query: who wrote the book how to solve it which outlines a general approach to problem solving

pos: How to Solve It look back at what you have done, what worked and what didn't. Doing this will enable you to predict what strategy to use to solve future problems, if these relate to the original problem. The book contains a dictionary-style set of heuristics, many of which have to do with generating a more accessible problem. For example: How to Solve It How to Solve It (1945) is a small volume by mathematician George Pólya describing methods of problem solving. "How to Solve It" suggests the following steps when solving a mathematical problem: If this technique fails, Pólya advises: "If you can't

pos: How to Solve It look back at what you have done, what worked and what didn't. Doing this will enable you to predict what strategy to use to solve future problems, if these relate to the original problem. The book contains a dictionary-style set of heuristics, many of which have to do with generating a more accessible problem. For example: How to Solve It How to Solve It (1945) is a small volume by mathematician George Pólya describing methods of problem solving. "How to Solve It" suggests the following steps when solving a mathematical problem: If this technique fails, Pólya advises: "If you can't

pos: How to Solve It How to Solve It How to Solve It (1945) is a small volume by mathematician George Pólya describing methods of problem solving. "How to Solve It" suggests the following steps when solving a mathematical problem: If this technique fails, Pólya advises: "If you can't solve a problem, then there is an easier problem you can solve: find it." Or: "If you cannot solve the proposed problem, try to solve first some related problem. Could you imagine a more accessible related problem?" "Understand the problem" is often neglected as being obvious and is not even mentioned in many mathematics classes. Yet

neg: Inventor's paradox Inventor's paradox The inventor's paradox is a phenomenon that occurs in seeking a solution to a given problem. Instead of solving a specific type of problem, which would seem intuitively easier, it can be easier to solve a more general problem, which covers the specifics of the sought-after solution. The "inventor's paradox" has been used to describe phenomena in mathematics, programming, and logic, as well as other areas that involve critical thinking. In the book "How to Solve It", George Pólya introduces what he defines as the inventor's paradox: Or, in other words, to solve what one desires to solve,

neg: Abel–Ruffini theorem but it did not provide conclusive proof. The first person who conjectured that the problem of solving quintics by radicals might be impossible to solve was Carl Friedrich Gauss, who wrote in 1798 in section 359 of his book "Disquisitiones Arithmeticae" (which would be published only in 1801) that “there is little doubt that this problem does not so much defy modern methods of analysis as that it proposes the impossible”. The next year, in his thesis, he wrote “After the labors of many geometers left little hope of ever arriving at the resolution of the general equation algebraically, it

neg: George Pólya Learning, and Teaching Problem Solving" (volumes 1 and 2). In "How to Solve It", Pólya provides general heuristics for solving a gamut of problems, including both mathematical and non-mathematical problems. The book includes advice for teaching students of mathematics and a mini-encyclopedia of heuristic terms. It was translated into several languages and has sold over a million copies. Russian physicist Zhores I. Alfyorov (Nobel laureate in 2000) praised it, noting that he was a fan. The American mathematician Terence Tao used the book to prepare for the International Mathematical Olympiad. The book is still used in mathematical education. Douglas Lenat's

neg: Transduction (machine learning) induction since, according to him, induction requires solving a more general problem (inferring a function) before solving a more specific problem (computing outputs for new cases): "When solving a problem of interest, do not solve a more general problem as an intermediate step. Try to get the answer that you really need but not a more general one." A similar observation had been made earlier by Bertrand Russell: "we shall reach the conclusion that Socrates is mortal with a greater approach to certainty if we make our argument purely inductive than if we go by way of 'all men are

neg: FORR FORR FORR (FOr the Right Reasons) is a cognitive architecture for learning and problem solving inspired by Herbert A. Simon's ideas of bounded rationality and satisficing. It was first developed in the early 1990s at the City University of New York. It has been used in game playing, robot pathfinding, recreational park design, spoken dialog systems, and solving NP-hard constraint satisfaction problems, and is general enough for many problem solving applications. FORR does not have perfect knowledge of how to solve a problem, but instead learns from experience. Intelligent agents are not optimal, but make decisions based on only a

neg: Cognitively Guided Instruction able to solve problems without direct instruction by drawing upon informal knowledge of everyday situations. For example, a study of kindergarten children showed that young children can solve problems involving what are normally considered advanced mathematics such as multiplication, division, and multistep problems, by using direct modeling. Direct modeling is an approach to problem solving in which the child, in the absence of more sophisticated knowledge of mathematics, constructs a solution to a story problem by modeling the action or structure. For example, about half of the children in a study of kindergartners' problem solving were able to solve this

neg: Subgoal labeling recent study, Learners who were given labels for subgoals used those labels when explaining how they solved a problem, suggesting that's how they mentally organized the information. Generally problem solving adopts a very procedural approach. Problem solving in the areas of science, technology, engineering and mathematics (STEM) has been highly procedural. The best approach so far is to teach these procedures through instructional text accompanied by specific worked examples. The role of instructional text is to define and describe the problem solving procedures whereas how to apply these procedures is shown through worked examples. Students can learn from step-by-step approach

neg: Lateral computing evolutionary-computing, machine learning and probabilistic-chaotic computing. Instead of solving a problem by creating a non-linear equation model of it, the biological neural network analogy is used for solving the problem. The neural network is trained like a human brain to solve a given problem. This approach has become highly successful in solving some of the pattern recognition problems. The genetic algorithm (GA) resembles the natural evolution to provide a universal optimization. Genetic algorithms start with a population of chromosomes which represent the various solutions. The solutions are evaluated using a fitness function and a selection process determines which solutions are

neg: Wolfgang Köhler Frankfurt for the island of Tenerife in the Canary Islands, where he had been named the director of the Prussian Academy of Sciences anthropoid research station. He worked there for six years, during which he wrote a book on problem solving titled "The Mentality of Apes" (1917). In this research, Köhler observed how chimpanzees solve problems, such as that of retrieving bananas when positioned out of reach. He found that they stacked wooden crates to use as makeshift ladders, in order to retrieve the food. If the bananas were placed on the ground outside of the cage, they used sticks

neg: Transposition-driven scheduling solving some positions. This incurs a severe communication overhead, meaning that a lot of all computers' time is spent communicating with the others instead of solving the problem. To solve this drawback, an approach has been taken that integrates solving the problem and load balancing. To begin, a function is defined that assigns a unique value to every board position. Every computer in the network is assigned a range of board positions for which it holds authority. Every computer has its own transposition table and a job queue. Whenever a computer is done with its current job it fetches a

