scholarly journals The plural still counts: Cross-linguistic study of the symbolic numerical magnitude comparison task in Polish- and German-speaking preschoolers

2020 ◽  
Author(s):  
Maciej Haman ◽  
Katarzyna Lipowska ◽  
Mojtaba Soltanlou ◽  
Krzysztof Cipora ◽  
Frank Domahs ◽  
...  
Keyword(s):  
Digit Span ◽  
Numerical Magnitude ◽  
Number Word ◽  
Numerical Comparison ◽  
Main Task ◽  
Comparison Task ◽  
Number Words ◽  
Symbolic Representations ◽  
German Speaking ◽  
Grammatical Number

Already in toddlerhood, children begin to master the system of number word meanings. The role of grammar, and in particular grammatical number inflection, in early stage of this process has been well documented. It is not clear, however, whether the influence of the grammatical language structure also extends to more complex later stages. In the current study, we have addressed this problem by using differences in the grammatical number paradigms between Polish and German, in particular, the inconsistency of the grammatical number of the verb and the noun for numbers above four. One-hundred-fifty-three Polish-speaking children and 124 German-speaking three-to-six-year-old children took part in the study. Their main task was to compare symbolic numbers (Arabic numerals and spoken number-words) in the range of small numbers (2-4) large numbers (5-9) and between ranges. In addition, counting skills (Give-a-number and count-list) and mapping between non-symbolic (dot sets) and symbolic representations of numbers were checked. The children also performed working memory tests (Corsi-blocks and digit span). Based on Give-a-number and mapping tasks, participants were divided into subset-knowers, CP-knowers-non-mappers and CP-knowers-mappers (cf. LeCorre, 2014). As expected, grammatical number structure influenced performance: Polish-speaking children, later than the German ones, achieved the CP-knowers stage and, after it was achieved, they fared worse in the numerical comparison task, which was further mediated by response side. Importantly, however, there were no significant differences in the mapping task between non-symbolic and symbolic representations of numbers between Polish and German groups. We conclude that cross-linguistic differences in the grammatical number paradigms can significantly affect the development of representations and processing of numbers not only at the stage of acquiring the meaning of the first number-words, but also at later stages, when dealing with symbolic numbers.

Units-first or tens-first: Does language matter when processing visually presented two-digit numbers?

2019 ◽  
Vol 73 (5) ◽  
pp. 726-738
Author(s):  
Alexandre Poncin ◽  
Amandine Van Rinsveld ◽  
Christine Schiltz
Keyword(s):  
Numerical Cognition ◽  
Fourth Graders ◽  
Number Word ◽  
Older Children ◽  
Mental Calculation ◽  
Magnitude Comparison ◽  
Simultaneous Condition ◽  
Number Words ◽  
French Speaking ◽  
German Speaking

The linguistic structure of number words can influence performance in basic numerical tasks such as mental calculation, magnitude comparison, and transcoding. Especially the presence of ten-unit inversion in number words seems to affect number processing. Thus, at the beginning of formal math education, young children speaking inverted languages tend to make relatively more errors in transcoding. However, it remains unknown whether and how inversion affects transcoding in older children and adults. Here we addressed this question by assessing two-digit number transcoding in adults and fourth graders speaking French and German, that is, using non-inverted and inverted number words, respectively. We developed a novel transcoding paradigm during which participants listened to two-digit numbers and identified the heard number among four Arabic numbers. Critically, the order of appearance of units and tens in Arabic numbers was manipulated mimicking the “units-first” and “tens-first” order of German and French. In a third “simultaneous” condition, tens and units appeared at the same time in an ecological manner. Although language did not affect overall transcoding speed in adults, we observed that German-speaking fourth graders were globally slower than their French-speaking peers, including in the “simultaneous” condition. Moreover, French-speaking children were faster in transcoding when the order of digit appearance was congruent with their number-word system (i.e., “tens-first” condition) while German-speaking children appeared to be similarly fast in the “units-first” and “tens-first” conditions. These findings indicate that inverted languages still impose a cognitive cost on number transcoding in fourth graders, which seems to disappear by adulthood. They underline the importance of language in numerical cognition and suggest that language should be taken into account during mathematics education.

