The Development of Numerical Estimation

@article{Siegler2003TheDO,
  title={The Development of Numerical Estimation},
  author={Robert S. Siegler and John E Opfer},
  journal={Psychological Science},
  year={2003},
  volume={14},
  pages={237 - 250}
}
We examined children's and adults' numerical estimation and the representations that gave rise to their estimates. The results were inconsistent with two prominent models of numerical representation: the logarithmic-ruler model, which proposes that people of all ages possess a single, logarithmically spaced representation of numbers, and the accumulator model, which proposes that people of all ages represent numbers as linearly increasing magnitudes with scalar variability. Instead, the data… 

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References

SHOWING 1-10 OF 35 REFERENCES

The Development of Numerical Understandings

Children's Judgments of Numerical Inequality.

SEKULER, ROBERT, and MIERKIEWICZ, DIANE. Children's Judgments of Numerical Inequality. CHILD DEVELOPMENT, 1977, 48, 630-633. When adults judge which of 2 digits is numerically larger, their response

Abstract representations of numbers in the animal and human brain

Numerical Subtraction in the Pigeon: Evidence for a Linear Subjective Number Scale

The results indicate that subjective number is linearly, not logarithmically, related to objective number.

Span and rate of apprehension in children and adults.

  • M. ChiD. Klahr
  • Psychology
    Journal of experimental child psychology
  • 1975

Non-verbal numerical cognition: from reals to integers

Nonverbal Counting in Humans: The Psychophysics of Number Representation

The results support the hypothesis that adult humans share with nonverbal animals a system for representing number by magnitudes that have scalar variability (a constant coefficient of variation) and provide a formal model of the underlying nonverbal meaning of the symbols.

The Development of Concepts and Strategies Used in Computational Estimation.

Twelve students at each of Grades 3, 5, 7, and 9 were individually given tasks that presented problems with solutions from hypothetical students, accompanied by questions requiring students to

Two subjective scales of number

The results indicate that the apparent magnitude of numbers increases with a decelerated power function of their arithmetic magnitude when a series samples from an open-ended range, however, when an upper boundary of the range is specified, the subjective scale seems to be linear.

Chapter 5 Strategy Choices in Children's Time-Telling