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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. APOS Theory takes a 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.
APOS Theory emphasizes four mental structures: Actions, Processes, Objects, and Schemas.
The mental structures are not necessarily gone through in a linear progression. [7]
A concept is an abstract idea that serves as a foundation for more concrete principles, thoughts, and beliefs. Concepts play an important role in all aspects of cognition. As such, concepts are studied within such disciplines as linguistics, psychology, and philosophy, and these disciplines are interested in the logical and psychological structure of concepts, and how they are put together to form thoughts and sentences. The study of concepts has served as an important flagship of an emerging interdisciplinary approach, cognitive science.
Educational psychology is the branch of psychology concerned with the scientific study of human learning. The study of learning processes, from both cognitive and behavioral perspectives, allows researchers to understand individual differences in intelligence, cognitive development, affect, motivation, self-regulation, and self-concept, as well as their role in learning. The field of educational psychology relies heavily on quantitative methods, including testing and measurement, to enhance educational activities related to instructional design, classroom management, and assessment, which serve to facilitate learning processes in various educational settings across the lifespan.
Lev Semyonovich Vygotsky was a Russian and Soviet psychologist, best known for his work on psychological development in children and creating the framework known as cultural-historical activity theory. After his early death, his books and research were banned in the Soviet Union until Joseph Stalin's death in 1953, with a first collection of major texts published in 1956.
Jean William Fritz Piaget 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.
In psychology, cognitivism is a theoretical framework for understanding the mind that gained credence in the 1950s. The movement was a response to behaviorism, which cognitivists said neglected to explain cognition. Cognitive psychology derived its name from the Latin cognoscere, referring to knowing and information, thus cognitive psychology is an information-processing psychology derived in part from earlier traditions of the investigation of thought and problem solving.
A mental model is an internal representation of external reality: that is, a way of representing reality within one's mind. Such models are hypothesized to play a major role in cognition, reasoning and decision-making. The term for this concept was coined in 1943 by Kenneth Craik, who suggested that the mind constructs "small-scale models" of reality that it uses to anticipate events. Mental models can help shape behaviour, including approaches to solving problems and performing tasks.
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.
In psychology and cognitive science, a schema describes a pattern of thought or behavior that organizes categories of information and the relationships among them. It can also be described as a mental structure of preconceived ideas, a framework representing some aspect of the world, or a system of organizing and perceiving new information, such as a mental schema or conceptual model. Schemata influence attention and the absorption of new knowledge: people are more likely to notice things that fit into their schema, while re-interpreting contradictions to the schema as exceptions or distorting them to fit. Schemata have a tendency to remain unchanged, even in the face of contradictory information. Schemata can help in understanding the world and the rapidly changing environment. People can organize new perceptions into schemata quickly as most situations do not require complex thought when using schema, since automatic thought is all that is required.
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.
Cognitive development is a field of study in neuroscience and psychology focusing on a child's development in terms of information processing, conceptual resources, perceptual skill, language learning, and other aspects of the developed adult brain and cognitive psychology. Qualitative differences between how a child processes their waking experience and how an adult processes their waking experience are acknowledged. Cognitive development is defined as the emergence of the ability to consciously cognize, understand, and articulate their understanding in adult terms. Cognitive development is how a person perceives, thinks, and gains understanding of their world through the relations of genetic and learning factors. There are four stages to cognitive information development. They are, reasoning, intelligence, language, and memory. These stages start when the baby is about 18 months old, they play with toys, listen to their parents speak, they watch TV, anything that catches their attention helps build their cognitive development.
The term conceptual model refers to any model that is formed after a conceptualization or generalization process. Conceptual models are often abstractions of things in the real world, whether physical or social. Semantic studies are relevant to various stages of concept formation. Semantics is fundamentally a study of concepts, the meaning that thinking beings give to various elements of their experience.
The model of hierarchical complexity (MHC) is a framework for scoring how complex a behavior is, such as verbal reasoning or other cognitive tasks. It quantifies the order of hierarchical complexity of a task based on mathematical principles of how the information is organized, in terms of information science. This model was developed by Michael Commons and Francis Richards in the early 1980s.
Cognitive description is a term used in psychology to describe the cognitive workings of the human mind.
Genetic epistemology or 'developmental theory of knowledge' is a study of the origins (genesis) of knowledge (epistemology) established by Swiss psychologist Jean Piaget. This theory opposes traditional epistemology and unites constructivism and structuralism. Piaget took epistemology as the starting point and adopted the method of genetics, arguing that all knowledge of the child is generated through interaction with the environment.
Transference-focused psychotherapy (TFP) is a highly structured, twice-weekly modified psychodynamic treatment based on Otto F. Kernberg's object relations model of borderline personality disorder (BPD). It views the individual with borderline personality organization (BPO) as holding unreconciled and contradictory internalized representations of self and significant others that are affectively charged. The defense against these contradictory internalized object relations leads to disturbed relationships with others and with oneself. The distorted perceptions of self, others, and associated affects are the focus of treatment as they emerge in the relationship with the therapist (transference). The treatment focuses on the integration of split-off parts of self and object representations, and the consistent interpretation of these distorted perceptions is considered the mechanism of change.
Cultural schema theory is a cognitive theory that explains how people organize and process information about events and objects in their cultural environment. According to the theory, individuals rely on schemas, or mental frameworks, to understand and make sense of the world around them. These schemas are shaped by culture, and they help people to quickly and efficiently process information that is consistent with their cultural background. Cultural schemas can include knowledge about social roles, customs, and beliefs, as well as expectations about how people will behave in certain situations. The theory posits that cultural schemas are formed through repeated interactions and experiences within a particular cultural group, and that they guide behavior in familiar social situations. Cultural schemas are distinct from other schemas in that they are shared among members of a particular cultural group, as opposed to being unique to individuals.
Domain-general learning theories of development suggest that humans are born with mechanisms in the brain that exist to support and guide learning on a broad level, regardless of the type of information being learned. Domain-general learning theories also recognize that although learning different types of new information may be processed in the same way and in the same areas of the brain, different domains also function interdependently. Because these generalized domains work together, skills developed from one learned activity may translate into benefits with skills not yet learned. Another facet of domain-general learning theories is that knowledge within domains is cumulative, and builds under these domains over time to contribute to our greater knowledge structure. Psychologists whose theories align with domain-general framework include developmental psychologist Jean Piaget, who theorized that people develop a global knowledge structure which contains cohesive, whole knowledge internalized from experience, and psychologist Charles Spearman, whose work led to a theory on the existence of a single factor accounting for all general cognitive ability.
Neo-Piagetian theories of cognitive development criticize and build upon Jean Piaget's theory of cognitive development.
Mental operations are operations that affect mental contents. Initially, operations of reasoning have been the object of logic alone. Pierre Janet was one of the first to use the concept in psychology. Mental operations have been investigated at a developmental level by Jean Piaget, and from a psychometric perspective by J. P. Guilford. There is also a cognitive approach to the subject, as well as a systems view of it.
Text and conversation is a theory in the field of organizational communication illustrating how communication makes up an organization. In the theory's simplest explanation, an organization is created and defined by communication. Communication "is" the organization and the organization exists because communication takes place. The theory is built on the notion, an organization is not seen as a physical unit holding communication. Text and conversation theory puts communication processes at the heart of organizational communication and postulates, an organization doesn't contain communication as a "causal influence", but is formed by the communication within. This theory is not intended for direct application, but rather to explain how communication exists. The theory provides a framework for better understanding organizational communication.