neg: Richard Rusczyk develop their mathematics and problem solving abilities. These include real-time competitions to solve math problems and on-line tools to learn how to solve problems with increasing difficulty as well as math forums. As of August 14, 2018, there have been 827,671 topics with a total of 7,225,228 posts on the site. Rusczyk has also published the Art of Problem Solving series of books aimed at a similar audience. The site also provides fee-based online mathematics classes, which range from Prealgebra to Group Theory and Calculus. Rusczyk founded and serves on the board of the nonprofit Art of Problem Solving Foundation,

neg: Problem solving ability to solve problems is important at any military rank, but is highly critical at the command and control level, where it is strictly correlated to the deep understanding of qualitative and quantitative scenarios. "Effectiveness" of problem solving is used to measure the result of problem solving, tied to accomplishing the goal. "Planning" for problem-solving is the process of determining how to achieve the goal Problem-solving strategies are the steps that one would use to find the problems that are in the way to getting to one's own goal. Some refer to this as the "problem-solving cycle". In this cycle

neg: Worked-example effect and a well-supported problem solving approach (Schwonke et al., 2009). "However, it is important to note that studying [worked-examples] loses its effectiveness with increasing expertise" (Renkl, 2005), an effect known as the expertise reversal effect (Kalyuga, 2007). Further limitations of the classical worked-example method include "focusing on one single correct solution and on algorithmic skill domains" (Renkl, 2005). Addressing such restrictions in multimedia learning environments remains an area of active research (Renkl, 2005). "A worked example is a step-by-step demonstration of how to perform a task or how to solve a problem" (Clark, Nguyen, Sweller, 2006, p. 190). Worked-examples are

neg: Mathematical problem John three. How many has he left?". Such questions are usually more difficult to solve than regular mathematical exercises like "5 − 3", even if one knows the mathematics required to solve the problem. Known as word problems, they are used in mathematics education to teach students to connect real-world situations to the abstract language of mathematics. In general, to use mathematics for solving a real-world problem, the first step is to construct a mathematical model of the problem. This involves abstraction from the details of the problem, and the modeller has to be careful not to lose essential aspects

neg: Incremental deformations matrix and it has the following form where each block is a matrix and its dimension depends on the dimension of the problem. Moreover, a crucial property of this approach is that formula_84, i.e. formula_85 is the hermitian matrix of formula_86. The Stroh formalism provides an optimal form to solve a great variety of elastic problems. Optimal means that one can construct an efficient numerical procedure to solve the incremental problem. By solving the incremental boundary value problem, one finds the relations among the material and geometrical parameters of the problem and the perturbation modes by which the wave propagates

neg: Subgoal labeling of worked examples which later can be helpful to them in solving similar problems on their own. Novices, however, often find it difficult to distinguish domain specific information and the information specific to solving that problem, which increases their cognitive load. This cognitive load can be reduced by use of subgoal labeling which is achieved by grouping functionally-similar steps under a label that describes that function. This approach can be helpful to students to form a mental model of the domain related problem which later can guide them to solve different problems in that domain. Understanding the structure of worked

neg: Jenny Calendar problems. As a Watcher, Giles is extremely knowledgeable about the creatures that Buffy must face. He has a large collection of books detailing the demon realms, upon which he relies as the main tool of research and problem-solving. Jenny challenges his traditional approach and helps him to solve the problem of how to find and kill the demon when Giles reveals himself to be a technophobe; she both frustrates and flirts with him in the process. Jenny's character was not intended to be recurring, but the chemistry exhibited between LaMorte and Head encouraged the writers to make her a regular

neg: Embodied design How could you have optimized your steps to reach that conclusion?" can be answered with manipulatives. One aim of problem solving in embodied design is to inspire students' creativity and curiosity, allowing personal connections to problems. If students are given a problem which involves tactile manipulation, the learning process may be more meaningful. For example, students can learn to solve a Rubik's Cube puzzle by using a series of algorithms and steps. The process involves orientation, following directions and spatial cognition. One approach to embodied design in mathematics is the use of creative tasks, such as arts and crafts. When

neg: Expertise reversal effect and for a variety of instructional techniques. Listed below are just a small set of examples, all of which are described more thoroughly in Kalyuga, Ayres, Chandler, & Sweller, 2003. Interactions between levels of knowledge and the worked-example effect: Worked examples provide a problem statement followed by a step-by-step demonstration of how to solve it. Worked examples are often contrasted with open-ended problem solving in which the learner is responsible for providing the step-by-step solution. Low-knowledge learners benefit more from studying structured worked-out examples than from solving problems on their own. However, as knowledge increases, open-ended problem solving becomes the

neg: Domain-general learning show the need for workers/employees to be adaptive. This may suggest that school curricular should incorporate activities focusing on developing the necessary skills for dynamic environments. People tend to use domain-general learning processes when initially learning how to perform and complete certain tasks, and less so once these tasks become extensively practiced. Problem solving is considered to be an individual’s ability to partake in cognitive processing in order to understand and solve problems where a solution may not be immediately apparent. Domain-specific problem solving skills may provide students with narrow knowledge and abilities. Because of this, school teachers, policy makers

neg: Open Space Technology solving a problem. The first Foo Camp was organized by Tim O'Reilly and Sara Winge; because Sara had been a student of Harrison Owen, many elements similar to OST are used in Foo Camp. A design sprint (a meeting technique related to design thinking and pioneered by Google Ventures) is similar to OST in that participants are invited by an organizer to work collaboratively on solving a problem, with the help of a facilitator who is trained in running such meetings. All participants are asked to contribute ideas toward what the problem is and how to solve it, but in

neg: Embodied design cognitive costs (such as motor coordination) are outweighed by their benefits (such as multimodal processing). Another application of embodied design in mathematics education is its effect on problem solving and the development of critical-thinking skills. Throughout the problem-solving process students use objects to develop understanding, conveying understanding and meaning through gestures. Problem solvers use gestures to connect their thoughts to the manipulatives with which they are familiar, and changing a manipulative's shape affects how a student connects with it and uses it to solve a problem. In a study by van Gog, Post, ten Napel and Deijkers, students performed better

