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Word Problem (mathematics Education)
In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation. As most word problems involve a narrative of some sort, they are sometimes referred to as story problems and may vary in the amount of technical language used. Example A typical word problem: Tess paints two boards of a fence every four minutes, but Allie can paint three boards every two minutes. If there are 240 boards total, how many hours will it take them to paint the fence, working together? Solution process Word problems such as the above can be examined through five stages: * 1. Problem Comprehension * 2. Situational Solution Visualization * 3. Mathematical Solution Planning * 4. Solving for Solution * 5. Situational Solution Visualization The linguistic properties of a word problem need to be addressed first. To begin the solutio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Word Problem (mathematics)
In computational mathematics, a word problem is the decision problem, problem of deciding whether two given expressions are equivalent with respect to a set of rewriting identities. A prototypical example is the word problem for groups, but there are many other instances as well. Some deep results of computational theory concern the undecidable problem, undecidability of this question in many important cases. Background and motivation In computer algebra one often wishes to encode mathematical expressions using an expression tree. But there are often multiple equivalent expression trees. The question naturally arises of whether there is an algorithm which, given as input two expressions, decides whether they represent the same element. Such an algorithm is called a ''solution to the word problem''. For example, imagine that x,y,z are symbols representing real numbers - then a relevant solution to the word problem would, given the input (x \cdot y)/z \mathrel (x/z)\cdot y, produ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radius
In classical geometry, a radius (: radii or radiuses) of a circle or sphere is any of the line segments from its Centre (geometry), center to its perimeter, and in more modern usage, it is also their length. The radius of a regular polygon is the line segment or distance from its center to any of its Vertex (geometry), vertices. The name comes from the Latin ''radius'', meaning ray but also the spoke of a chariot wheel.Definition of Radius at dictionary.reference.com. Accessed on 2009-08-08. The typical abbreviation and mathematical symbol for radius is ''R'' or ''r''. By extension, the diameter ''D'' is defined as twice the radius:Definition of radius at mathwords.com. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rhind Mathematical Papyrus
The Rhind Mathematical Papyrus (RMP; also designated as papyrus British Museum 10057, pBM 10058, and Brooklyn Museum 37.1784Ea-b) is one of the best known examples of ancient Egyptian mathematics. It is one of two well-known mathematical papyri, along with the Moscow Mathematical Papyrus. The Rhind Papyrus is the larger, but younger, of the two. In the papyrus' opening paragraphs Ahmes presents the papyrus as giving "Accurate reckoning for inquiring into things, and the knowledge of all things, mysteries ... all secrets". He continues: This book was copied in regnal year 33, month 4 of Season of the Inundation, Akhet, under the majesty of the King of Upper and Lower Egypt, Awserre, given life, from an ancient copy made in the time of the King of Upper and Lower Egypt Nimaatre. The scribe Ahmose writes this copy. Several books and articles about the Rhind Mathematical Papyrus have been published, and a handful of these stand out. ''The Rhind Papyrus'' was published in 192 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ancient Egypt
Ancient Egypt () was a cradle of civilization concentrated along the lower reaches of the Nile River in Northeast Africa. It emerged from prehistoric Egypt around 3150BC (according to conventional Egyptian chronology), when Upper and Lower Egypt were amalgamated by Menes, who is believed by the majority of List of Egyptologists, Egyptologists to have been the same person as Narmer. The history of ancient Egypt unfolded as a series of stable kingdoms interspersed by the "Periodization of ancient Egypt, Intermediate Periods" of relative instability. These stable kingdoms existed in one of three periods: the Old Kingdom of Egypt, Old Kingdom of the Early Bronze Age; the Middle Kingdom of Egypt, Middle Kingdom of the Middle Bronze Age; or the New Kingdom of Egypt, New Kingdom of the Late Bronze Age. The pinnacle of ancient Egyptian power was achieved during the New Kingdom, which extended its rule to much of Nubia and a considerable portion of the Levant. After this period, Egypt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Babylonia
Babylonia (; , ) was an Ancient history, ancient Akkadian language, Akkadian-speaking state and cultural area based in the city of Babylon in central-southern Mesopotamia (present-day Iraq and parts of Kuwait, Syria and Iran). It emerged as an Akkadian-populated but Amorites, Amorite-ruled state . During the reign of Hammurabi and afterwards, Babylonia was retrospectively called "the country of Akkad" ( in Akkadian), a deliberate archaism in reference to the previous glory of the Akkadian Empire. It was often involved in rivalry with the older ethno-linguistically related state of Assyria in the north of Mesopotamia and Elam to the east in Ancient Iran. Babylonia briefly became the major power in the region after Hammurabi (floruit, fl. –1752 BC middle chronology, or –1654 BC, short chronology timeline, short chronology) created a short-lived empire, succeeding the earlier Akkadian Empire, Third Dynasty of Ur, and Old Assyrian Empire. The Babylonian Empire rapidly fell apar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semantics
Semantics is the study of linguistic Meaning (philosophy), meaning. It examines what meaning is, how words get their meaning, and how the meaning of a complex expression depends on its parts. Part of this process involves the distinction between sense and reference. Sense is given by the ideas and concepts associated with an expression while reference is the object to which an expression points. Semantics contrasts with syntax, which studies the rules that dictate how to create grammatically correct sentences, and pragmatics, which investigates how people use language in communication. Lexical semantics is the branch of semantics that studies word meaning. It examines whether words have one or several meanings and in what lexical relations they stand to one another. Phrasal semantics studies the meaning of sentences by exploring the phenomenon of compositionality or how new meanings can be created by arranging words. Formal semantics (natural language), Formal semantics relies o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Teacher Education
