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.

Fixated in more familiar territory: Providing an explicit midpoint for typical and atypical number lines

2020 ◽  
pp. 174702182096761
Author(s):  
Sabrina Di Lonardo Burr ◽  
Jo-Anne LeFevre
Keyword(s):  
Eye Tracking ◽  
Number Line ◽  
Estimation Accuracy ◽  
Tracking Data ◽  
Number Lines ◽  
Number Line Estimation

Does providing an explicit midpoint affect adults’ performance differently for typical and atypical number line tasks? Participants ( N = 29) estimated the location of target numbers on typical (i.e., 0–10,000) and atypical (i.e., 0–7,000) number lines with either an explicitly labelled midpoint or no midpoint. For the typical number line, estimation accuracy did not differ for the explicit- and implicit-midpoint conditions. For the atypical number line, participants in the explicit-midpoint condition were more accurate than those in the implicit-midpoint condition and their pattern of error was similar to that seen for typical number lines (i.e., M-shaped). In contrast, for participants in the implicit-midpoint condition, the pattern of error on the atypical line was tent-shaped, with less accurate estimates around the midpoint and quartiles than the endpoints. Eye-tracking data showed that, for all number lines, participants used the middle of the line to guide their estimates, but participants in the explicit-midpoint condition were more likely to make their first fixation around the true midpoint than those in the implicit–midpoint condition. We conclude that adults have difficulty in estimating on atypical number lines because they incorrectly calculate the numerical value of the midpoint.

scholarly journals Strategy use on bounded and unbounded number lines in typically developing adults and adults with dyscalculia: An eye-tracking study

2018 ◽  
Vol 4 (2) ◽  
pp. 337-359 ◽  
Author(s):  
Fae Aimée van der Weijden ◽  
Erica Kamphorst ◽  
Robin Hella Willemsen ◽  
Evelyn H. Kroesbergen ◽  
Anne H. van Hoogmoed
Keyword(s):  
Eye Tracking ◽  
Number Sense ◽  
Number Line ◽  
Strategy Use ◽  
Typically Developing ◽  
Target Number ◽  
Gaze Patterns ◽  
Pure Number ◽  
Number Lines ◽  
New Strategies

Recent research suggests that bounded number line tasks, often used to measure number sense, measure proportion estimation instead of pure number estimation. The latter is thought to be measured in recently developed unbounded number line tasks. Children with dyscalculia use less mature strategies on unbounded number lines than typically developing children. In this qualitative study, we explored strategy use in bounded and unbounded number lines in adults with (N = 8) and without dyscalculia (N = 8). Our aim was to gain more detailed insights into strategy use. Differences in accuracy and strategy use between individuals with and without dyscalculia on both number lines may enhance our understanding of the underlying deficits in individuals with dyscalculia. We combined eye-tracking and Cued Retrospective Reporting (CRR) to identify strategies on a detailed level. Strategy use and performance were highly similar in adults with and without dyscalculia on both number lines, which implies that adults with dyscalculia may have partly overcome their deficits in number sense. New strategies and additional steps and tools used to solve number lines were identified, such as the use of the previous target number. We provide gaze patterns and descriptions of strategies that give important first insights into new strategies. These newly defined strategies give a more in-depth view on how individuals approach a number lines task, and these should be taken into account when studying number estimations, especially when using the unbounded number line.

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 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 Reconstructing the origins of the space-number association: spatial and number-magnitude codes must be used jointly to elicit spatially organised mental number lines

2018 ◽  
Author(s):  
Mario Pinto ◽  
Michele Pellegrino ◽  
Fabio Marson ◽  
Stefano Lasaponara ◽  
Fabrizio Doricchi
Keyword(s):  
Spatial Representation ◽  
Response Selection ◽  
Number Line ◽  
Mental Number Line ◽  
Number Magnitude ◽  
Number Lines ◽  
Series Of Experiments ◽  
Blue Arrow ◽  
Spatial Positioning ◽  
The Right