neg: George Pólya Alto, California, United States. Early in his career, Pólya wrote with Gábor Szegő two influential problem books "Problems and Theorems in Analysis" ("I: Series, Integral Calculus, Theory of Functions" and "II: Theory of Functions. Zeros. Polynomials. Determinants. Number Theory. Geometry"). Later in his career, he spent considerable effort to identify systematic methods of problem-solving to further discovery and invention in mathematics for students, teachers, and researchers. He wrote five books on the subject: "How to Solve It", "Mathematics and Plausible Reasoning" ("Volume I: Induction and Analogy in Mathematics", and "Volume II: Patterns of Plausible Inference"), and "Mathematical Discovery: On Understanding,

neg: Object-oriented design Object-oriented design Object-oriented design is the process of planning a system of interacting objects for the purpose of solving a software problem. It is one approach to software design. An object contains encapsulated data and procedures grouped together to represent an entity. The 'object interface' defines how the object can be interacted with. An object-oriented program is described by the interaction of these objects. Object-oriented design is the discipline of defining the objects and their interactions to solve a problem that was identified and documented during object-oriented analysis. What follows is a description of the class-based subset of object-oriented design,

neg: Distributed artificial intelligence tools. Two types of DAI has emerged: DAI can apply a bottom-up approach to AI, similar to the subsumption architecture as well as the traditional top-down approach of AI. In addition, DAI can also be a vehicle for emergence. Areas where DAI have been applied are: Notion of Agents: Agents can be described as distinct entities with standard boundaries and interfaces designed for problem solving. Notion of Multi-Agents:Multi-Agent system is defined as a network of agents which are loosely coupled working as a single entity like society for problem solving that an individual agent cannot solve. The key concept used

neg: Cutting stock problem needed. For the one-dimensional case, the new patterns are introduced by solving an auxiliary optimization problem called the knapsack problem, using dual variable information from the linear program. The knapsack problem has well-known methods to solve it, such as branch and bound and dynamic programming. The Delayed Column Generation method can be much more efficient than the original approach, particularly as the size of the problem grows. The column generation approach as applied to the cutting stock problem was pioneered by Gilmore and Gomory in a series of papers published in the 1960s. Gilmore and Gomory showed that this approach

neg: Problem solving is represented can make a vast difference in how difficult the problem is to be overcome. Whether a problem is represented visually, verbally, spatially, or mathematically, irrelevant information can have a profound effect on how long a problem takes to be solved; or if it's even possible. The Buddhist monk problem is a classic example of irrelevant information and how it can be represented in different ways: This problem is near impossible to solve because of how the information is represented. Because it is written out in a way that represents the information verbally, it causes us to try and

neg: Three-part lesson of a constructivist approach to mathematical instruction, provides an example of an inquiry-based question from which a three-part lesson could be created: "one bus has 47 students in it; another has 38. How many students are on both buses?" Students engage in solving math problems individually, in pairs, or in small groups, and "record the mathematical thinking they used to develop solutions". Students then plan the strategies, methods, and concrete materials they will use to solve the problem. The teacher will circulate and make observations about the ways students are interacting, and will note the mathematical language they are using

neg: Michele Weiner-Davis be saved. In 1996 Weiner-Davis released her third book, "Change Your Life and Everyone In It": "How to". It was written in order to expand upon the other more personal issues outside of relationships that she believed an effective (SFBT) approach might be able to solve or help with. The book used real life case examples of past experiences she had seen during therapy over the years in helping others to deal with personal problems caused by stress, depression and anxiety. The book was originally released in 1995 with the title "Fire Your Shrink!" before being renamed. She outlines techniques

neg: Problem solving related and 34 indirectly related). Yet of the people who had dreams that apparently solved the problem, only seven were actually able to consciously know the solution. The rest (46 out of 53) thought they did not know the solution. Mark Blechner conducted this experiment and obtained results similar to Dement's. He found that while trying to solve the problem, people had dreams in which the solution appeared to be obvious from the dream, but it was rare for the dreamers to realize how their dreams had solved the puzzle. Coaxing or hints did not get them to realize it,

neg: Situational theory of problem solving a more general concept of life "problems." A new variable, situational motivation in problem solving, was added to mediate the effects of predictive variables of communicative behavior. The extent to which an individual wants to know more about a problem. This concept mediates the effect of problem recognition, constraint recognition, and involvement recognition. Referent criterion would be independent of this variable because it is more cognitive than perceptual. When an individual tries to solve a problem, his or her communicative activeness increases in three domains of communication action: information acquisition, selection, and transmission. The communicative action that is relevant to

neg: Optical computing be to solve NP-complete problems as those are difficult problems for the conventional computers. There are 2 basic properties of light that are actually used in this approach: When solving a problem with time-delays the following steps must be followed: The first problem attacked in this way was the Hamiltonian path problem. Later, other problems have been tackled in this way. The simplest one is the subset sum problem. An optical device solving an instance with 4 numbers {a1, a2, a3, a4} is depicted below: The light will enter in Start node. It will be divided into 2 (sub)rays of

neg: Social problem-solving everyday life and ones assessment of their ability to solve said problems. The problem orientation may be positive and constructive to the problem solving process or negative and therefore dysfunctional in the process. Problem-solving proper is known as the second major process in social problem-solving. This process refers to the skills and techniques one uses to search for solutions and applying these skills to find the best solutions available. This model has been expanded by McFall and Liberman and colleagues. In these variations social problem-solving is considered to be a multi-step process including the adoption of a general orientation, defining

neg: Applied folklore Applied folklore Applied folklore is the branch of folkloristics concerned with the study and use of folklore and traditional cultural materials to address or solve real social problems. The term was coined in 1939 in a talk by folklorist Benjamin A. Botkin who, along with Alan Lomax, became the foremost proponent of this approach over the next thirty years. Applied folklore is similar in its rationale and approach to applied anthropology and other applied social sciences, and like these other applied approaches often distinguishes itself from "pure" research, that which has no explicit problem-solving aims. Botkin's development of the approach

neg: Lateral computing Lateral computing Lateral computing is a lateral thinking approach to solving computing problems. Lateral thinking has been made popular by Edward de Bono. This thinking technique is applied to generate creative ideas and solve problems. Similarly, by applying lateral-computing techniques to a problem, it can become much easier to arrive at a computationally inexpensive, easy to implement, efficient, innovative or unconventional solution. The traditional or conventional approach to solving computing problems is to either build mathematical models or have an IF- THEN -ELSE structure. For example, a brute-force search is used in many chess engines, but this approach is computationally

