scholarly journals Linguistic Inversion and Numerical Estimation

2020 ◽  
Author(s):  
Sophie Savelkouls ◽  
Katherine Williams ◽  
Hilary Barth
Keyword(s):  
Arabic Numeral ◽  
Number Line ◽  
Read Aloud ◽  
Number Word ◽  
Numerical Estimation ◽  
Digit Number ◽  
Number Words ◽  
Number Line Estimation ◽  
English Speaking ◽  
The Right

Number line estimation (NLE) performance is usually believed to depend on the magnitudes of presented numerals, rather than on the particular digits instantiating those magnitudes. Recent research, however, shows that NLE placements differ considerably for target numerals with nearly identical magnitudes, but instantiated with different leftmost digits (Lai, Zax, & Barth, 2018). Here we investigate whether this left digit effect may be due, in part, to the ordering of digits in number words. In English, the leftmost digit of an Arabic numeral is spoken first (“forty-one”), but Dutch number words are characterized by the inversion property: the rightmost digit of a two-digit number word is spoken first (“eenenveertig” - one and forty in Dutch). Participants (N = 40 Dutch-English bilinguals and N = 20 English-speaking monolinguals) completed a standard 0-100 NLE task. Target numerals were read aloud by an experimenter in either English or Dutch. Preregistered analyses revealed a strong left digit effect in monolingual English speakers’ estimates: e.g., 41 was placed more than two units to the right of 39. No left digit effect was observed among Dutch-English bilingual participants tested in either language. These findings are consistent with the idea that the order in which digits are spoken might influence multi-digit number processing, and suggests linguistic influences on numerical estimation performance.

scholarly journals Linguistic inversion and numerical estimation

2020 ◽  
Vol 6 (3) ◽  
pp. 263-274
Author(s):  
Sophie Savelkouls ◽  
Katherine Williams ◽  
Hilary Barth
Keyword(s):  
Arabic Numeral ◽  
Number Line ◽  
Read Aloud ◽  
Number Word ◽  
Numerical Estimation ◽  
Digit Number ◽  
Number Words ◽  
Number Line Estimation ◽  
English Speaking ◽  
The Right

Number line estimation (NLE) performance is usually believed to depend on the magnitudes of presented numerals, rather than on the particular digits instantiating those magnitudes. Recent research, however, shows that NLE placements differ considerably for target numerals with nearly identical magnitudes, but instantiated with different leftmost digits. Here we investigate whether this left digit effect may be due, in part, to the ordering of digits in number words. In English, the leftmost digit of an Arabic numeral is spoken first (“forty-one”), but Dutch number words are characterized by the inversion property: the rightmost digit of a two-digit number word is spoken first (“eenenveertig” – one and forty in Dutch). Participants (N = 40 Dutch-English bilinguals and N = 20 English-speaking monolinguals) completed a standard 0-100 NLE task. Target numerals were read aloud by an experimenter in either English or Dutch. Preregistered analyses revealed a strong left digit effect in monolingual English speakers’ estimates: e.g., 41 was placed more than two units to the right of 39. No left digit effect was observed among Dutch-English bilingual participants tested in either language. These findings are consistent with the idea that the order in which digits are spoken might influence multi-digit number processing, and suggests linguistic influences on numerical estimation performance.

scholarly journals Analogical mapping in numerical development

2019 ◽  
Author(s):  
Elisabeth Marchand ◽  
David Barner
Keyword(s):  
Numerical Cognition ◽  
Number Line ◽  
Number Word ◽  
Numerical Estimation ◽  
Analogical Thinking ◽  
Number Words ◽  
Numerical Development ◽  
Analogical Mapping ◽  
Number Line Estimation ◽  
Abstract Content

This chapter outlines the contribution of analogical thinking in numerical cognition and specifically, to number words learning and numerical estimation. We begin with an overview of number word learning, followed by a description of analogical mapping as defined by Gentner (1983, 2010), and discuss how children might acquire the meaning of counting based on analogical mapping. Next, we review the claim that very similar processes of analogical mapping may support numerical estimation, based on findings from studies of dot-array and number line estimation. These studies suggest that children’s knowledge of how the count list is structured – and in particular the ordering and distance between numbers – affects their ability to make accurate estimates. Finally, we discuss extensions of this idea to other cases where analogy has been proposed as a source of representational change. We conclude that analogical mappings enrich how humans transcend core numerical abilities to represent abstract content.