AbstractIn a series of recent studies we have pointed out that the use of contrasting left/right spatial codes, whether indirectly related to number magnitudes through response selection or directly associated to the same magnitudes to guide their spatial positioning on a mental number line, is crucial in eliciting space-number associations (Aiello, 2012; Fattorini et al., 2015; 2016; Pinto et al., 2018). Nonetheless, this conclusion is based on experiments in which spatial and number-magnitudes codes are used jointly during task performance. Here, in a series of unimanual Go/No-Go tasks with intermixed central numerical and pictorial targets, i.e. arrows pointing to the left or to the right, we explore whether spatial codes used in isolation inherently evoke the left-to-right representation of number magnitudes and, vice-versa, whether number-magnitude codes used in isolation inherently evoke the conceptual activation of left/right spatial codes. In a first series of experiments participants were asked to provide unimanual Go/N-Go responses based on instructions that activated only magnitude codes, e.g. “push only if the number is lower than 5 and whenever an arrow appears”, or only spatial codes, e.g. “push only when an arrow points to the left and whenever a number appears”. In a second series of experiments, the same numerical instructions were combined with the request of responding only to arrows in a specific colour, e.g. “push when the number is lower than 5 and whenever a blue arrow appears”. At variance with a recent experiment by Shaki and Fischer (2018), in our experiments no constant association was present between a specific arrow colour and a specific arrow direction. The results of these experiments highlight no space-number congruency effects: e.g. no faster RTs to arrows pointing to the left rather than to the right when participants attend to numbers lower than 5 and, vice-versa, no faster RTs to numbers lower than 5 rather than higher, when participants attend to arrows pointing to the left. Based on these findings it must be concluded that neither space codes used in isolation can elicit a spatial representation of number magnitudes nor number-magnitude codes used in isolation can trigger the activation of spatial codes. Thus, spatial and numerical codes must be used jointly to evoke spatially organised mental number lines.

Pseudoneglect for the Bisection of Mental Number Lines

2009 ◽  
Vol 62 (5) ◽  
pp. 925-945 ◽  
Author(s):  
Andrea M. Loftus ◽  
Michael E. R. Nicholls ◽  
Jason B. Mattingley ◽  
Heidi L. Chapman ◽  
John L. Bradshaw
Keyword(s):  
Temporal Order ◽  
Spatial Configuration ◽  
Number Line ◽  
Task Demands ◽  
Spatial Neglect ◽  
Leftward Bias ◽  
Number Lines ◽  
Intact Brain ◽  
Logarithmic Scaling ◽  
The Right

Patients with unilateral neglect of the left side bisect physical lines to the right whereas individuals with an intact brain bisect lines slightly to the left (pseudoneglect). Similarly, for mental number lines, which are arranged in a left-to-right ascending sequence, neglect patients bisect to the right. This study determined whether individuals with an intact brain show pseudoneglect for mental number lines. In Experiment 1, participants were presented with visual number triplets (e.g., 16, 36, 55) and determined whether the numerical distance was greater on the left or right side of the inner number. Despite changing the spatial configuration of the stimuli, or their temporal order, the numerical length on the left was consistently overestimated. The fact that the bias was unaffected by physical stimulus changes demonstrates that the bias is based on a mental representation. The leftward bias was also observed for sets of negative numbers (Experiment 2)—demonstrating not only that the number line extends into negative space but also that the bias is not the result of an arithmetic distortion caused by logarithmic scaling. The leftward bias could be caused by a rounding-down effect. Using numbers that were prone to large or small rounding-down errors, Experiment 3 showed no effect of rounding down. The task demands were changed in Experiment 4 so that participants determined whether the inner number was the true arithmetic centre or not. Participants mistook inner numbers shifted to the left to be the true numerical centre—reflecting leftward overestimation. The task was applied to 3 patients with right parietal damage with severe, moderate, or no spatial neglect (Experiment 5). A rightward bias was observed, which depended on the severity of neglect symptoms. Together, the data demonstrate a reliable and robust leftward bias for mental number line bisection, which reverses in clinical neglect. The bias mirrors pseudoneglect for physical lines and most likely reflects an expansion of the space occupied by lower numbers on the left side of the line and a contraction of space for higher numbers located on the right.

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