neg: Quantum algorithm for linear systems of equations advance was the demonstration of how to use HHL to solve for the radar cross-section of a complex shape. This was one of the first end to end examples of how to use HHL to solve a concrete problem exponentially faster than the best known classical algorithm. Dominic Berry proposed a new algorithm for solving linear time dependent differential equations as an extension of the quantum algorithm for solving linear systems of equations. Berry provides an efficient algorithm for solving the full-time evolution under sparse linear differential equations on a quantum computer. Wiebe et al. provide a new quantum algorithm

neg: Eight disciplines problem solving and are well known to many companies. Ford's 60 page manual covers details associated with each step in their 8D problem solving manual and the actions to take to deal with identified problems. The exact history of the 8D method remains disputed as many publications and websites state that it originates from the US military. Indeed, MIL-STD-1520C outlines a set of requirements for their contractors on how they should organize themselves with respect to non-conforming materials. Developed in 1974 and cancelled in February 1995 as part of the Perry memo, you can compare it best to the ISO 9001 standard

neg: Heuristic guesstimate, stereotyping, profiling, or common sense. Heuristics are the strategies derived from previous experiences with similar problems. These strategies rely on using readily accessible, though loosely applicable, information to control problem solving in human beings, machines, and abstract issues. The most fundamental heuristic is trial and error, which can be used in everything from matching nuts and bolts to finding the values of variables in algebra problems. Here are a few other commonly used heuristics, from George Pólya's 1945 book, "How to Solve It": In psychology, heuristics are simple, efficient rules, learned or hard-coded by evolutionary processes, that have been

neg: John Robert Anderson (psychologist) an increased fluency in retrieving declarative information, as students required less activity in these regions to solve the problems. In a 2012 study, Anderson and Fincham (a Carnegie Mellon University colleague) conducted a study that looked at the cognitive stages participants engaged in when solving mathematical problems. These stages included encoding, planning, solving, and response. The study determined how much time participants spent in each problem solving stage when presented with a mathematical problem. Multi-voxel pattern recognition techniques and Hidden Markov models were used to determine participants' problem solving stages. Results of the study showed that the time spent in

neg: Mathematics of Sudoku are also called "blocks" or "boxes". Horizontally adjacent "rows" are a "band", and vertically adjacent "columns" are a "stack". A "proper" puzzle has a unique solution. See Glossary of Sudoku for other terminology. Solving Sudokus from the viewpoint of a player has been explored in Denis Berthier's book "The Hidden Logic of Sudoku" (2007) which considers strategies such as "hidden xy-chains". The general problem of solving Sudoku puzzles on "n"×"n" grids of "n"×"n" blocks is known to be NP-complete. For "n"=3 (classical Sudoku), however, this result is of little relevance: algorithms such as Dancing Links can solve puzzles in fractions

neg: Similarity heuristic approach that will likely reveal the problem’s source. Problem solving in general is benefited by the similarity heuristic. When new problems arise similar to previous problems, the similarity heuristic selects an approach that previously yielded favorable results. Even if the current problem is novel, any similarity to previous issues will help choose a proper course of action. Similarity heuristic The similarity heuristic is a psychological heuristic pertaining to how people make judgments based on similarity. More specifically, the similarity heuristic is used to account for how people make judgments based on the similarity between current situations and other situations or

neg: List ranking List ranking In parallel algorithms, the list ranking problem involves determining the position, or rank, of each item in a linked list. That is, the first item in the list should be assigned the number 1, the second item in the list should be assigned the number 2, etc. Although it is straightforward to solve this problem efficiently on a sequential computer, by traversing the list in order, it is more complicated to solve in parallel. As wrote, the problem was viewed as important in the parallel algorithms community both for its many applications and because solving it led to

neg: Arousal of low pressure stimulations. Problem solving is the cognitive process that someone uses to achieve a goal whenever a solution cannot be determined by others. For example, you are with your buddies on a trip and get a flat tire. Everyone looks around nervously because nobody knows how to change a flat. But then you remember that you took an automotive class in college where you learned to change flat tires. You change the tire and solve the issue with your cognitive problem solving. Cognitively, the utilization of logical analysis and problem solving has been associated with higher levels of

neg: Einstellung effect Einstellung effect Einstellung is the development of a mechanized state of mind. Often called a problem solving set, Einstellung refers to a person's predisposition to solve a given problem in a specific manner even though better or more appropriate methods of solving the problem exist. The Einstellung effect is the negative effect of previous experience when solving new problems. The Einstellung effect has been tested experimentally in many different contexts. The most famous example (which led to Luchins and Luchins' coining of the term) is the Luchins' water jar experiment, in which subjects were asked to solve a series of

neg: Action research on the job and, if successful and reinforcing, become a part of the system's repertoire of problem-solving behavior. Action research is problem centered, client centered, and action oriented. It involves the client system in a diagnostic, active-learning, problem-finding and problem-solving process. Action research Action research is either research initiated to solve an immediate problem or a reflective process of progressive problem solving led by individuals working with others in teams or as part of a "community of practice" to improve the way they address issues and solve problems. There are two types of action research: participatory and practical. Denscombe (2010,

neg: Equation solving used to find a numerical solution to an equation, which, for some applications, can be entirely sufficient to solve some problem. Equations involving matrices and vectors of real numbers can often be solved by using methods from linear algebra. There is a vast body of methods for solving various kinds of differential equations, both numerically and analytically. A particular class of problem that can be considered to belong here is integration, and the analytic methods for solving this kind of problems are now called symbolic integration. Equation solving In mathematics, to solve an equation is to find its solutions, which

neg: George Humphrey (psychologist) that the context in which a stimulus is presented majorly affects how the subject learns to respond, which he discussed in his second book, "The Nature of Learning" (1933). This book is considered by Queen's University to be his most important work. It brought attention to the concept of living organisms being "systems" that are regulated by homeostasis, physiologically and psychologically. In 1951, he wrote "Thinking: An Introduction to Its Experimental Psychology", which had considerable success as it provided a written description of all research done on mental problem solving in humans conducted by Otto Selz, the Würzburg School, and

neg: Solver universal problem solver, that theoretically can be used to solve every possible problem that can be formalized in a symbolic system, given the right input configuration. It was the first computer program which separated its knowledge of problems (in the form of domain rules) from its strategy of how to solve problems (as a general search engine). General solvers typically use an architecture similar to the GPS to decouple a problem's definition from the strategy used to solve it. The advantage in this decoupling is that the solver doesn't depend on the details of any particular problem instance. The strategy

