Formal Operational Stage of Piaget's Cognitive Development Theory: An Implication in Learning Mathematics
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IntroductionJean Piaget a well-known psychologist belonged to Switzerland. He developed Cognitive Development theory in 1952 and was known as Piaget's Theory. He was concerned with children cognitive learning and proved that how they responded to their surroundings. Piaget's theory centered on a rule that cognitive development starts in a sequence of four separate, universal stages. These four stages work for all time in similar order and each stage constructs on the basis of the prior stage. Piaget stated that cognitive development was a reformation progress of mind as a result of genetic, biological maturation and surrounding practice. Children pass through four stages of cognitive development up to the adulthood (Wadsworth, 2003).Cognitive development process is the formation and composition of thinking processes. It includes particularly identification, recall, solve difficulties, problems, hindrances, and make decisions about something from childhood to adulthood. Piaget's theory of cognitive development is concerned with information, knowledge and understanding, how a human being gains knowledge, builds knowledge as well as applies knowledge (Wadsworth, 2003). In view of Piaget (1964) cognitive development in early period contains processes which are based upon some actions and in later period cognitive development involves mental operations. Ojose, (2008) asserted that Piaget's theory on cognitive development stages are Sensorimotor (0 - 2 years), Pre operations (2 - 7 years), Concrete operations (7 - 11 years), and Formal operations (12 - 16 years).Cherry (2014) explained that in view of Jean Piaget, children grow within four stages of cognitive development. Each stage is characterized, how children understand the world around. According to Piaget, children are like little scientists. They try to discover the world around them. Piaget proposed that there is a qualitative change in kids during these four stages. During the sensorimotor stage (0 - 2 years), infants gain knowledge through sensory practices, using different things. Piaget (1977) distributed the first stage into six sub-stages having specific time of each sub-stage with composition of actions such as visualization, seeing, hearing, investigation, physical and motor practices e.g. catching, sucking something, and trying to stand. Piaget explained that ability to count numbers or things like one cock, two cats, three dogs, four tigers etc are additional features of sensorimotor stage. According to Essa (1999), language and some symbolic actions are developed in preoperational stage. However, thought process is not consistent up to this stage. Children comprehend simple categorization, ordering, function, games, etc. Piaget (1977) explained that at the preoperational stage (2 - 7 years), children gain knowledge through imaginary play. They try to use their senses and acquire opinion of other people. During the concrete operational stage (7 - 11 years), children start thinking more logically, but their thinking may be inflexible. Children make an effort with abstract and theoretical thought.Cherry (2014) stated that the formal operational stage (12 - 16 years) of Piaget's cognitive development theory involves increase in sense or intellect, the ability to exercise deductive way of thinking plus understanding of conceptual thoughts. In this period, children build up their ability to reflect on abstract concepts and develop ability of logical thoughts (use general principles to find out specific results), deductive reasoning, and systematic arrangement. In abstract concepts, children think about probable result and effects of any activity. Abstract concepts are helpful in long-term planning. Deductive logic is required especially in science and mathematics. Children are able to solve a problem quickly in an organized way. Brain and Mukherji (2005) stated that in formal operational stage, actual things are no longer required and intellectual operations can work 'in the mind' using conceptual words. …Keywords:
Stage theory
Constructivism (international relations)
Mental operations
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The present investigation was designed to study the development of children’s conceptions of family, in relation to cognitive and cultural aspects. Sixty Mexican children and 60 French children were sampled from primary government schools. Twenty subjects from first, third and sixth grade levels composed each experimental group. Children were presented with an interview including 9 questions exploring the following aspects: type of bonds that children recognize in the family group, types of groupings considered as families by children, elements that children include as part of the family group and certain parental roles. Results showed both age and cultural group differences. Children’s conceptions are initially based on concrete and external aspects, while older children are more likely to employ abstract relational criteria for family definition. Nevertheless, complexity of children’s answers was related both to cognitive level and cultural group of origin, since Mexican children’s considerations about certain groupings as families, differed from French children’s considerations for the same groupings. Results are discussed in terms of actual findings about social knowledge developmental levels, and the relation between social influences upon cognitive structures.