The Universal SNARC Effect

2005 ◽  
Vol 52 (3) ◽  
pp. 187-194 ◽  
Author(s):  
Hans-Christoph Nuerk ◽  
Guilherme Wood ◽  
Klaus Willmes
Keyword(s):  
Arabic Numeral ◽  
Number Line ◽  
Snarc Effect ◽  
Auditory Presentation ◽  
Number Word ◽  
Visual Modality ◽  
Magnitude Representation ◽  
Left Hand ◽  
Number Magnitude ◽  
The Right

Abstract. It is thought that number magnitude is represented in an abstract and amodal way on a left-to-right oriented mental number line. Major evidence for this idea has been provided by the SNARC effect ( Dehaene, Bossini, & Giraux, 1993 ): responses to relatively larger numbers are faster for the right hand, those to smaller numbers for the left hand, even when number magnitude is irrelevant. The SNARC effect has been used to index automatic access to a central semantic and amodal magnitude representation. However, this assumption of modality independence has never been tested and it remains uncertain if the SNARC effect exists in other modalities in a similar way as in the visual modality. We have examined this question by systematically varying modality/notation (auditory number word, visual Arabic numeral, visual number word, visual dice pattern) in a within-participant design. The SNARC effect was found consistently for all modality/notation conditions, including auditory presentation. The size of the SNARC effect in the auditory condition did not differ from the SNARC effect in any visual condition. We conclude that the SNARC effect is indeed a general index of a central semantic and amodal number magnitude representation.

Fixated in unfamiliar territory: Mapping estimates across typical and atypical number lines

2019 ◽  
Vol 73 (2) ◽  
pp. 279-294
Author(s):  
Sabrina Michelle Di Lonardo ◽  
Matthew G Huebner ◽  
Katherine Newman ◽  
Jo-Anne LeFevre
Keyword(s):  
Numerical Range ◽  
Number Line ◽  
Strategy Use ◽  
Reverse Direction ◽  
Tracking Data ◽  
Spatial Processes ◽  
Number Lines ◽  
Number Line Estimation ◽  
The Right ◽  
Typical Range

Adults ( N = 72) estimated the location of target numbers on number lines that varied in numerical range (i.e., typical range 0–10,000 or atypical range 0–7,000) and spatial orientation (i.e., the 0 endpoint on the left [traditional] or on the right [reversed]). Eye-tracking data were used to assess strategy use. Participants made meaningful first fixations on the line, with fixations occurring around the origin for low target numbers and around the midpoint and endpoint for high target numbers. On traditional direction number lines, participants used left-to-right scanning and showed a leftward bias; these effects were reduced for the reverse direction number lines. Participants made fixations around the midpoint for both ranges but were less accurate when estimating target numbers around the midpoint on the 7,000-range number line. Thus, participants are using the internal benchmark (i.e., midpoint) to guide estimates on atypical range number lines, but they have difficulty calculating the midpoint, leading to less accurate estimates. In summary, both range and direction influenced strategy use and accuracy, suggesting that both numerical and spatial processes influence number line estimation.

scholarly journals Language effects in early development of number writing and reading

2021 ◽  
Vol 7 (3) ◽  
pp. 368-387 ◽  
Author(s):  
Anna F. Steiner ◽  
Sabrina Finke ◽  
Francina J. Clayton ◽  
Chiara Banfi ◽  
Ferenc Kemény ◽  
...  
Keyword(s):  
Grade Level ◽  
Longitudinal Design ◽  
Number Word ◽  
Number Words ◽  
Language Effects ◽  
English Speaking ◽  
Linguistic Challenges ◽  
The Impact ◽  
Accuracy Rates ◽  
Specific Number

Reading and writing multidigit numbers requires accurate switching between Arabic numbers and spoken number words. This is particularly challenging in languages with number-word inversion such as German (24 is pronounced as four-and-twenty), as reported by Zuber, Pixner, Moeller, and Nuerk (2009, https://doi.org/10.1016/j.jecp.2008.04.003). The current study aimed to replicate the qualitative error analysis by Zuber et al. and further extended their study: 1) A cross-linguistic (German, English) analysis enabled us to differentiate between language-dependent and more general transcoding challenges. 2) We investigated whether specific number structures influence accuracy rates. 3) To consider both transcoding directions (from Arabic numbers to number words and vice versa), we assessed performance for number reading in addition to number writing. 4) Our longitudinal design allowed us to investigate transcoding development between Grades 1 and 2. We assessed 170 German- and 264 English-speaking children. Children wrote and read the same set of 44 one-, two- and three-digit numbers, including the same number structures as Zuber et al. For German, we confirmed that a high amount of errors in number writing was inversion-related. For English, the percentage of inversion-related errors was very low. Accuracy rates were strongly related to number syntax. The impact of number structures was independent of transcoding direction or grade level and revealed cross-linguistic challenges of transcoding multidigit numbers. For instance, transcoding of three-digit numbers containing syntactic zeros (e.g., 109) was significantly more accurate than transcoding of items with lexical zeros (e.g., 190). Based on our findings, we suggest adaptations of current transcoding models.

scholarly journals The Acquisition of French Un

2021 ◽  
Author(s):  
Elisabeth Marchand ◽  
David Barner
Keyword(s):  
Morphological Structure ◽  
English Word ◽  
Linguistic Variation ◽  
Number Word ◽  
Grammatical Structure ◽  
Number Words ◽  
Indefinite Article ◽  
French Speaking ◽  
English Speaking