neg: Neuroepistemology Neuroepistemology Neuroepistemology is an empirical approach to epistemology—the study of knowledge in a general, philosophical sense—which is informed by modern neuroscience, especially the study of the structure and operation of the brain involving neural networks and neuronal epistemology. Philosopher Patricia Churchland has written about the topic and, in her book "Brain-Wise", characterised the problem as "how meat knows". Georg Northoff, in his "Philosophy of the Brain", wrote that it "focuses on direct linkage between the brain on one hand and epistemic abilities and inabilities on the other." Menachem Mazabow wrote that it "is necessary... to state the set of assumptions

neg: David Singmaster was a pioneer of the general Layer by Layer approach for solving the Cube. If you managed to solve the Cube using his method then Singmaster suggested that you should: The book also contained a catalogue of pretty patterns including his "cube in a cube in a cube" pattern which he had discovered himself "and was very pleased with". In 1981, at the height of the Rubik's Cube craze, the book was republished by Penguin Books, with a US edition by Enslow Publishers. There were also Dutch and Spanish translations. He estimates that he sold around 50 to 60 000

neg: Formative assessment education, it is important for teachers to see how their students approach the problems and how much mathematical knowledge and at what level students use when solving the problems. That is, knowing how students think in the process of learning or problem solving makes it possible for teachers to help their students overcome conceptual difficulties and, in turn, improve learning. In that sense, formative assessment is diagnostic. To employ formative assessment in the classrooms, a teacher has to make sure that each student participates in the learning process by expressing their ideas; there is a trustful environment in which students

neg: Transposition-driven scheduling fetches a new job from the queue. What makes the big difference between traditional transposition based problem solving and TDS is that asking some computer if it has solved a problem follows a request-response approach, in which the computer asking the other computer has to wait for a response. In TDS, forwarding a job to another computer does not involve any waiting, because you know (by design) that the other computer will accept the job and try to solve it. This means that latency (the main cause of delays in request-response models) is not an issue, because a computer simply

neg: Attribute hierarchy method by the teacher to focus instructional efforts in areas where the student is requiring additional assistance. Assessment results can also provide feedback to the teacher on the effectiveness of instruction for promoting the learning objectives. The AHM is a promising method for cognitive diagnostic assessment. Using a principled test design approach, integrating cognition into test development, can promote stronger inferences about how students actually think and solve problems. With this knowledge, students can be provided with additional information that can guide their learning, leading to improved performance on future educational assessments and problem solving tasks. Leighton, J. P., & Gierl,

neg: Nicolas Hammond Today, as well as appearing on "The Adventure Game" with Graeme Garden, Carol Chell and Lesley Judd on 2 November 1981. In December 2006, almost 25 years after his first appearance on TV, Hammond appeared on "Swap Shop" and solved the Rubik's Cube in 36 seconds. Hammond wrote the book "How To Solve The Cube in 37 Seconds", published by DRG Blackhall in 1981. The book describes the various techniques that Hammond uses to solve the cube. It is based on the bottom, middle, upper layer approach and includes tables to help improve speed. The book also includes a simple,

neg: Insight phenomenology Insight phenomenology Insight is a sudden understanding of a problem or a strategy that aids in solving a problem. Usually, this involves conceptualizing the problem in a completely new way. Although insights may appear to be sudden, they are actually the result of prior thought and effort. While insight can be involved in solving well-structured problems, it is more often associated with ill-structured problems. When people solve, or attempt to solve an insight puzzle, they experience a common phenomenology, that is, a set of behavioural properties that accompany problem-solving activity (for a useful edited review of insight problems and their

neg: Sam Glucksberg in his model. A famous experiment that involves comprehension is the candle problem, which has to deal with problem solving. The candle problem is a test by Karl Duncker that measures the functional fixedness problem in problem solving. Participants are asked to construct a device holding a candle on the wall. The tools are a book of matches and a box of tacks. Many participants found other ways to hold the candle on the wall like tacking it directly to the wall. Glucksberg was interested to see how labeling influenced the candle problem. He developed three scenarios for participants: all

neg: Constraint (computational chemistry) which are functions of the generalized coordinates q. If "M" constraints are present, the coordinates must also satisfy "M" time-independent algebraic equations where the index "j" runs from 1 to "M". For brevity, these functions "g" are grouped into an "M"-dimensional vector g below. The task is to solve the combined set of differential-algebraic (DAE) equations, instead of just the ordinary differential equations (ODE) of Newton's second law. This problem was studied in detail by Joseph Louis Lagrange, who laid out most of the methods for solving it. The simplest approach is to define new generalized coordinates that are unconstrained;

neg: Optimal control Rudolf Kalman. Optimal control problems are generally nonlinear and therefore, generally do not have analytic solutions (e.g., like the linear-quadratic optimal control problem). As a result, it is necessary to employ numerical methods to solve optimal control problems. In the early years of optimal control ( 1950s to 1980s) the favored approach for solving optimal control problems was that of "indirect methods". In an indirect method, the calculus of variations is employed to obtain the first-order optimality conditions. These conditions result in a two-point (or, in the case of a complex problem, a multi-point) boundary-value problem. This boundary-value problem actually

neg: Trial and error which was later refined and extended by B.F. Skinner's operant conditioning. Trial and error is also a heuristic method of problem solving, repair, tuning, or obtaining knowledge. In the field of computer science, the method is called generate and test. In elementary algebra, when solving equations, it is "guess and check". This approach can be seen as one of the two basic approaches to problem solving, contrasted with an approach using insight and theory. However, there are intermediate methods which for example, use theory to guide the method, an approach known as "guided empiricism". This approach is far more far

neg: Computational complexity theory the notion of decision problems. However, this is not really the case, since function problems can be recast as decision problems. For example, the multiplication of two integers can be expressed as the set of triples ("a", "b", "c") such that the relation "a" × "b" = "c" holds. Deciding whether a given triple is a member of this set corresponds to solving the problem of multiplying two numbers. To measure the difficulty of solving a computational problem, one may wish to see how much time the best algorithm requires to solve the problem. However, the running time may, in