Teacher education or teacher training refers to programs, policies, procedures, and provision designed to equip (prospective) teachers with the knowledge, attitude (psychology), attitudes, behaviors, approaches, methodologies and skills they require to perform their tasks effectively in the classroom, school, and wider community. The professionals who engage in training the prospective teachers are called teacher educators (or, in some contexts, teacher trainers). There is a longstanding and ongoing debate about the most appropriate term to describe these activities. The term 'teacher training' (which may give the impression that the activity involves training staff to undertake relatively routine tasks) seems to be losing ground, at least in the U.S., to 'teacher education' (with its connotation of preparing staff for a professional role as a reflective practitioner). The two major components of teacher education are in-service teacher education and pre-service teacher education.se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Attention
Attention or focus, is the concentration of awareness on some phenomenon to the exclusion of other stimuli. It is the selective concentration on discrete information, either subjectively or objectively. William James (1890) wrote that "Attention is the taking possession by the mind, in clear and vivid form, of one out of what seem several simultaneously possible objects or trains of thought. Focalization, concentration, of consciousness are of its essence." Attention has also been described as the allocation of limited cognitive processing resources. Attention is manifested by an attentional bottleneck, in terms of the amount of data the brain can process each second; for example, in human vision, less than 1% of the visual input data stream of 1MByte/sec can enter the bottleneck, leading to inattentional blindness. Attention remains a crucial area of investigation within education, psychology, neuroscience, cognitive neuroscience, and neuropsychology. Areas of activ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Working Memory
Working memory is a cognitive system with a limited capacity that can Memory, hold information temporarily. It is important for reasoning and the guidance of decision-making and behavior. Working memory is often used synonymously with short-term memory, but some theorists consider the two forms of memory distinct, assuming that working memory allows for the manipulation of stored information, whereas short-term memory only refers to the short-term storage of information. Working memory is a theoretical concept central to cognitive psychology, neuropsychology, and neuroscience. History The term "working memory" was coined by George Armitage Miller, Miller, Eugene Galanter, Galanter, and Karl H. Pribram, Pribram, and was used in the 1960s in the context of Computational theory of mind, theories that likened the mind to a computer. In 1968, Atkinson–Shiffrin memory model, Atkinson and Shiffrin used the term to describe their "short-term store". The term short-term store was the na ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sentence Processing
Sentence processing takes place whenever a reader or listener processes a language utterance, either in isolation or in the context of a conversation or a text. Many studies of the human language comprehension process have focused on reading of single utterances (sentences) without context. Extensive research has shown that language comprehension is affected by context preceding a given utterance as well as many other factors. Ambiguity Sentence comprehension has to deal with ambiguity in spoken and written utterances, for example lexical, structural, and semantic ambiguities. Ambiguity is ubiquitous, but people usually resolve it so effortlessly that they do not even notice it. For example, the sentence '' Time flies like an arrow'' has (at least) the interpretations ''Time moves as quickly as an arrow'', ''A special kind of fly, called time fly, likes arrows'' and ''Measure the speed of flies like you would measure the speed of an arrow''. Usually, readers will be aware of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mental Chronometry
Mental chronometry is the scientific study of processing speed or reaction time on cognitive tasks to infer the content, duration, and temporal sequencing of mental operations. Reaction time (RT; also referred to as "response time") is measured by the elapsed time between stimulus onset and an individual's response on elementary cognitive tasks (ECTs), which are relatively simple perceptual-motor tasks typically administered in a laboratory setting. Mental chronometry is one of the core methodological paradigms of human experimental, cognitive, and differential psychology, but is also commonly analyzed in psychophysiology, cognitive neuroscience, and behavioral neuroscience to help elucidate the biological mechanisms underlying perception, attention, and decision-making in humans and other species. Mental chronometry uses measurements of elapsed time between sensory stimulus onsets and subsequent behavioral responses to study the time course of information processing in th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Visual Thinking
Visual thinking, also called visual or spatial learning or picture thinking, is the phenomenon of thinking through visual processing. Visual thinking has been described as seeing words as a series of pictures. It is common in approximately 60–65% of the general population. "Real picture thinkers", those who use visual thinking almost to the exclusion of other kinds of thinking, make up a smaller percentage of the population. Research by child development theorist Linda Kreger Silverman suggests that less than 30% of the population strongly uses visual/spatial thinking, another 45% uses both visual/spatial thinking and thinking in the form of words, and 25% thinks exclusively in words. According to Kreger Silverman, of the 30% of the general population who use visual/spatial thinking, only a small percentage would use this style over and above all other forms of thinking, and can be said to be true "picture thinkers". Non-verbal thought Thinking in mental images is one of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