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Abstract Over the course of some 60 years, Jean Piaget (1896–1980), a Swiss biologist and philosopher, formulated a theory of the development of intellectual competence that continues to influence contemporary theories in this domain. Piaget maintained that logical thought depended on learning, social cooperation, biological maturation, and development , by which he meant a series of fundamental changes such that the later ways of thinking are dependent on, yet qualitatively distinct from, the earlier ones, always moving in the direction of greater logical consistency and coherence. He formulated subsidiary theories of the development of moral judgment and reasoning, perception, images, and memory, but always from the perspective of how each was constrained by various levels of intellectual competence.
Logical reasoning
Intellectual development
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Research into children's ideas about science and mathematics-whether known under the title of 'alternative frameworks', 'misconceptions', 'preconceptions', etc. —has at least one important characteristic in common with the work of Piaget: it takes the child's view of the world seriously. Piaget was one of the first to put forward the notion that children construct their own knowledge, this knowledge being seen as different in kind from that of an adult, evolving and changing over the years.
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Conceptualization and representational abilities were shown to exist long before the emergence of language and the symbolic function that were presumed by Jean Piaget to index the emergence of such competencies. The genetic epistemology emerging in the post-Piaget boom of infancy research is an epistemology that puts much more emphasis on the initial biological readiness of children, hence the evolutionary roots of what might define the starting state of cognitive development. As Piaget was ending his life, baby research took the field of developmental psychology like a storm. The behavioral orientation of newborns and their detection of invariant features in the environment all point to an experiential awareness at birth that is organized within a stable spatial and temporal structure. The post-Piagetian wave of infancy research indicates that cognitive development would start with an experience of the world that is much more unified and organized, less disjointed and blind than what Piaget portrays.
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Jean Piaget’s approach to the development of children’s cognition has come to be known as constructivism. Piaget’s starting point is a biological one: cognition is an example of the adaptation between organism and environment seen throughout the living world. When children encounter new experiences or concepts, their existing frameworks or schema have to adjust. This causes a state of disequilibrium, or cognitive conflict–confusion–which acts as motivation to learning until a state of equilibrium is restored. A fundamental basis on which Piaget’s theories have been criticized is their suggested universality. Piaget emphasizes the importance of readiness in children’s development, suggesting that there is little that an adult, or other person, can do to accelerate children’s development. Neo-Piagetian theories emerged as an effort to preserve core theoretical aspects of Piaget’s work, whilst also addressing criticisms of his ideas. Core Knowledge theories have aspects in common with both Piagetian and information processing theories, but they also differ in important ways.
Constructivism (international relations)
Schema (genetic algorithms)
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Affect
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Abstract The prolific work of Jean Piaget (1896–1980) is credited for launching the field of cognitive development and for providing the roots of contemporary developmental inquiry into specific cognitive subfields. Perhaps the most renowned aspect of Piaget's theoretical perspective is his characterization of intellectual development as occurring in a fixed sequence of four qualitatively distinct stages (sensorimotor, preoperational, concrete operational, and formal operational). Research across a wide range of cultures has replicated many of Piaget's observations and claims regarding behavioral features of these proposed stages, particularly those in very early childhood; however, research has also convincingly challenged some of his interpretations and propositions. Following decades of studies that can trace their inspiration back to Piaget, modern scholars have largely abandoned a traditional Piagetian account of comprehensive, stage‐based cognitive transformations in favor of domain‐specific theories that address conceptual advances in particular knowledge areas.