neg: Tree alignment n leaf nodes. The sequence, which is assigned to the internal node, is called core sequence. When we use combinatorial optimization strategy to transform the multiple sequence alignment into pair sequence alignment, the main problem is changed from “How to improve the efficiency of multiple sequence alignment” to “How to improve the efficiency of pairwise sequence alignment.” The Keyword Tree Theory and Aho-Corasick search algorithm is an efficient approach to solve the pairwise sequence alignment problem. The aim of combining the keyword tree theory and Aho-Corasick search algorithm is to solve this kind of problem: for a given long string

neg: Gifted pull-out in any significant academic progress because they are not tied directly to the core curriculum. Winebrenner (2001) recommends those same ineffective practices, including creative problem solving, chess, logic puzzles, and academic competitions. Oddly, Winebrenner also recommends that students selected for pull-out should be those who are capable in the areas the pull-out will address. This is exactly the opposite of the approach recommended by most gifted literature, which argues for matching the instruction "to the student," not vice versa. Jan and Bob Davidson of the Davidson Institute for Talent Development criticize pull-outs in their book, "Genius Denied: How to Stop

neg: Horizontal and vertical décalage décalage. A further criticism is that restructuring the presentation of a problem has a significant bearing on the child's ability to solve the problem, which demonstrates that problem solving ability might depend on the presentation of the problem more so than on the child's cognitive development. According to Wordsworth and other Piagetian supporters, however, Piaget's main idea that all children have the same general course of development is so significant that it outweighs the criticisms of his methodology in which so many others find fault. Horizontal and vertical décalage Horizontal and vertical décalage are terms coined by developmental psychologist Jean

neg: Conflict-driven clause learning checking, and cryptography. Related algorithms to CDCL are the DP and DPLL algorithm described before. The DP algorithm uses resolution refutation and it has potential memory access problem. Whereas the DPLL algorithm is OK for randomly generated instances, it is bad for instances generated in practical applications. CDCL is a more powerful approach to solve such problems in that applying CDCL provides less state space search in comparison to DPLL. Conflict-driven clause learning In computer science, conflict-driven clause learning (CDCL) is an algorithm for solving the Boolean satisfiability problem (SAT). Given a Boolean formula, the SAT problem asks for an

neg: Eureka effect immediately. In fact equal recall rates were obtained for both "easy" and "hard" sentences which were initially noncomprehensible. It seems to be this noncomprehension to comprehension which results in better recall. The essence of the aha feeling underling insight problem solving was systemically empirically investigated by Danek et al. and Shen and his colleagues. Currently there are two theories for how people arrive at the solution for insight problems. The first is the progress monitoring theory. The person will analyze the distance from their current state to the goal state. Once a person realizes that they cannot solve the problem

neg: Steve Blank Steps to the Epiphany: Successful Strategies for Products that Win", (K&S Ranch Press) which details his approach to the Customer Development process. In the book, Blank outlines his views about how entrepreneurship is a practice that can be actively managed rather than an art which must be passively experienced. The book is viewed in entrepreneurship circles as the definitive source on the Customer Development methodology. Blank released a second book in 2010, "Not All Those Who Wander Are Lost" which relates stories from his life as an entrepreneur. The collection of material develops a narrative about how to live life

neg: Peter Westergaard's tonal theory unlikely to change in the near future. Consequently, our best strategy is to address the psychological questions directly, more or less at the level of introspection ("ITT", pp. 3–7). Such an approach, however, immediately raises the problem of developing a metalanguage for discussing tonal music: how do we accurately describe "what we hear"? Reasoning that the process of solving this problem will itself lead inevitably to substantive insights into how music is actually heard, Westergaard takes the construction of a metalanguage for tonal music as his task for the main part of the book ("ITT", pp. 7–9). Music is conceived

neg: Insight when solving insight versus non-insight problems that happens right before the solving of the problem. This conclusion has been supported also by eye tracking data which shows an increased eye blink duration and frequency when people solve problems via Insight. This latter result, paired with an eye pattern oriented to look away from sources of visual inputs ( such as looking at blank wall, or out the window at the sky )proves different attention involvement in Insight problem solving vs problem solving via analysis. It was found that groups typically perform better on insight problems (in the form of rebus

neg: Morphological analysis (problem-solving) Morphological analysis (problem-solving) Morphological analysis or general morphological analysis is a method developed by Fritz Zwicky (1967, 1969) for exploring all the possible solutions to a multi-dimensional, non-quantified complex problem. General morphology was developed by Fritz Zwicky, the Bulgarian-born, Swiss-national astrophysicist based at the California Institute of Technology. Among others, Zwicky applied morphological analysis (MA) to astronomical studies and the development of jet and rocket propulsion systems. As a problem-structuring and problem-solving technique, MA was designed for multi-dimensional, non-quantifiable problems where causal modeling and simulation do not function well, or at all. Zwicky developed this approach to address seemingly non-reducible

neg: Lean manufacturing core management principles are articulated around the twin pillars of Continuous Improvement (relentless elimination of waste) and Respect for People (engagement in long term relationships based on continuous improvement and mutual trust). This formalization stems from problem solving. As Toyota expanded beyond its home base for the past 20 years, it hit the same problems in getting TPS properly applied that other western companies have had in copying TPS. Like any other problem, it has been working on trying a series of countermeasures to solve this particular concern. These countermeasures have focused on culture: how people behave, which is the

neg: Edward Burger days as a stand-up comic at the Laff Stop Comedy Club in Austin in the late-1980s. Burger states that "mathematics is basically an approach to solving difficult problems. The techniques and strategies that we can learn in mathematics are techniques and strategies we can use to solve any difficult problem." In the textbook he co-authored with Michael Starbird, "The Heart of Mathematics", they offer their favorite top ten mathematical ways of thinking: Recently, Burger and Starbird expanded their scope beyond mathematics while distilling their "top ten" list down to just five in their book, "The 5 Elements of Effective Thinking"

neg: Math wars and curricula, which differ significantly in approach and content. The largest supporter of reform in the US has been the National Council of Teachers of Mathematics. One aspect of the debate is over how explicitly children must be taught skills based on formulas or algorithms (fixed, step-by-step procedures for solving math problems) versus a more inquiry-based approach in which students are exposed to real-world problems that help them develop fluency in number sense, reasoning, and problem-solving skills. In this latter approach, conceptual understanding is a primary goal and algorithmic fluency is expected to follow secondarily. Some parents and other stakeholders

