Compression is evident in children's unbounded and bounded numerical estimation: Reply to Cohen and Ray (2020)

Area of Science:

• Cognitive Psychology
• Numerical Cognition
• Mathematical Development

Background:

• Previous research (Kim & Opfer, 2017) indicated logarithmic number-line estimates in both bounded and unbounded conditions.
• The role of response space restrictions in generating this logarithmic pattern required further investigation.

Purpose of the Study:

• To examine if logarithmicity in number-line estimates is influenced by response space limitations.
• To investigate the relationship between numerical value, response space, and estimation patterns.

Main Methods:

• Replicated number-line estimation tasks, adapting procedures from Cohen and Ray (2020).
• Utilized Bayesian modeling to analyze estimation data from bounded and unbounded conditions.
• Compared logarithmicity across different numerical values and response space constraints.

Main Results:

• Logarithmic estimation patterns were observed in both bounded and unbounded tasks, confirming prior findings.
• The degree of logarithmicity correlated with the numerical value of estimates, not solely the response space.
• A transition from logarithmic to linear estimation was identified.
• Bayesian models suggested unbounded tasks exhibit greater logarithmicity than bounded ones, despite qualitative similarities.

Conclusions:

• The findings support and extend the generality of Kim and Opfer's (2017) original results on number-line estimation.
• Logarithmic scaling in number-line tasks is robust and not merely an artifact of response space restrictions.
• Unbounded tasks may elicit stronger logarithmic representations of numerical magnitudes.