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  2. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    In the 19th century, mathematicians such as Karl Weierstrass and Richard Dedekind increasingly focused their research on internal problems, that is, pure mathematics. [111] [115] This led to split mathematics into pure mathematics and applied mathematics, the latter being often considered as having a lower value among mathematical purists ...

  3. Mathematics and Plausible Reasoning - Wikipedia

    en.wikipedia.org/wiki/Mathematics_and_plausible...

    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."

  4. Adaptive reasoning - Wikipedia

    en.wikipedia.org/wiki/Adaptive_reasoning

    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]

  5. How to Solve It - Wikipedia

    en.wikipedia.org/wiki/How_to_Solve_It

    How to Solve It suggests the following steps when solving a mathematical problem: . First, you have to understand the problem. [2]After understanding, make a plan. [3]Carry out the plan.

  6. Interactive Mathematics Program - Wikipedia

    en.wikipedia.org/wiki/Interactive_Mathematics...

    Kramer reported that grade 12 IMP students in his study performed better on all areas of mathematics tested by the NAEP test, [13] and Webb and Dowling reported IMP students performed significantly better on statistics questions from the Second International Mathematics Study, on mathematical reasoning and problem solving tasks designed by the ...

  7. Problem solving - Wikipedia

    en.wikipedia.org/wiki/Problem_solving

    Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to turn on an appliance) to complex issues in business and technical fields.

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