Direct evidence for linguistic influences in two-digit number processing

© 2018 American Psychological Association. Language-specific differences in number words influence number processing even in nonverbal numerical tasks. For instance, the unit-decade compatibility effect in two-digit number magnitude comparison (compatible number pairs [42_57: 4 2]) was shown to be influenced by the inversion of number words (e.g., in German the number word for 42 is zweiundvierzig [literally: two-and-forty]). In two studies, we used articulatory suppression to investigate whether previously observed cross-linguistic differences in two-digit number processing are indeed driven by differences in number word formation. In a two-digit number comparison task, German- and English-speaking participants had to identify the larger of two numbers presented in Arabic digits. In Study 1, participants performed the same task twice, with and without articulatory suppression. In Study 2, the percentage of within-decade filler items (36_39) was manipulated additionally. As expected, in both studies between-groups differences in the compatibility effect disappeared under articulatory suppression irrespective of the percentage of fillers included. Furthermore, paralleling results of previous studies including 33% or less filler items, we found that the compatibility effect was larger in German compared with English speakers in the 20% filler condition. However, this pattern was reversed in the 50% filler condition in both studies. Thus, results provide first direct evidence for influences of verbal number word formation on symbolic number processing. Moreover, these new findings suggest that linguistic influences and those of cognitive control processes associated with characteristics of the stimulus set interact in symbolic number processing

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

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

Verkörperlichte Kognitionen oder warum 42 rechts ist. [Embodied cognition or why 42 is on the right side]

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Forty-two or two-and-forty: learning maths in different languages

Doing basic maths seems to be a pretty common thing. 2 + 2 equals 4, both in France and in China. 7 × 8 equals 56, both in the United States of America and in Germany. Although most of us use the same symbols to write down numbers (1, 2, 3, 4 ...), we use very different words for these numbers simply because we speak different languages. In this article, we will give examples of what number words in different languages look like. We also show how the way multi-digit number words are built can make learning maths and dealing with large numbers easier or more difficult. </div

Cognitive control in number processing: new evidence from task switching

© 2020, The Author(s). Recently, it was demonstrated that even basic numerical cognition such as the processing of number magnitude is under cognitive control. However, evidence so far primarily came from adaptation effects to stimulus characteristics (e.g., relative frequency of specific stimulus categories). Expanding this approach, we evaluated a possible influence of more active exertion of cognitive control on basic number processing in task switching. Participants had to perform a magnitude comparison task while we manipulated the order of compatible and incompatible input–output modalities (i.e., auditory/vocal input–visual/manual output vs. auditory/visual input–manual/vocal output, respectively) on the trial level, differentiating repeat vs. switch trials. Results indicated that the numerical distance effect but not the problem size effect was increased after a switch in input–output modality compatibility. In sum, these findings substantiate that basic number processing is under cognitive control by providing first evidence that it is influenced by the active exertion of cognitive control as required in task switching

Feinmotorik, Fingergnosie und frühe mathematische Fähigkeiten

Hintergrund:  In zahlreichen Studien wurden inzwischen die Zusammenhänge zwischen Feinmotorik, Fingergnosie und frühen mathematischen Fähigkeiten untersucht. Ziel der vorliegenden Arbeit ist es, einen Überblick über diese Studien zu geben und diese qualitativ dahingehend auszuwerten, für welche mathematischen Fähigkeitsbereiche bereits Zusammenhänge mit Feinmotorik und/oder Fingergnosie nachgewiesen wurden und inwiefern für unterschiedliche feinmotorische Aufgabenbereiche differenzierte Ergebnisse vorliegen.  Methoden:  In einer systematischen Literaturrecherche wurden 32 empirische Arbeiten als relevant identifiziert. Ergebnisse: Insgesamt zeigten sich für die Bereiche Zahlwortreihe und Zählen, Zahlgröße verstehen (nur für Feinmotorik), Zahlraumvorstellung (nur für Fingergnosie) sowie Rechnen Befundlagen, die für positive Zusammenhänge mit Feinmotorik und/oder Fingergnosie sprechen – wenn auch unter Einschränkungen. Für den Bereich Zahlsymbole lesen und schreiben spricht die Befundlage tendenziell für keinen signifikanten Zusammenhang mit der Fingergnosie.  Diskussion:  Die insgesamt recht uneinheitliche Befundlage deutet darauf hin, dass die Zusammenhänge zwischen Feinmotorik, Fingergnosie und früher mathematischer Entwicklung differenziert zu betrachten sind. Feinmotorik scheint darüber hinaus eher indirekt durch fingerbasierte Strategien (z.B. Fingerzählen) und/oder exekutive mit mathematischen Fähigkeiten verknüpft zu sein. Implikationen für Forschung und Praxis werden diskutiert. Background:  An increasing number of studies investigated associations between fine motor skills, finger gnosis, and early mathematical skills so far. The present study aimed to provide an overview of these studies and to evaluate them qualitatively in terms of which mathematical skills have been shown to link to fine motor skills and / or finger gnosis and to what extent results are available for different fine motor tasks.  Methods:  A systematic literature review identified 32 relevant empirical studies. Results: Findings for number word sequence and counting, number magnitude understanding (only for fine motor skills), number line estimation (only for finger gnosis), and arithmetic indicate – with some limitations – positive associations with fine motor skills and / or finger gnosis. For reading and writing number symbols, findings tend to indicate no significant association with finger gnosis.  Discussion:  All in all, results tended to be rather inconsistent, suggesting that the relation between fine motor skills, finger gnosia, and early mathematical development needs to be considered in a differentiated way. Moreover, fine motor skills seem to be associated rather indirectly with mathematical abilities though finger-based strategies (e. g., finger counting) and / or executive functions. Implications for research and practice are discussed.</p

