No CrossRef data available.
Article contents
Non-symbolic and symbolic number and the approximate number system
Published online by Cambridge University Press: 15 December 2021
Abstract
The distinction between non-symbolic and symbolic number is poorly addressed by the authors despite being relevant in numerical cognition, and even more important in light of the proposal that the approximate number system (ANS) represents rational numbers. Although evidence on non-symbolic number and ratios fits with ANS representations, the case for symbolic number and rational numbers is still open.
- Type
- Open Peer Commentary
- Information
- Copyright
- Copyright © The Author(s), 2021. Published by Cambridge University Press
References
Binzak, J. V., & Hubbard, E. M. (2020). No calculation necessary: Accessing magnitude through decimals and fractions. Cognition 199:104219.CrossRefGoogle ScholarPubMed
Bonato, M., Fabbri, S., Umiltà, C., & Zorzi, M. (2007). The mental representation of numerical fractions: Real or integer? Journal of Experimental Psychology: Human Perception and Performance 33(6):1410–1419.Google ScholarPubMed
Gabriel, F., Szucs, D., & Content, A. (2013). The mental representations of fractions: Adults’ same-different judgments. Frontiers in Psychology 4:385.CrossRefGoogle ScholarPubMed
Gómez, D. M., & Dartnell, P. (2019). Middle schoolers’ biases and strategies in a fraction comparison task. International Journal of Science and Mathematics Education 17:1233–1250.CrossRefGoogle Scholar
Henik, A., & Tzelgov, J. (1982). Is three greater than five: The relation between physical and semantic size in comparison tasks. Memory & Cognition 10(4):389–395.CrossRefGoogle ScholarPubMed
Kallai, A. Y., & Tzelgov, J. (2012). When meaningful components interrupt the processing of the whole: The case of fractions. Acta Psychologica 139:358–369.CrossRefGoogle ScholarPubMed
Morales, N., Dartnell, P., & Gómez, D. M. (2020). A study on congruency effects and numerical distance in fraction comparison by expert undergraduate students. Frontiers in Psychology 11:1190.CrossRefGoogle Scholar
Moyer, S., & Landauer, T. K. (1967). Time required for judgements of numerical inequality. Nature 215:1519–1520.CrossRefGoogle ScholarPubMed
Ni, Y., & Zhou, Y.-D. (2005). Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational Psychologist 40(1):27–52.CrossRefGoogle Scholar
Nuerk, H.-C., Moeller, K., Klein, E., Willmes, K., & Fischer, M. H. (2011). Extending the mental number line: A review of multi-digit number processing. Zeitschrift für Psychologie 219(1):3–22.CrossRefGoogle Scholar
Nuerk, H.-C., Weger, U., & Willmes, K. (2001). Decade breaks in the mental number line? Putting the tens and units back in different bins. Cognition 82:B25–B33.CrossRefGoogle Scholar
Obersteiner, A., Van Dooren, W., Van Hoof, J., & Verschaffel, L. (2013). The natural number bias and magnitude representation in fraction comparison by expert mathematicians. Learning and Instruction 28:64–72.CrossRefGoogle Scholar
Schneider, M., & Siegler, R. S. (2010). Representations of the magnitudes of fractions. Journal of Experimental Psychology: Human Perception and Performance 36(5):1227–1238.Google ScholarPubMed
Van Hoof, J., Lijnen, T., Verschaffel, L., & Van Dooren, W. (2013). Are secondary school students still hampered by the natural number bias? A reaction time study on fraction comparison tasks. Research in Mathematics Education 15(2):154–164.CrossRefGoogle Scholar
Target article
The number sense represents (rational) numbers
Related commentaries (26)
A rational explanation for links between the ANS and math
Constructing rationals through conjoint measurement of numerator and denominator as approximate integer magnitudes in tradeoff relations
Contents of the approximate number system
Distinguishing the specific from the recognitional and the canonical, and the nature of ratios
Non-symbolic and symbolic number and the approximate number system
Not so rational: A more natural way to understand the ANS
Numbers in action
Numerical cognition needs more and better distinctions, not fewer
Numerical cognition: Unitary or diversified system(s)?
Numerosities are not ersatz numbers
Numerosity, area-osity, object-osity? Oh my
Perceived number is not abstract
Positing numerosities may be metaphysically extravagant; positing representation of numerosities is not
Ratio-based perceptual foundations for rational numbers, and perhaps whole numbers, too?
Real models: The limits of behavioural evidence for understanding the ANS
Representation of pure magnitudes in ANS
Second-order characteristics don't favor a number-representing ANS
Sizes, ratios, approximations: On what and how the ANS represents
The approximate number system represents magnitude and precision
The approximate number system represents rational numbers: The special case of an empty set
The number sense does not represent numbers, but cardinality comparisons
The number sense represents multitudes and magnitudes
The perception of quantity ain't number: Missing the primacy of symbolic reference
Unwarranted philosophical assumptions in research on ANS
Weighted numbers
What are we doing when we perceive numbers?
Author response
Numbers, numerosities, and new directions