Published online by Cambridge University Press: 27 July 2017
In response to the commentaries, we have refined our suggested model and discussed ways in which the model could be further expanded. In this context, we have elaborated on the role of specific continuous magnitudes. We have also found it important to devote a section to evidence considered the “smoking gun” of the approximate number system theory, including cross-modal studies, animal studies, and so forth. Lastly, we suggested some ways in which the scientific community can promote more transparent and collaborative research by using an open science approach, sharing both raw data and stimuli. We thank the contributors for their enlightening comments and look forward to future developments in the field.
Target article
From “sense of number” to “sense of magnitude”: The role of continuous magnitudes in numerical cognition
Related commentaries (29)
A “sense of magnitude” requires a new alternative for learning numerical symbols
Approximate number sense theory or approximate theory of magnitude?
Commentary on Leibovich et al.: What next?
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Controlling for continuous variables is not futile: What we can learn about number representation despite imperfect control
Direct and rapid encoding of numerosity in the visual stream
Evidence for a number sense
From continuous magnitudes to symbolic numbers: The centrality of ratio
How not to develop a sense of number
Infants discriminate number: Evidence against the prerequisite of visual object individuation and the primacy of continuous magnitude
Infants, animals, and the origins of number
Innateness of magnitude perception? Skill can be acquired and mastered at all ages
Is the ANS linked to mathematics performance?
Magnitude rather than number: More evidence needed
Magnitude, numerosity, and development of number: Implications for mathematics disabilities
Multitudes are adaptable magnitudes in the estimation of number
Number faculty is alive and kicking: On number discriminations and number neurons
Numerical intuitions in infancy: Give credit where credit is due
Numerical magnitude evaluation as a foundation for decision making
Perceiving numerosity from birth
Right idea, wrong magnitude system
Selecting the model that best fits the data
The contribution of fish studies to the “number sense” debate
The contributions of non-numeric dimensions to number encoding, representations, and decision-making factors
The evolvement of discrete representations from continuous stimulus properties: A possible overarching principle of cognition
The number sense is neither last resort nor of primary import
What is a number? The interplay between number and continuous magnitudes
What is the precise role of cognitive control in the development of a sense of number?
Why try saving the ANS? An alternative proposal
Author response
Toward an integrative approach to numerical cognition