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A mathematical problem is a problem that can be represented, analyzed, and possibly solved, with the methods of mathematics.This can be a real-world problem, such as computing the orbits of the planets in the solar system, or a problem of a more abstract nature, such as Hilbert's problems.
The use of multiple representations supports and requires tasks that involve decision-making and other problem-solving skills. [2] [3] [4] The choice of which representation to use, the task of making representations given other representations, and the understanding of how changes in one representation affect others are examples of such mathematically sophisticated activities.
In this system, pieces of bread serve as a metaphor for narrative elements (i.e. the start, continuation, or end of an account) and filling of the sandwich serves as a metaphor for a problem that students are asked to solve. A decision-forcing case in which one protagonist is faced with two problems is thus a "triple-decker case."
One such component is the emotional valence of "real-world" problems, which can either impede or aid problem-solving performance. Researchers have focused on the role of emotions in problem solving, [ 11 ] demonstrating that poor emotional control can disrupt focus on the target task, impede problem resolution, and lead to negative outcomes ...
These studies have shown that active problem solving early in the learning process is a less effective instructional strategy than studying worked examples (Sweller and Cooper, 1985; Cooper and Sweller, 1987). Certainly active problem solving is useful as learners become more competent, and better able to deal with their working memory limitations.
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 ...
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