scholarly journals Automatic place-value activation in magnitude-irrelevant parity judgement

2018 ◽  
Author(s):  
Krzysztof Cipora ◽  
Mojtaba Soltanlou ◽  
Stefan Smaczny ◽  
Silke Melanie Goebel ◽  
Hans-Christoph Nuerk

Research on multi-digit number processing suggests that, in Arabic numerals, their place-value magnitude is automatically activated, whenever a magnitude-relevant task was employed: However, so far, it is unknown, whether place-value is also activated when the target task is magnitude-irrelevant. The current study examines this question by using the parity congruency effect in two-digit numbers: It describes that responding to decade-digit parity congruent numbers (e.g., 35, 46; same parity of decades and units) is faster than to decade-digit parity incongruent numbers (e.g., 25; 36; different parities of decades and units). Here we investigate the (a-)symmetry of the parity congruency effect; i.e. whether it makes a difference whether participants are assessing the parity of the unit digit or the decade digit. We elaborate, how and why such an asymmetry is related to place-value processing, because the parity of the unit digit only interferes with the parity of the decade digit, while the parity of the decade digit interferes with both the parity of the unit digit and the integrated parity of the whole two-digit number. We observed a significantly larger parity congruency effect in the decade parity decision than in the unit parity decision. This suggests that automatic place-value processing also takes place in a typical parity judgment task, in which magnitude is irrelevant. Finally, because of the cross-lingual design of the study, we can show that these results and their implications were language-independent.

Author(s):  
Hans-Christoph Nuerk ◽  
Korbinian Moeller ◽  
Klaus Willmes

Only recently the focus in numerical cognition research has considered multi-digit number processing as a relatively new and yet understudied domain in mathematical cognition. In this chapter: (i) we argue that single-digit number processing is not sufficient to understand multi-digit number processing; (ii) provide an overview on which representations and effects have been investigated for multi-digit numbers; (iii) suggest a conceptual distinction between place-identification, place-value activation, and place-value computation; (iv) identify language influences on multi-digit number processing along that conceptual distinction; and (v) argue that for numerical development indices of multi-digit number processing may be more suitable predictors of later arithmetical performance than classical single-digit measure such as the distance effect or non-numerical variables (e.g., working memory). In the final section, we summarize the important issues in multi-digit number processing, outline future directions and try to encourage readers to contribute to a new, exciting, yet understudied domain of numerical cognition.


2011 ◽  
Vol 219 (1) ◽  
pp. 42-49 ◽  
Author(s):  
Anne Mann ◽  
Korbinian Moeller ◽  
Silvia Pixner ◽  
Liane Kaufmann ◽  
Hans-Christoph Nuerk

To process a multi-digit number its constituting digits need to be integrated into the place-value structure of the Arabic number system. For two-digit numbers, processes of unit-decade integration are reflected by the compatibility effect in magnitude comparison. Recent research in adults indicated that the size of the compatibility effect increases when stimuli prevent to focus on the decade digits as achieved by the inclusion of within-decade items (43_47). In the present study within- and between-decade items (47_62) were used to assess the compatibility effect in children. We observed reliable compatibility effects that increased with grade level and that were larger than in a previous study without within-decade stimuli. Furthermore, evaluation of the developmental trajectories showed that two-digit number processing develops to more automatic parallel processing of the constituent digits of tens and units. From these results we conclude that (i) even for children attentional processes can strongly influence multi-digit number processing and (ii) with increasing age and experience more parallel and automated understanding of two-digit numbers develops which seems to remain relatively stable once achieved.


Author(s):  
Wouter Duyck ◽  
Evelyne Lagrou ◽  
Wim Gevers ◽  
Wim Fias

Abstract. Earlier research with monolinguals and bilinguals showed that numbers may be named through both a semantic and a phonological route, depending on the number's language and format (Arabic or verbal), task demands, and naming language. The present study investigated the importance of the semantic route for the processing of a third representation of magnitude, namely Roman digits. Using an interference paradigm, we showed that the processing of Roman target digits is influenced by Arabic digit distractors, both in a naming task and a parity judgment task. Roman digits were processed faster if the target and distractor were of the same magnitude. If this was not the case, processing speed slowed down as the numerical distance between target and distractor increased. This strongly suggests that semantic access is mandatory when naming Roman digits. Implications are discussed for the number processing domain and for models of translation in bilinguals.


Author(s):  
Michael Wiemers ◽  
Harold Bekkering ◽  
Oliver Lindemann

Abstract. Many studies demonstrated interactions between number processing and either spatial codes (effects of spatial-numerical associations) or visual size-related codes (size-congruity effect). However, the interrelatedness of these two number couplings is still unclear. The present study examines the simultaneous occurrence of space- and size-numerical congruency effects and their interactions both within and across trials. In a magnitude judgment task physically small or large digits were presented left or right from screen center. The reaction times analysis revealed that space- and size-congruency effects coexisted in parallel and combined additively. Moreover, a selective sequential modulation of the two congruency effects was found. The size-congruency effect was reduced after size incongruent trials. The space-congruency effect, however, was only affected by the previous space congruency. The observed independence of spatial-numerical and within-magnitude associations is interpreted as evidence that the two couplings reflect different attributes of numerical meaning possibly related to ordinality and cardinality.


2020 ◽  
Vol 73 (12) ◽  
pp. 2188-2196
Author(s):  
Liat Goldfarb ◽  
Ram Naaman ◽  
Tal Balanero-Madmon

It is well documented that the ability to perceive numbers depends on perception of size. However, size consists of two different dimensions: height and width. In previous size-congruency experiments, the changes in the size dimension were confounded by changes in both the height and width dimensions. Hence, it is not clear if two digits that are equal in size but with different width and height produce a congruency effect and if so, which dimension (height or width) will be associated with quantity more prominently. In fact, different theories might predict different outcomes for the association of height versus width with numbers. To resolve this issue, this study included two experiments in which two equal-size digits that differed from each other in the height and width dimensions were presented and participants were asked to decide which digit is numerically larger. The results revealed a novel congruency effect in which larger numbers are associated more prominently with the height dimension when compared with the width dimension. This effect has important implications for understanding the relationship between number processing and the spatial perception system.


2011 ◽  
Vol 109 (3) ◽  
pp. 263-274 ◽  
Author(s):  
Winnie Wai Lan Chan ◽  
Terry K. Au ◽  
Joey Tang

2013 ◽  
Vol 4 ◽  
Author(s):  
E. Klein ◽  
J. Bahnmueller ◽  
A. Mann ◽  
S. Pixner ◽  
L. Kaufmann ◽  
...  

2010 ◽  
Vol 75 (4) ◽  
pp. 290-306 ◽  
Author(s):  
K. Moeller ◽  
S. Huber ◽  
H.-C. Nuerk ◽  
K. Willmes

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