Design and empirical evaluation of a multitouch interaction game-like app for fostering early embodied math learning

The ubiquity of mobile devices has made mobile touchscreen interaction a promising avenue for learning. Although children start using educational apps from early age, only a few apps adhere to interaction design recommendations and undergo empirical evaluation of their educational potential. In this paper, we describe the concept and design of an app developed for promoting early math learning through finger-based multi-touch interactions in kindergarten children. Drawing from research on embodied cognition, our app provides games for fostering finger counting as well as finger-based representation of cardinal magnitude and part-whole relations. The app's efficiency was empirically evaluated through a pre-post-intervention study design with two control conditions. Results revealed that a short-term intervention with the math app did not significantly improve children's math skills when compared to learning gains of both a content-matched, unplugged math training program and a passive, waiting list control group. We discuss possible methodological reasons underlying these results, considering key curricular differences for the effectiveness of app-based interventions in early childhood education. Finally, we reflect on the appropriateness of complex multitouch interaction for young kindergarten children and suggest future directions for research in child-centered interaction design

Influences of cognitive control on number processing: new evidence from switching between two numerical tasks

A growing body of research suggests that basic numerical abilities such as number magnitude and number parity processing are influenced by cognitive control. So far, however, evidence for number processing being influenced by cognitive control came primarily from observed adaptations to stimulus set characteristics (e.g., ratio or order of specific stimulus types) and switches between a numerical and non-numerical task. Complementing this previous research, the present study employed a task switching paradigm exclusively involving numerical tasks (i.e., magnitude comparisons and parity judgements) to examine how cognitive control processes influence number processing. Participants were presented with a single-digit number and had to either judge its parity or compare its magnitude to a standard of 5 depending on a preceding cue. Based on previous results, we expected the numerical distance effect and the SNARC effect to be modulated in switch trials requiring the exertion of cognitive control. Partly in line with our expectations, the numerical distance effect was reduced in switch trials. However, no significant modulation of the SNARC effect was observed. The results pattern suggests that influences of cognitive control on number processing depend on task requirements and the type of numerical information that is processed (i.e., numerical magnitude vs. spatial association of numbers). To reconcile present and previous results, we propose an information prioritization account, suggesting that cognitive control primarily influences the processing of the information type that requires the most explicit processing.</p

Cognitive control in number processing: new evidence from number compatibility effects in task-switching

A growing body of research suggests that basic numerical abilities such as number magnitude processing are influenced by cognitive control processes. So far, evidence for number processing being affected by cognitive control processes stems primarily from observed adaptations of numerical effects to stimulus set characteristics (e.g., order or ratio of specific stimulus types). Complementing previous research on adaptation to stimulus set characteristics as an index of influences of cognitive control, the present study employed a task-switching paradigm to examine how cognitive control processes influence number processing. Participants were presented with a two-digit number and had to either judge its parity or compare its magnitude to a standard depending on a preceding cue. We expected numerical congruency effects (i.e., the unit-decade compatibility effect for magnitude comparisons and the parity congruity effect for parity judgements) to be larger in switch trials, as persisting activation of the task set of the preceding trial should increase interference. In contrast to our expectations, both numerical congruity effects were reduced following task switches as compared to repetitions. This interaction of task-switching with numerical congruency effects suggests an influence of cognitive control on basic number processing in form of persisting inhibition of previously abandoned task sets, so that these exert less influence on current number processing demands

Ties of math and language: A cognitive developmental perspective

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