neg: Seymour Sarason on projective techniques during his first few years at Yale. Although Sarason is not well-known for his work on projective techniques, he appreciated this work because it gave him insight into how human problem solving adapts based on the specific task at hand. Based largely on his experiences at the Southbury Training School, Sarason published his first book in 1949: Psychological Problems in Mental Deficiency. This book provided a new approach to intellectual disabilities that emphasized social and cultural factors that affect our understanding of intellectual disability. This book became popular in schools of education, and Sarason became well-known in

neg: Free Solo on camera with how to film and not affect Honnold’s climb. According to Elizabeth Chai Vasarhelyi, the key to solving this problem was in the extended preparation. One of the hardest problems was getting sound from Honnold, who often was too far from the camera to use wireless mics. Meanwhile, the wiring of the mic couldn’t interfere with his climbing, and any recorder on his body would need to withstand the rigors of climbing. To solve the problem, they turned to production sound recordist Jim Hurst, who was a climber himself. He utilized a recorder that could transmit a signal

neg: Sharon Presley laws regarding prostitution. She also says that the customers of prostitutes should not be prosecuted. In this regard, Presley differs from feminists who wish to restrict prostitution. She says that, despite the general agreement among feminists that violent pornography is degrading to women, that there should be no government laws limiting such pornography, which she describes as a symptom of a societal problem. Instead, she suggests that the problem's cause should be identified and treated with education. She disagrees with Susan Brownmiller that anti-obscenity laws would solve the problem. Presley's self-help book, "Standing Up to Experts and Authorities: How to

neg: Dynamic programming he discounts future utility by a factor each period, where formula_32 be capital in period . Assume initial capital is a given amount formula_33, and suppose that this period's capital and consumption determine next period's capital as formula_34, where is a positive constant and formula_35 subject to formula_36 for all formula_37 Written this way, the problem looks complicated, because it involves solving for all the choice variables formula_38. (Note that formula_39 is not a choice variable—the consumer's initial capital is taken as given.) The dynamic programming approach to solve this problem involves breaking it apart into a sequence of smaller

neg: Jumpstart Academy Africa Academy’s program nurtures critical thinking, principled leadership, and an entrepreneurial method of problem-solving along with civic engagement. The approach can help many youth between 14 and 18 years of age to turn out as esteemed contributors in the job market. Jumpstart Academy Africa Jumpstart Academy Africa is a for impact social venture which utilizes entrepreneurial leadership and mentoring to solve Africa’ human capital problem which starts at the secondary school level. The founding mission of the Academy is to create a wave of entrepreneurial leaders by pioneering a world class Leadership and Entrepreneurship curriculum. The Academy was launched in Cameroon

neg: Ars Magna (Gerolamo Cardano) him the formula for solving a type of cubic equations and that the same formula had been discovered by Scipione del Ferro. He also acknowledges that it was Ferrari who found a way of solving quartic equations. Since at the time negative numbers were not generally acknowledged, knowing how to solve cubics of the form "x" + "ax" = "b" did not mean knowing how to solve cubics of the form "x" = "ax" + "b" (with "a","b" > 0), for instance. Besides, Cardano, also explains how to reduce equations of the form "x" + "ax" + "bx" + "c"

neg: Going to School send in their problems to be solved. Every episode would be structured around solving a problem in a community somewhere in India. Parents, families, send in the problem to be solved by postcard, tweet, letter. Kid reporters in a newsroom made of junk (and once-loved things) present the problem and interview famous people to get insight into how to solve it. Then, getting to the bottom of the problem, kids go out of the newsroom and into the streets to find out ‘why the problem exists’ interviewing everyone they meet. The show format has segments to interview anyone and everyone

neg: Problem solving working out the consequences of the hypothesis." There also are empirical studies of how people can think consciously about a problem before going to sleep, and then solve the problem with a dream image. Dream researcher William C. Dement told his undergraduate class of 500 students that he wanted them to think about an infinite series, whose first elements were OTTFF, to see if they could deduce the principle behind it and to say what the next elements of the series would be. He asked them to think about this problem every night for 15 minutes before going to sleep

neg: Problem solving Secondly, functional fixedness often causes solvers to make more attempts to solve a problem than they would have made if they were not experiencing this cognitive barrier. In the worst case, functional fixedness can completely prevent a person from realizing a solution to a problem. Functional fixedness is a commonplace occurrence, which affects the lives of many people. Unnecessary constraints are another very common barrier that people face while attempting to problem-solve. This particular phenomenon occurs when the subject, trying to solve the problem subconsciously, places boundaries on the task at hand, which in turn forces him or her to

neg: Reduction (complexity) Reduction (complexity) In computability theory and computational complexity theory, a reduction is an algorithm for transforming one problem into another problem. A reduction from one problem to another may be used to show that the second problem is at least as difficult as the first. Intuitively, problem A is reducible to problem B if an algorithm for solving problem B efficiently (if it existed) could also be used as a subroutine to solve problem A efficiently. When this is true, solving A cannot be harder than solving B. "Harder" means having a higher estimate of the required computational resources in

neg: Problem solving as narrow minded thinking, which is defined as a way in which one is not able to see or accept certain ideas in a particular context. Functional fixedness is very closely related to this as previously mentioned. This can be done intentionally and or unintentionally, but for the most part it seems as if this process to problem solving is done in an unintentional way. Functional fixedness can affect problem solvers in at least two particular ways. The first is with regards to time, as functional fixedness causes people to use more time than necessary to solve any given problem.

neg: Routing and wavelength assignment need to consider signal quality. Many of the optical impairments are nonlinear, so a standard shortest path algorithm can't be used to solve them optimally even if we know the exact state of the network. This is usually not a safe assumption, so solutions need to be efficient using only limited network information. Given the complexity of RWA, there are two general methodologies for solving the problem: Fixed path routing is the simplest approach to finding a lightpath. The same fixed route for a given source and destination pair is always used. Typically this path is computed ahead of time

neg: Problem-oriented development studying the cognitive structures that domain experts develop of problems, as well as for better understanding human approaches to problem solving. The Domain Theory is one example of the influence of cognitive science in Problem-Oriented Development research. Problem-oriented development Problem-Oriented Development is an emerging paradigm of computing that emphasises problems (as opposed to requirements) as the primary subject of scrutiny by software engineers. As such, Problem-Oriented Development is concerned with: Knowledge Engineering is a field of computer science which offers a significant body of work on problem-solving methods. Problem-solving methods are patterns of reasoning that are applied to solve specific