scholarly journals Quantitative and qualitative differences in the canonical and the reverse distance effect and their selective association with arithmetic and mathematical competencies

2021 ◽  
Author(s):  
Stephan Vogel ◽  
Thomas J. Faulkenberry ◽  
Roland H. Grabner
Keyword(s):  
Standardized Test ◽  
Reaction Times ◽  
Distance Effect ◽  
Numerical Magnitude ◽  
Numerical Comparison ◽  
Central Research ◽  
Comparison Task ◽  
Mathematical Competencies ◽  
Numerical Order ◽  
Underlying Mechanisms

Understanding the relationship between symbolic numerical abilities and individual differences in mathematical competencies has become a central research endeavor in the last years. Evidence on this foundational relationship is often based on two behavioral signatures of numerical magnitude and numerical order processing: the canonical and the reverse distance effect. The former indicates faster reaction times for the comparison of numerals that are far in distance (e.g., 2 8) compared to numerals that are close in distance (e.g., 2 3). The latter indicates faster reaction times for the ordinal judgment of numerals (i.e., are numerals in ascending/descending order) that are close in distance (e.g., 2 3 4) compared to numerals that are far in distance (e.g., 2 4 6). While a substantial body of literature has reported consistent associations between the canonical distance effect and arithmetic abilities, rather inconsistent findings have been found for the reverse distance effect. Here, we tested the hypothesis that estimates of the reverse distance effect show qualitative differences (i.e., not all participants show a reverse distance effect in the expected direction) rather than quantitative differences (i.e., all individuals show a reverse distance effect, but to a different degree), and that inconsistent findings might be a consequence of this variation. We analyzed data from 397 adults who performed a computerized numerical comparison task, a computerized numerical order verification task (i.e., are three numerals presented in order or not), a paper pencil test of arithmetic fluency, as well as a standardized test to assess more complex forms of mathematical competencies. We found discriminatory evidence for the two distance effects. While estimates of the canonical distance effect showed quantitative differences, estimates of the reverse distance effect showed qualitative differences. Comparisons between individuals who demonstrated an effect and individuals who demonstrated no reverse distance effect confirmed a significant moderation on the correlation with mathematical abilities. Significantly larger effects were found in the group who showed an effect. These findings confirm that estimates of the reverse distance effect are subject to qualitative differences and that we need to better characterize the underlying mechanisms/strategies that might lead to these qualitative differences.

scholarly journals Quantitative and Qualitative Differences in the Canonical and the Reverse Distance Effect and Their Selective Association With Arithmetic and Mathematical Competencies

2021 ◽  
Vol 6 ◽  
Author(s):  
Stephan E. Vogel ◽  
Thomas J. Faulkenberry ◽  
Roland H. Grabner
Keyword(s):  
Standardized Test ◽  
Reaction Times ◽  
Distance Effect ◽  
Numerical Magnitude ◽  
Numerical Comparison ◽  
Central Research ◽  
Comparison Task ◽  
Mathematical Competencies ◽  
Numerical Order ◽  
Underlying Mechanisms

