Mathematical Word Problem

A Mathematical Word Problem is a mathematical problem that is a word problem (presented as natural language text).

• Context:
  • It can (typically) be a part of a Mathematics Education Curriculum.
  • It can (typically) involve applying Mathematical Concepts to solve a real-world scenario described in text.
  • It can (typically) require the conversion of Natural Language Text into a Mathematical Expression or Equation for solution.
  • It can (often) be included in Educational Textbooks and Mathematics Teaching Materials.
  • It can be used as a Test Item in Mathematical Assessments.
  • It can involve real-world contexts and scenarios to illustrate mathematical concepts.
  • It can range from being a Simple Math Word Problem to being a Complex Math Word Problem, depending on the complexity of the mathematical concepts and mathematical operations involved.
  • It can be a subject of study in the fields of Natural Language Processing and AI in Education.
  • It can be used to evaluate Mathematical Reasoning abilities.
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• Example(s):
  • an Arithmetic Word Problem, such as: "A bookstore has 450 books. If 60% of the books are fiction, how many fiction books are there in the bookstore?".
  • a Geometry Word Problem, such as: "Calculate the area of a rectangle given its length and width.".
  • an Algebra Word Problem, such as: "John is twice as old as his sister Mary. The sum of their ages is 36. How old is each?".
  • a Train Movement Word Problem, such as: "Two trains leave different stations at the same time. One is traveling at a speed of 60 mph, and the other is traveling at a speed of 70 mph. The trains are traveling in opposite directions. After 2 hours, the first train changes its direction and starts traveling in the same direction as the second train. How long will it take for the first train to catch up to the second train?".
  • an International Mathematical Olympiad (IMO) Problem, such as: "Let 'ABC' be a triangle with 'AB = c', 'AC = b', and 'BC = a'. Let 'P' be the incenter of 'ABC', and let 'r' be the inradius of triangle 'ABC'. Prove that: [math]\displaystyle{ PA + PB + PC = 2r \left( \frac{a}{\sin A} + \frac{b}{\sin B} + \frac{c}{\sin C} \right) }[/math].".
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• Counter-Example(s):
  • a Direct Mathematical Task, such as: "Solve the equation 2x - 3 = 7.".
  • a Problem-Solving Word Problem.
• See: Mathematical Expression, Mathematics Teaching, Educational Assessment, Natural Language Understanding Task, Problem Solving, Russell's Paradox, Representation (Mathematics).

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References

2023

• (Wikipedia, 2023) ⇒ https://en.wikipedia.org/wiki/word_problem Retrieved:2023-5-16.
  • Word problem may refer to:
    • Word problem (mathematics), a decision problem for algebraic identities in mathematics and computer science

2023

• (Wikipedia, 2023) ⇒ https://en.wikipedia.org/wiki/Word_problem_(mathematics) Retrieved:2023-5-16.
  • In computational mathematics, a word problem is the problem of deciding whether two given expressions are equivalent with respect to a set of rewriting identities. A prototypical example is the word problem for groups, but there are many other instances as well. A deep result of computational theory is that answering this question is in many important cases undecidable.

2023

• (Wikipedia, 2023) ⇒ https://en.wikipedia.org/wiki/mathematical_problem Retrieved:2023-5-16.
  • 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. It can also be a problem referring to the nature of mathematics itself, such as Russell's Paradox.

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