each point that satisfy some Axiom#Non-logical axioms, axioms formalizing the concept of closeness. There are several equivalent definitions of a topology, the most commonly used of which is the definition through open sets, which is easier than the others to manipulate. A topological space is the most general type of a space (mathematics), mathematical space that allows for the definition of Limit (mathematics), limits, Continuous function (topology), continuity, and Connected space, connectedness. Common types ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
