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The concept of real numbers includes all the values that can be represented on a continuous number line. The system began with basic counting values used for enumeration. It later expanded to include values that represent the absence of quantity and opposites of the counting values. When situations required expressing parts of a whole or dividing quantities evenly, values capable of representing such proportions were developed. When written using decimal notation, these values can end or repeat...
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A rational function is defined as the quotient of two polynomials:  where Q(x)≠0, These functions often exhibit asymptotes, which are the lines that the graph approaches but never touches. These asymptotes are classified based on how the function behaves near specific values of the input.Vertical asymptotes occur where the denominator is zero, and the numerator is not, causing the function to be undefined. These are found by solving Q(x)=0. For example:  has a vertical...
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A nonlinear inequality describes a comparison involving an expression that curves or behaves more complexly than a straight line. These inequalities often appear in forms that include squares, products, or variables in the denominator.To solve such an inequality, one starts by rewriting it so that zero appears on one side. For example, the inequality:  can be factored as: This form makes it easier to identify the values that cause the expression to equal zero. In this case, the...
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Multimedia Battery for Assessment of Cognitive and Basic Skills in Mathematics BM-PROMA
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How do people choose among rational number notations?

Jing Tian1, David W Braithwaite2, Robert S Siegler3

  • 1Temple University, Department of Psychology, 1701 N. 13th St., Philadelphia, PA 19122, USA.

Cognitive Psychology
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PubMed
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People prefer different rational number notations based on how they quantify ratios. Exact enumeration favors fractions, while estimation favors decimals and percentages, especially when precision is not paramount.

Keywords:
DecimalsFractionsNumerical cognitionPercentagesRational numbers

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Area of Science:

  • Cognitive Psychology
  • Mathematical Cognition
  • Decision Science

Background:

  • Fractions, decimals, and percentages have coexisted for centuries, implying distinct functional roles.
  • The cognitive processes underlying the choice of rational number notation remain poorly understood.

Purpose of the Study:

  • To propose and test Quantification Process Theory, explaining preferences for fractions, decimals, and percentages.
  • To elucidate how quantification processes influence notation choice in representing ratios.

Main Methods:

  • Four experiments were conducted to investigate notation preferences.
  • Participants' choices were analyzed based on whether they used exact enumeration or estimation to generate ratios.

Main Results:

  • Preferences for fractions, decimals, and percentages align with Quantification Process Theory predictions.
  • Exact enumeration led to a preference for fractions.
  • Estimation led to a preference for decimals and percentages, with percentages favored for less precise approximations.

Conclusions:

  • Quantification processes significantly influence the choice of rational number notation.
  • Understanding these processes has implications for mathematical education and communication.