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Proportional Reasoning
Reasoning based on relations of proportionality is one form of what in Piaget's theory of cognitive development is called "formal operational reasoning", which is acquired in the later stages of intellectual development. There are methods by which teachers can guide students in the correct application of proportional reasoning. In mathematics and physics In mathematics and in physics, proportionality is a mathematical relation between two quantities; it can be expressed as an equality of two ratios: :\frac = \frac Functionally, proportionality can be a relationship between variables in a mathematical equation. For example, given the following equation for the force of gravity (according to Newton): :F = G \frac the force of gravity between two masses is directly proportional to the product of the two masses and inversely proportional to the square of the distance between the two masses. Intellectual development In Piaget's model of intellectual development, the fourth and fin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reason
Reason is the capacity of Consciousness, consciously applying logic by Logical consequence, drawing conclusions from new or existing information, with the aim of seeking the truth. It is closely associated with such characteristically human activities as philosophy, science, language, mathematics, and art, and is normally considered to be a distinguishing ability possessed by humans. Reason is sometimes referred to as rationality. Reasoning is associated with the acts of Thought, thinking and cognition, and involves the use of one's intellect. The field of logic studies the ways in which humans can use formal reasoning to produce Validity (logic), logically valid arguments. Reasoning may be subdivided into Logical form, forms of logical reasoning, such as: deductive reasoning, inductive reasoning, and abductive reasoning. Aristotle drew a distinction between logical discursive reasoning (reason proper), and Intuition (psychology), intuitive reasoning, in which the reasoning proces ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Child Development
Child development involves the Human development (biology), biological, developmental psychology, psychological and emotional changes that occur in human beings between birth and the conclusion of adolescence. Childhood is divided into 3 stages of life which include early childhood, middle childhood, and late childhood (preadolescence). Early childhood typically ranges from infancy to the age of 6 years old. During this period, development is significant, as many of life's milestones happen during this time period such as first words, learning to crawl, and learning to walk. There is speculation that middle childhood/preadolescence or ages 6–12 are the most crucial years of a child's life. Adolescence is the stage of life that typically starts around the major onset of puberty, with markers such as menarche and spermarche, typically occurring at 12–13 years of age. It has been defined as ages 10 to 19 by the World Health Organization. In the course of development, the individu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thought Experiments
A thought experiment is a hypothetical situation in which a hypothesis, theory, or principle is laid out for the purpose of thinking through its consequences. History The ancient Greek ''deiknymi'' (), or thought experiment, "was the most ancient pattern of mathematical proof", and existed before Euclidean mathematics, where the emphasis was on the conceptual, rather than on the experimental part of a thought-experiment. Johann Witt-Hansen established that Hans Christian Ørsted was the first to use the German term ' (lit. thought experiment) circa 1812. Ørsted was also the first to use the equivalent term ' in 1820. By 1883 Ernst Mach used the term ' in a different way, to denote exclusively the conduct of a experiment that would be subsequently performed as a by his students. Physical and mental experimentation could then be contrasted: Mach asked his students to provide him with explanations whenever the results from their subsequent, real, physical experiment differed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constant-sum
Zero-sum game is a mathematical representation in game theory and economic theory of a situation which involves two sides, where the result is an advantage for one side and an equivalent loss for the other. In other words, player one's gain is equivalent to player two's loss, therefore the net improvement in benefit of the game is zero. If the total gains of the participants are added up, and the total losses are subtracted, they will sum to zero. Thus, cutting a cake, where taking a more significant piece reduces the amount of cake available for others as much as it increases the amount available for that taker, is a zero-sum game if all participants value each unit of cake equally. Other examples of zero-sum games in daily life include games like poker, chess, and bridge where one person gains and another person loses, which results in a zero-net benefit for every player. In the markets and financial instruments, futures contracts and options are zero-sum games as well. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cognitive Dissonance
In the field of psychology, cognitive dissonance is the perception of contradictory information, and the mental toll of it. Relevant items of information include a person's actions, feelings, ideas, beliefs, values, and things in the environment. Cognitive dissonance is typically experienced as psychological stress when persons participate in an action that goes against one or more of those things. According to this theory, when two actions or ideas are not psychologically consistent with each other, people do all in their power to change them until they become consistent. The discomfort is triggered by the person's belief clashing with new information perceived, wherein the individual tries to find a way to resolve the contradiction to reduce their discomfort.Festinger, L. (1957). ''A Theory of Cognitive Dissonance''. California: Stanford University Press. In '' When Prophecy Fails: A Social and Psychological Study of a Modern Group That Predicted the Destruction of the World'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proportionality (mathematics)
In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio, which is called the coefficient of proportionality or proportionality constant. Two sequences are inversely proportional if corresponding elements have a constant product, also called the coefficient of proportionality. This definition is commonly extended to related varying quantities, which are often called ''variables''. This meaning of ''variable'' is not the common meaning of the term in mathematics (see variable (mathematics)); these two different concepts share the same name for historical reasons. Two functions f(x) and g(x) are ''proportional'' if their ratio \frac is a constant function. If several pairs of variables share the same direct proportionality constant, the equation expressing the equality of these ratios is called a proportion, e.g., (for details see Ratio). Proportionality is closely r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Karplus
Robert Karplus (February 23, 1927 – March 20, 1990) was a theoretical physicist and leader in the field of science education. Early life Robert Karplus was born in Vienna, where he lived until the German occupation of Austria in 1938. He emigrated with his mother and brother to escape the ''Anschluss''. After a six-month stay in Switzerland, the family moved to the United States and settled in the Boston area. He entered Harvard University in 1943 and completed his Ph.D at the age of twenty-one. His thesis under E. Bright Wilson was on microwave spectroscopy and included both experimental and theoretical work. He was recognized by those he worked with for his brilliance, originality, energy, and cheerful, positive outlook. His grandfather, Johann Paul Karplus (1866-1936) was a highly acclaimed professor of psychiatry at the University of Vienna. He is nephew, by marriage, of the famous sociologist, philosopher and musicologist Theodor W. Adorno and grandnephew of the physicist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bärbel Inhelder
Bärbel Elisabeth Inhelder (15 April 1913 – 17 February 1997) was a Swiss psychologist most known for her work under psychologist and epistemologist Jean Piaget and their contributions toward child development. Born in St. Gallen, Switzerland, Inhelder initially showed interest in education. While attending high school she became interested in Sigmund Freud's writing and information on adolescents. She then moved to Geneva where she studied at the University of Geneva Institut Jean-Jacques Rousseau earning her bachelor's and doctoral degrees both in psychology. Inhelder continued her work at the University of Geneva up until her retirement. During her time at Geneva, she worked alongside Jean Piaget collaborating on experimental work targeted toward child development. Their collaboration began with her dissertation on children's conservation and continued for 50 years. Inhelder's work was significant in the discovery of the formal operational stage Piaget's theory of cognitiv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