Understanding the relationship between symbolic numerical abilities and individual differences in mathematical competencies has become a central research endeavor in the last years. Evidence on this foundational relationship is often based on two behavioral signatures of numerical magnitude and numerical order processing: the canonical and the reverse distance effect. The former indicates faster reaction times for the comparison of numerals that are far in distance (e.g., 2 8) compared to numerals that are close in distance (e.g., 2 3). The latter indicates faster reaction times for the ordinal judgment of numerals (i.e., are numerals in ascending/descending order) that are close in distance (e.g., 2 3 4) compared to numerals that are far in distance (e.g., 2 4 6). While a substantial body of literature has reported consistent associations between the canonical distance effect and arithmetic abilities, rather inconsistent findings have been found for the reverse distance effect. Here, we tested the hypothesis that estimates of the reverse distance effect show qualitative differences (i.e., not all participants show a reverse distance effect in the expected direction) rather than quantitative differences (i.e., all individuals show a reverse distance effect, but to a different degree), and that inconsistent findings might be a consequence of this variation. We analyzed data from 397 adults who performed a computerized numerical comparison task, a computerized numerical order verification task (i.e., are three numerals presented in order or not), a paper pencil test of arithmetic fluency, as well as a standardized test to assess more complex forms of mathematical competencies. We found discriminatory evidence for the two distance effects. While estimates of the canonical distance effect showed quantitative differences, estimates of the reverse distance effect showed qualitative differences. Comparisons between individuals who demonstrated an effect and individuals who demonstrated no reverse distance effect confirmed a significant moderation on the correlation with mathematical abilities. Significantly larger effects were found in the group who showed an effect. These findings confirm that estimates of the reverse distance effect are subject to qualitative differences and that we need to better characterize the underlying mechanisms/strategies that might lead to these qualitative differences.

EXPRESS: Sometimes nothing is simply nothing: Automatic processing of empty sets

2021 ◽  
pp. 174702182110664
Author(s):  
Yam Zagury ◽  
Rut Zaks-Ohayon ◽  
Joseph Tzelgov ◽  
Michal Pinhas
Keyword(s):  
Visual Cues ◽  
Automatic Processing ◽  
Congruity Effect ◽  
Numerical Magnitude ◽  
Numerical Comparison ◽  
Comparison Task ◽  
Numerical Comparisons ◽  
Perceptual Dominance ◽  
Size Congruity Effect

Previous work using the numerical comparison task has shown that an empty set, the nonsymbolic manifestation of zero, can be represented as the smallest quantity of the numerical magnitude system. In the present study, we examined whether an empty set can be represented as such under conditions of automatic processing in which deliberate processing of stimuli magnitudes is not required by the task. In Experiment 1, participants performed physical and numerical comparisons of empty sets (i.e., empty frames) and of other numerosities presented as framed arrays of 1 to 9 dots. The physical sizes of the frames varied within pairs. Both tasks revealed a size congruity effect (SCE) for comparisons of non-empty sets. In contrast, comparisons to empty sets produced an inverted SCE in the physical comparison task, while no SCE was found for comparisons to empty sets in the numerical comparison task. In Experiment 2, participants performed an area comparison task using the same stimuli as Experiment 1 to examine the effect of visual cues on the automatic processing of empty sets. The results replicated the findings of the physical comparison task in Experiment 1. Taken together, our findings indicate that empty sets are not perceived as “zero”, but rather as “nothing”, when processed automatically. Hence, the perceptual dominance of empty sets seems to play a more important role under conditions of automatic processing, making it harder to abstract the numerical meaning of zero from empty sets.

Exploring the Boundaries of the Number–Temporal Order Association

2015 ◽  
Vol 62 (3) ◽  
pp. 198-205 ◽  
Author(s):  
Dana Ganor-Stern
Keyword(s):  
Embodied Cognition ◽  
Mental Representation ◽  
Temporal Order ◽  
Past Research ◽  
Numerical Comparison ◽  
Negative Number ◽  
Comparison Task ◽  
Negative Numbers ◽  
The Past

Past research has shown that numbers are associated with order in time such that performance in a numerical comparison task is enhanced when number pairs appear in ascending order, when the larger number follows the smaller one. This was found in the past for the integers 1–9 ( Ben-Meir, Ganor-Stern, & Tzelgov, 2013 ; Müller & Schwarz, 2008 ). In the present study we explored whether the advantage for processing numbers in ascending order exists also for fractions and negative numbers. The results demonstrate this advantage for fraction pairs and for integer-fraction pairs. However, the opposite advantage for descending order was found for negative numbers and for positive-negative number pairs. These findings are interpreted in the context of embodied cognition approaches and current theories on the mental representation of fractions and negative numbers.

