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Problem-solving consists of using generic or ad hoc methods, in an orderly manner, for finding solutions to problems. Some of the problem-solving techniques developed and used in artificial intelligence, computer science, engineering, mathematics, medicine, etc. are related to mental problem-solving techniques studied in psychology.
Theoretical computer science
In theoretical computer science, a computational problem is a mathematical object representing a collection of questions that computers might want to solve. For example, the problem of factoring
is a computational problem. Computational problems are one of the main objects of study in theoretical computer science. The field of algorithms studies methods of solving computational problems efficiently. The complementary field of computational complexity attempts to explain why certain computational problems are intractable for computers.
Theoretical computer science is a division or subset of general computer science and mathematics which focuses on more abstract or mathematical aspects of computing and includes the theory of computation.
It is not easy to circumscribe the theory areas precisely and the ACM's Special Interest Group on Algorithms and Computation Theory (SIGACT) describes its mission as the promotion of theoretical computer science and notes:
In contemporary education, mathematics education is the practice of teaching and learning mathematics, along with the associated scholarly research.
Researchers in mathematics education are primarily concerned with the tools, methods and approaches that facilitate practice or the study of practice, however mathematics education research, known on the continent of Europe as the didactics or pedagogy of mathematics, has developed into an extensive field of study, with its own concepts, theories, methods, national and international organisations, conferences and literature. This article describes some of the history, influences and recent controversies.
Additive Schwarz method
In computability theory and computational complexity theory, a decision problem is a question in some formal system with a yes-or-no answer, depending on the values of some input parameters. For example, the problem "given two numbers x and y, does x evenly divide y?" is a decision problem. The answer can be either 'yes' or 'no', and depends upon the values of x and y.
Decision problems typically appear in mathematical questions of decidability, that is, the question of the existence of an effective method to determine the existence of some object or its membership in a set; some of the most important problems in mathematics are undecidable.
In mathematics, the additive Schwarz method, named after Hermann Schwarz, solves a boundary value problem for a partial differential equation approximately by splitting it into boundary value problems on smaller domains and adding the results.
Educational psychology is the study of human learning. This involves studying instructional processes within the classroom setting. The study of learning processes, both cognitive and affective, allows researchers to the understand individual differences in behavior, personality, intellect, and self- concept. The field of educational psychology heavily relies on testing, measurement, assessment, evaluation, and training to enhance educational activities and learning processes.
Educational psychology can in part be understood through its relationship with other disciplines. It is informed primarily by psychology, bearing a relationship to that discipline analogous to the relationship between medicine and biology. It is also informed by neuroscience. Educational psychology in turn informs a wide range of specialities within educational studies, including instructional design, educational technology, curriculum development, organizational learning, special education and classroom management. Educational psychology both draws from and contributes to cognitive science and the learning sciences. In universities, departments of educational psychology are usually housed within faculties of education, possibly accounting for the lack of representation of educational psychology content in introductory psychology textbooks.
Neuropsychological assessment was traditionally carried out to assess the extent of impairment to a particular skill and to attempt to determine the area of the brain which may have been damaged following brain injury or neurological illness. With the advent of neuroimaging techniques, location of space-occupying lesions can now be more accurately determined through this method, so the focus has now moved on to the assessment of cognition and behaviour, including examining the effects of any brain injury or neuropathological process that a person may have experienced.
A core part of neuropsychological assessment is the administration of neuropsychological tests for the formal assessment of cognitive function, though neuropsychological testing is more than the administration and scoring of tests and screening tools. It is essential that neuropsychological assessment also include an evaluation of the person's mental status. This is especially true in assessment of Alzheimer's disease and other forms of dementia. Aspects of cognitive functioning that are assessed typically include orientation, new-learning/memory, intelligence, language, visuoperception, and executive function. However, clinical neuropsychological assessment is more than this and also focuses on a person's psychological, personal, interpersonal and wider contextual circumstances.