How does cross-linguistic variation in grammatical structure affect children’s acquisition of number words? In this study, we addressed this question by investigating the case study of young speakers of French, a language in which the number one and the indefinite article a are phonologically the same (i.e., un). We tested how French-speaking children interpret un, and whether it more closely resembles the English word a or one. We found that French-speaking children almost always accepted sets of 1 for un, but that their responses for sets of 2 were more equivocal, with many children saying “Oui” (Yes) when asked whether there was un. Overall, French children’s interpretation of un differed from how English-speaking interpret both a and one. This suggests that French-speaking children’s interpretation of un reflects the ambiguity of the input that they are exposed to. We conclude that French morphological structure may pose a challenge to French- speaking children in acquiring an exact numerical meaning for the word un, potentially causing a delay in number word learning.

scholarly journals Unbounded number line estimation as a measure of numerical estimation

PLoS ONE ◽  
2019 ◽  
Vol 14 (3) ◽  
pp. e0213102 ◽  
Author(s):  
Regina Miriam Reinert ◽  
Matthias Hartmann ◽  
Stefan Huber ◽  
Korbinian Moeller
Keyword(s):  
Number Line ◽  
Numerical Estimation ◽  
Number Line Estimation

scholarly journals Left digit effects in numerical estimation across development

2021 ◽  
Author(s):  
Katherine Williams ◽  
Alexandra Zax ◽  
Andrea Patalano ◽  
Hilary Barth
Keyword(s):  
Cognitive Development ◽  
Numerical Cognition ◽  
Number Line ◽  
Effect Sizes ◽  
Numerical Estimation ◽  
Instructional Tool ◽  
Learning And Development ◽  
Number Line Estimation

Number line estimation (NLE) tasks are widely used to investigate numerical cognition, learning, and development, and as an instructional tool. Interpretation of these tasks generally involves an implicit expectation that responses are driven by the overall magnitudes of target numerals, in the sense that the particular digits conveying those magnitudes are unimportant. However, recent evidence shows that numbers with similar magnitudes but different leftmost digits are estimated very differently. For example, “798” is placed systematically much too far to the left of “801” in a 0-1000 NLE task by children aged 7-11 and adults (Lai et al., 2018). Here we ask whether this left digit effect generalizes to two-digit numerals in a 0-100 NLE task and whether it emerges in younger children. Children aged 5-8 (Study 1, N = 73), adults (Study 2, N = 44), and children aged 9-11 (Study 3, N = 27) completed a standard 0-100 NLE task on a touchscreen tablet. We observed left digit effects for two-digit numerals in children aged 8-11 and adults, with large effect sizes, demonstrating that these effects generalize to smaller numerical ranges. Left digit effects were not apparent in 5- to 7-year-olds, suggesting that these effects do not emerge at younger ages for smaller, more familiar numerical ranges. We discuss developmental emergence of left digit effects in number line estimation and implications within and beyond the field of cognitive development.

Sex differences in number line estimation: The role of numerical estimation

2016 ◽  
Vol 108 (2) ◽  
pp. 334-350 ◽  
Author(s):  
Regina M. Reinert ◽  
Stefan Huber ◽  
Hans-Christoph Nuerk ◽  
Korbinian Moeller
Keyword(s):  
Sex Differences ◽  
Number Line ◽  
Numerical Estimation ◽  
Number Line Estimation

scholarly journals The mental representation of non-numerical quantifiers: The Spatial-Linguistic Association of Response Codes (SLARC) effect.

2021 ◽  
Author(s):  
MARTINA ABBONDANZA ◽  
Luca Rinaldi ◽  
Francesca Foppolo ◽  
Marco Marelli
Keyword(s):  
Mental Representation ◽  
Spatial Representation ◽  
Human Mind ◽  
Snarc Effect ◽  
Number Word ◽  
Left Hand ◽  
Number Words ◽  
Word Task ◽  
The Right ◽  
Intense Debate

How quantifiers are represented in the human mind is still a topic of intense debate. Seminal studies have addressed the issue of how a subclass of quantifiers, i.e. number words, is spatially coded displaying the SNARC (Spatial-numerical Association of Response Codes) effect; yet, none of these studies have explored the spatial representation of non-numerical quantifiers such as “some” or “many”. The aim of the present study is to investigate whether non-numerical quantifiers are spatially coded in the human mind. We administered two typical comparison tasks to 52 participants: the first task involved non-numerical quantifiers; the second task involved number words. Results showed a response-side compatibility effect for both number words and non-numerical quantifiers, suggesting that both types of quantifiers are encoded in a spatial format; quantifiers referring to “small” quantities are responded to faster with the left hand and quantifiers referring to “large” quantities are responded to faster with the right hand. We labeled this effect for non-numerical quantifiers as the SLARC (Spatial-Linguistic Association of Response Codes) effect. Notably, we found that the SNARC and the SLARC effects were strictly related to each other, namely more a participant was sensitive to the SNARC effect in the number word task, the more a SLARC effect was detectable in the non-numerical quantifier task. These findings add evidence to the tendency of humans to align magnitude information on a mental line that is coded from left to right. This article is in press in The Journal of Experimental Psychology: Learning, Memory and Cognition.

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