The Flip Side of the Auditory Spatial Selection Benefit

2015 ◽  
Vol 62 (1) ◽  
pp. 66-74 ◽  
Author(s):  
Iring Koch ◽  
Vera Lawo
Keyword(s):  
Task Switching ◽  
Auditory Task ◽  
Numerical Magnitude ◽  
Attention Shifting ◽  
Gender Selection ◽  
Spatial Selection ◽  
Number Words ◽  
Switch Costs ◽  
Mixing Costs ◽  
Experimental Group

In cued auditory task switching, one of two dichotically presented number words, spoken by a female and a male, had to be judged according to its numerical magnitude. One experimental group selected targets by speaker gender and another group by ear of presentation. In mixed-task blocks, the target-defining feature (male/female vs. left/right) was cued prior to each trial, but in pure blocks it remained constant. Compared to selection by gender, selection by ear led to better performance in pure blocks than in mixed blocks, resulting in larger “global” mixing costs for ear-based selection. Selection by ear also led to larger “local” switch costs in mixed blocks, but this finding was partially mediated by differential cue-repetition benefits. Together, the data suggest that requirements of attention shifting diminish the auditory spatial selection benefit.

Intentional attention switching in dichotic listening: Exploring the efficiency of nonspatial and spatial selection

2014 ◽  
Vol 67 (10) ◽  
pp. 2010-2024 ◽  
Author(s):  
Vera Lawo ◽  
Janina Fels ◽  
Josefa Oberem ◽  
Iring Koch
Keyword(s):  
Dichotic Listening ◽  
Target Selection ◽  
Stimulus Onset ◽  
Numerical Magnitude ◽  
Relevant Feature ◽  
Attention Switching ◽  
Number Words ◽  
Switch Costs ◽  
Feature Dimension ◽  
Listening Task

Using an auditory variant of task switching, we examined the ability to intentionally switch attention in a dichotic-listening task. In our study, participants responded selectively to one of two simultaneously presented auditory number words (spoken by a female and a male, one for each ear) by categorizing its numerical magnitude. The mapping of gender (female vs. male) and ear (left vs. right) was unpredictable. The to-be-attended feature for gender or ear, respectively, was indicated by a visual selection cue prior to auditory stimulus onset. In Experiment 1, explicitly cued switches of the relevant feature dimension (e.g., from gender to ear) and switches of the relevant feature within a dimension (e.g., from male to female) occurred in an unpredictable manner. We found large performance costs when the relevant feature switched, but switches of the relevant feature dimension incurred only small additional costs. The feature-switch costs were larger in ear-relevant than in gender-relevant trials. In Experiment 2, we replicated these findings using a simplified design (i.e., only within-dimension switches with blocked dimensions). In Experiment 3, we examined preparation effects by manipulating the cueing interval and found a preparation benefit only when ear was cued. Together, our data suggest that the large part of attentional switch costs arises from reconfiguration at the level of relevant auditory features (e.g., left vs. right) rather than feature dimensions (ear vs. gender). Additionally, our findings suggest that ear-based target selection benefits more from preparation time (i.e., time to direct attention to one ear) than gender-based target selection.

scholarly journals The association between number magnitude and space is dependent on notation: Evidence from an adaptive perceptual orientation task

2019 ◽  
Vol 5 (1) ◽  
pp. 38-54
Author(s):  
Tianwei Gong ◽  
Baichen Li ◽  
Limei Teng ◽  
Zijun Zhou ◽  
Xuefei Gao ◽  
...  
Keyword(s):  
Judgment Task ◽  
Snarc Effect ◽  
Number Word ◽  
Reaction Time Difference ◽  
Number Words ◽  
Number Magnitude ◽  
Spatial Response ◽  
Orientation Task ◽  
Arabic Digits ◽  
Perceptual Orientation