Intellectual development
TRACE (psycholinguistics)
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The present study aims at exploring and assessing Piaget's views on language acquisition and language-thought relationship. Based on his writings, Piaget considers language as one type of symbolic functions Language development is subordinated to thought especially that type of thought which is manifested during the sensorimotor stage. Although Piaget accepts some of the innatist claims on language acquisition, he accepts only the functional aspect, and not the structure itself. Therefore, his theory, known as the constructivist theory is different from both Chomsky's innatist theory and the behaviorist theory. However, Piaget is criticized for not giving adequate attention to the linguistic developments which take place during the preoperational stage at which the language is acquired. With regard to the language - thought relationship, Piaget believes that the role of language, during the concrete and formal operation stages, is necessary but not sufficient for thought formation, although it is more crucial during the final stage Piaget's theory is, therefore, different from Vygotsky's which emphasizes the different roots of both language and thought and that some stages of cognitive development are determined in part by language. تهدف هذه الدراسة إلى تقويم راي جان بياجية، أحد ابرز علماء علم نفس النمو والابستمولوجي، في قضية اكتساب اللغة وعلاقتها بالفكر. كشفت الدراسة من خلال ما كتبه بياجية عن أنه عالج قضية اكتساب اللغة من خلال اعتبارها أحد عناصر الوظائف الرمزية. فنمو اللغة يتم على أساس نخو الفكر في المرحلة الحسية – الحركية وهي المرحلة الأولى في النمو المعرفي. وعلى الرغم من أن بياجية يقبل بعض مزاعم النظرية الفطرية فإن ما يقبل به هو الجانب الوظيفي فقط وليس الجانب التركيبي المتعلق بالمحتوى. وهنا يرى اختلافه مع تشومسكي. يطرح بياجيه بدلا من ذلك نظريته التي تعرف ب " التكوينية " والتي تختلف عن النظريتين الفطرية والسلوكية. إلا أن أحد أهم عيوب نظرية بياجية هو أنه أغفل مرحلة ما قبل العمليات والتي يتم خلالها اكتساب اللغة بنظامها الاساسي. أما بخصوص علاقة اللغة بالفكر فإن بياجية يرى أن دور اللغة وخاصة في المرحلتين المادية والمرحلة التشكيلية-الفرضية للنمو المعرفي يتمثل في كون اللغة ضرورية إلا أنها ليست كافية لتشكيل الفكر. على أن دور اللغة في المرحلة الأخيرة أكثر أهمية. وهنا نرى أن نظرية بياجية تختلف عن تلك التي يتبناها العالم الشهير فيجوتسكي والتي تؤكد على اختلاف أصول اللغة والفكر وأن جزءا من النمو المعرفي يتحدد بواسطة اللغة.
Constructivism (international relations)
Language and thought
Developmental linguistics
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Piaget's study of intellectual processes has led him to conclude that, at around 7 years of age, the average child reaches a stage of development marked by the ability to use certain logical operations in his thinking. In this paper, I shall discuss Piaget's findings and his methods in this area and shall present for consideration an alternative view of the facts. Piaget's comments on this stage are presented in his book on the development of intelligence (1946c); his position is set forth in more detail in his studies of the development of concepts of quantity, time, movement, and speed (1946a, 1946b; Piaget and Inhelder, i94i), of operations of measurement and of geometric concepts and relations (Piaget, Inhelder, and Szeminska, 1948; Piaget and Inhelder, 1948), and of concepts of number and of class (Piaget and Szeminska, 1941; Inhelder and Piaget, I959). These studies, of course, comprise only a part of Piaget's work. The present discussion will not be relevant to his ideas about development in the first two years of life (1936, 1937a, 1945) nor to his many experiments on perception in children. Although parts of this treatment are relevant to his work on adolescent reasoning (Piaget and Inhelder, 1953; Inhelder and Piaget (1955), none of the special problems raised by this work will be discussed. While the segment of Piaget's work under consideration is almost always concerned with fundamental, and usually neglected, problems, his methodology is vulnerable from several points of view, and its flaws often serve to prevent a clear formulation of his research problems. My primary purpose in examining Piaget's methods is to achieve a clear restatement of the basic problems in a manner which does not presuppose Piaget's Weltanschauung. In the pages to follow, I shall address a number of questions of method. At the most general level I shall compare certain elements of Piaget's theory and research strategy with those of modern behavior theory. At a somewhat more specific level, I shall question the adequacy of verbal methods in investigating the processes Piaget has treated. Third, I shall be concerned with
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