neg: Pragmatic theory of truth I want to know how to return home safely, the true answer will be whatever is useful to solving that problem. Later on, when faced with a different problem, what I came to believe with the earlier problem may now be false. As my problems change, and as the most useful way to solve a problem shifts, so does the property of truth. C.S. Peirce considered the idea that beliefs are true at one time but false at another (or true for one person but false for another) to be one of the "seeds of death" by which James allowed

neg: Constraint satisfaction in particular a form of backtracking or local search. Constraint propagation are other methods used on such problems; most of them are incomplete in general, that is, they may solve the problem or prove it unsatisfiable, but not always. Constraint propagation methods are also used in conjunction with search to make a given problem simpler to solve. Other considered kinds of constraints are on real or rational numbers; solving problems on these constraints is done via variable elimination or the simplex algorithm. Constraint satisfaction originated in the field of artificial intelligence in the 1970s (see for example ). During the

neg: Genghis Robot and Space Museum. Genghis Robot The Genghis robot was a six legged, insect-like, robot that was created by roboticist Rodney Brooks at MIT. Brooks wanted to solve the problem of how to make robots intelligent and suggested that it is possible to create robots that displayed intelligence by using a "subsumption architecture" which is a type of reactive robotic architecture where a robot can react to the world around them. His paper ""Intelligence Without Representation"", which is still widely respected in the fields of robotics and Artificial Intelligence, further outlines his theories on this. The design of the Genghis robot

neg: Genghis Robot Genghis Robot The Genghis robot was a six legged, insect-like, robot that was created by roboticist Rodney Brooks at MIT. Brooks wanted to solve the problem of how to make robots intelligent and suggested that it is possible to create robots that displayed intelligence by using a "subsumption architecture" which is a type of reactive robotic architecture where a robot can react to the world around them. His paper ""Intelligence Without Representation"", which is still widely respected in the fields of robotics and Artificial Intelligence, further outlines his theories on this. The design of the Genghis robot was inspired by

neg: Center for Court Innovation working in problem-solving courts. In recent years, the Center has also helped organize trainings for judges in general court calendars to educate them about problem-solving principles. In 2005, for instance, the Center helped convene two dozen upstate judges for a day-long training exploring how approaches used in problem-solving courts might be adaptable to general calendars. The training was the first of its kind in the country. The Center works closely with technologists at the New York State Court System's Office of Court Administration in an effort to promote the use of innovative technology and support the expansion of problem-solving justice.

neg: Marian Small problems. "There is a strongly held belief in the mathematics education community", wrote Small, "that mathematics is best learned when students are actively engaged in constructing their own understandings. This is only likely to happen in classrooms that emphasize rich problem solving and the exchange of many approaches to mathematical situations, and that give attention to and value students’ mathematical reasoning". To demonstrate this approach, Small provides an example of students learning to add 47 and 38. A traditional approach to math instruction would show students how to add these two numbers by "grouping the ones, trading, and then grouping

neg: Educational psychology did research on college students and their problem solving processes. He found that they differ in understanding the basis of the problem and the ideas in the problem. He also found that students differ in process of problem solving in their approach and attitude toward the problem. Nathaniel Gage (1917 -2008) is an important figure in educational psychology as his research focused on improving teaching and understanding the processes involved in teaching. He edited the book "Handbook of Research on Teaching" (1963), which helped develop early research in teaching and educational psychology. Gage founded the Stanford Center for Research and

neg: Topology optimization thus a key part of design for additive manufacturing. A topology optimization problem can be written in the general form of an optimization problem as: The problem statement includes the following: Evaluating formula_7 often includes solving a differential equation. This is most commonly done using the finite element method since these equations do not have a known analytical solution. There are various implementation methodologies that have been used to solve TO problems. Solving TO problems in a discrete sense is done by discretizing the design domain into finite elements. The material densities inside these elements are then treated as the

neg: How to Be a Conservative How to Be a Conservative How to Be a Conservative is a 2014 book by the English philosopher Roger Scruton, in which the author outlines the conservative ideology, its opposition to materialism, and argues how it can be applied to crucial contemporary issues. Jesse Norman wrote in "The Spectator": "There are occasional missteps and the odd mini-rant, but the book is highly engaging, and studded with insights into topics as diverse as international treaties, alienation and the nature of laughter." In "Standpoint", David Willetts wrote that the book "communicates a distinctive conservative disposition with great charm and formidable learning." Willetts

neg: Learning through play “Through make-believe games children can be anyone they wish and go anywhere they want. When they engage in sociodramatic play, they learn how to cope with feelings, how to bring the large, confusing world into a small, manageable size; and how to become socially adept as they share, take turns and cooperate with each other. When children play, they are learning new words, how to problem solve, and how to be flexible”. As children learn through purposeful, quality play experience, they build critical basic skills for cognitive development and academic achievement. These include verbalization, language comprehension, vocabulary, imagination, questioning, problem-solving,

neg: Problem-based learning mentoring provided to the students. Appropriate scaffolding should be done by the mentors to ensure that students are successful in attaining their project goals to solve the problem. Communication between the team should also be open and constructive in nature for achieving the necessary milestones. Problem-based learning Problem-based learning (PBL) is a student-centered pedagogy in which students learn about a subject through the experience of solving an open-ended problem found in trigger material. The PBL process does not focus on problem solving with a defined solution, but it allows for the development of other desirable skills and attributes. This includes

neg: Artificial intelligence, situated approach community has presented several solutions to modeling decision-making processes, also known as action selection mechanisms. The first attempt to solve this problem goes back to "subsumption architectures", which were in fact more an implementation technique than an algorithm. However, this attempt paved the way to several others, in particular the "free-flow hierarchies" and "activation networks". A comparison of the structure and performances of these two mechanisms demonstrated the advantage of using "free-flow hierarchies" in solving the action selection problem. However, "motor schemas" and "process description languages" are two other approaches that have been used with success for autonomous robots. Artificial

neg: Computational complexity theory general, depend on the instance. In particular, larger instances will require more time to solve. Thus the time required to solve a problem (or the space required, or any measure of complexity) is calculated as a function of the size of the instance. This is usually taken to be the size of the input in bits. Complexity theory is interested in how algorithms scale with an increase in the input size. For instance, in the problem of finding whether a graph is connected, how much more time does it take to solve a problem for a graph with 2"n" vertices