Research on adults' numerical abilities suggests that number representations are spatially oriented. This association of numbers with spatial response is referred to as the SNARC (i.e., spatial–numerical association of response codes) effect. The notation-independence hypothesis of numeric processing predicts that the SNARC effect will not vary with notation (e.g., Arabic vs. number word). To test such assumption, the current study introduced an adaptive experimental procedure based on a simple perceptual orientation task that can automatically smooth out the mean reaction time difference between Arabic digits and traditional Chinese number. We found that the SNARC effect interacted with notation, showing a SNARC effect for Arabic digits, but not for verbal number words. The results of this study challenged the commonly held view that notation does not affect numerical processes associated with spatial representations. We introduced a parallel model to explain the notation-dependent SNARC effect in the perceptual orientation judgment task.

scholarly journals Inversion effects on mental arithmetic in English- and Polish-speaking adults

2019 ◽  
Vol 73 (1) ◽  
pp. 91-103
Author(s):  
Carolin Annette Lewis ◽  
Julia Bahnmueller ◽  
Marta Wesierska ◽  
Korbinian Moeller ◽  
Silke Melanie Göbel
Keyword(s):  
Mental Arithmetic ◽  
Word Formation ◽  
Place Value ◽  
Number Word ◽  
Problem Size ◽  
Number Range ◽  
Number Words ◽  
Language Groups ◽  
Addition Problem ◽  
The Cost

In some languages the order of tens and units in number words is inverted compared with the symbolic digital notation (e.g., German 23 → “ dreiundzwanzig,” literally: “ three-and-twenty”). In other languages only teen-numbers are inverted (e.g., English 17 → “ seventeen”; Polish 17 → “ siedemnaście” literally “ seventeen”). Previous studies have focused on between group comparisons of inverted and non-inverted languages and showed that number word inversion impairs performance on basic numerical tasks and arithmetic. In two independent experiments, we investigated whether number word inversion affects addition performance within otherwise non-inverted languages (Exp. 1: English, Exp. 2: Polish). In particular, we focused on the influence of inverted ( I; English: teen-numbers ⩾ 13, Polish: numbers 11–19) and non-inverted ( N) summands with sums between 13 and 39. Accordingly, three categories of addition problems were created: N + N, N + I, and I + I with problem size matched across categories. Across both language groups, we observed that problems with results in the 20 and 30 number range were responded to faster when only non-inverted summands were part of the problems as opposed to problems with one or two inverted summands. In line with this, the cost of a carry procedure was the largest for two inverted summands. The results support the notion that both language-specific and language-invariant aspects contribute to addition problem-solving. In particular though, regarding language-specific aspects, the results indicate that inverted number word formation of teens influences place-value processing of Arabic digits even in otherwise non-inverted languages.

The Number Language used by Preschool Children and their Mothers in the Context of Cooking

1996 ◽  
Vol 21 (1) ◽  
pp. 16-20 ◽  
Author(s):  
Jennifer M. Young-Loveridge
Keyword(s):  
Preschool Children ◽  
Mathematics Learning ◽  
Free Play ◽  
Number Word ◽  
Word Use ◽  
Number Words ◽  
Degree Of Control ◽  
The Relationship ◽  
Play Context

The present study was designed to explore the spontaneous use of number language by preschool children and their mothers in the context of cooking. The results show that preschool children use a variety of number words in this context. Mothers made substantially greater use of number words than did their children, possibly because the cooking context required a greater degree of control by the adult than would have been the case in a free-play context. Many instances of number-word use by mothers and by children went unacknowledged by their conversational partners. Although the relationship between children's number word use and that of their mothers was relatively weak (r=.34), there was a considerably stronger relationship between the numbers of reciprocal numeracy episodes and children's number-word use (r=.59). These findings support the idea that contingent responsiveness by adults is important for enhancing children's mathematics learning.

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