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Adaptive reasoning also includes reasoning based on pattern, analogy or metaphor." [1] "Capacity for logical thought, reflection, explanation and justification." [2] "The ability of an agent to intelligently adapt its behavior, both short-term and long-term in response to the changing needs of its problem-solving situation" [3]
The skill at choosing an appropriate strategy is best learned by solving many problems. You will find choosing a strategy increasingly easy. A partial list of strategies is included: Guess and check [9] Make an orderly list [10] Eliminate possibilities [11] Use symmetry [12] Consider special cases [13] Use direct reasoning; Solve an equation ...
Mathematics and Plausible Reasoning is a two-volume book by the mathematician George Pólya describing various methods for being a good guesser of new mathematical results. [ 1 ] [ 2 ] In the Preface to Volume 1 of the book Pólya exhorts all interested students of mathematics thus: "Certainly, let us learn proving, but also let us learn guessing."
Problem-based learning (PBL) is a teaching method 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.
Lateral thinking is a manner of solving problems using an indirect and creative approach via reasoning that is not immediately obvious. Synonymous to thinking outside the box , it involves ideas that may not be obtainable using only traditional step-by-step logic . [ 1 ]
The Clay Institute has pledged a US $1 million prize for the first correct solution to each problem. The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP ...
The incorrect additive strategy can be expressed as T – S = 2; this is a constant difference relation. Here is the graph for these two equations. For the numeric values involved in the problem statement, these graphs are "similar" and it is easy to see why individuals consider their incorrect answers perfectly reasonable.
A bar model used to solve an addition problem. This pictorial approach is typically used as a problem-solving tool in Singapore math. Singapore math teaches students mathematical concepts in a three-step learning process: concrete, pictorial, and abstract. [3] This learning process was based on the work of an American psychologist, Jerome Bruner.