Operational Momentum in Numerosity Production Judgments of Multi-Digit Number Problems

2011 ◽  
Vol 219 (1) ◽  
pp. 50-57 ◽  
Author(s):  
Oliver Lindemann ◽  
Michael D. Tira
Keyword(s):  
Empirical Support ◽  
Number Processing ◽  
Production Task ◽  
Momentum Effect ◽  
Digit Number ◽  
Judgment Bias ◽  
Operational Momentum ◽  
Calculation Task ◽  
Addition And Subtraction ◽  
Random Dot Patterns

The current study demonstrates a numerosity production task and investigates approximate mental calculations with two-digit numbers. Participants were required to produce random dot patterns to indicate the size of two-digit numbers and the results of addition and subtraction problems. The stimuli in the calculation task consisted of problems requiring a carry operation (e.g., 24 + 18) or no-carry problems (e.g., 24 + 53) or zero problems (e.g., 24 + 0). Our analysis revealed that the outcomes of additions were estimated to be larger than the outcomes of subtractions. Interestingly, this judgment bias was present for no-carry and zero problems but not for carry problems. Taken together, the presented data provide empirical support for the presence of an operational momentum effect (OM effect) in multi-digit number arithmetic. These findings and the dissociation of the OM effect for carry and no-carry problems are discussed in the context of recent models on multi-digit number processing.

scholarly journals Identifikasi Mental Computation Siswa Disleksia dalam Melakukan Operasi Penjumlahan dan Pengurangan Bilangan Bulat

2017 ◽  
Vol 2 (2) ◽  
pp. 106-119
Author(s):  
Lisanul Uswah Sadieda ◽  
Agustin Eka Cahyani
Keyword(s):  
Qualitative Approach ◽  
Arithmetic Problem ◽  
Subtraction Problem ◽  
Digit Number ◽  
Mental Computation ◽  
Reading And Writing ◽  
Dyslexic Student ◽  
Addition And Subtraction ◽  
The Right ◽  
Dyslexic Students

To describe mental computation strategies of the dyslexic student in performing the addition and subtraction of 1-digit and 2-digit integer. Mental computation is a process of doing arithmetic calculations without using other tools. This strategy will help dyslexic students find more accurate and flexible solution while solving the arithmetic problem because it can minimize their weaknesses in terms of reading and writing. This research uses the qualitative approach. Data were collected by using a task-based interview for two dyslexic students. The results of this study indicate that dyslexic students use the spin-around strategy to solve the addition for the 1-digit number and the working from the right and from the left strategies to solve the addition for the 2-digit number. Meanwhile, to solve the subtraction problem, dyslexic students use think addition and counting back strategies for the 1-digit number and Working from The Right strategy for the 2-digit number.

Multi-digit Number Processing

2014 ◽  
Author(s):  
Hans-Christoph Nuerk ◽  
Korbinian Moeller ◽  
Klaus Willmes
Keyword(s):  
Numerical Cognition ◽  
Distance Effect ◽  
Number Processing ◽  
Place Value ◽  
Digit Number ◽  
Single Digit ◽  
Numerical Development ◽  
Conceptual Distinction ◽  
Place Identification

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.

scholarly journals Operational momentum effect in children with and without developmental dyscalculia

2013 ◽  
Vol 4 ◽  
Author(s):  
Karin Kucian ◽  
Fabienne Plangger ◽  
Ruth O'Gorman ◽  
Michael von Aster
Keyword(s):  
Momentum Effect ◽  
Developmental Dyscalculia ◽  
Operational Momentum

scholarly journals Exploring the developmental changes in automatic two-digit number processing

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

scholarly journals Language influences on numerical development—Inversion effects on multi-digit number processing

2013 ◽  
Vol 4 ◽  
Author(s):  
E. Klein ◽  
J. Bahnmueller ◽  
A. Mann ◽  
S. Pixner ◽  
L. Kaufmann ◽  
...  
Keyword(s):  
Number Processing ◽  
Digit Number ◽  
Numerical Development ◽  
Inversion Effects

Two-digit number processing: holistic, decomposed or hybrid? A computational modelling approach

2010 ◽  
Vol 75 (4) ◽  
pp. 290-306 ◽  
Author(s):  
K. Moeller ◽  
S. Huber ◽  
H.-C. Nuerk ◽  
K. Willmes
Keyword(s):  
Computational Modelling ◽  
Number Processing ◽  
Digit Number ◽  
Modelling Approach

scholarly journals A role for attentional reorienting during approximate multiplication and division

2017 ◽  
Vol 3 (2) ◽  
pp. 246-269 ◽  
Author(s):  
Curren Katz ◽  
Hannes Hoesterey ◽  
André Knops
Keyword(s):  
Cognitive Processes ◽  
Incorrect Response ◽  
Number Representation ◽  
Momentum Effect ◽  
Division Problems ◽  
Operational Momentum ◽  
Response Alternatives ◽  
Attentional Shifts ◽  
Fact Retrieval ◽  
Subsequent Target

When asked to estimate the outcome of arithmetic problems, participants overestimate for addition problems and underestimate for subtraction problems, both in symbolic and non-symbolic format. This bias is referred to as operational momentum effect (OM). The attentional shifts account holds that during computation of the outcome participants are propelled too far along a spatial number representation. OM was observed in non-symbolic multiplication and division while being absent in symbolic multiplication and division. Here, we investigate whether (a) the absence of the OM in symbolic multiplication and division was due to the presentation of the correct outcome amongst the response alternatives, putatively triggering verbally mediated fact retrieval, and whether (b) OM is correlated with attentional parameters, as stipulated by the attentional account. Participants were presented with symbolic and non-symbolic multiplication and division problems. Among seven incorrect response alternatives participants selected the most plausible result. Participants were also presented with a Posner task, with valid (70%), invalid (15%) and neutral (15%) cues pointing to the position at which a subsequent target would appear. While no OM was observed in symbolic format, non-symbolic problems were subject to OM. The non-symbolic OM was positively correlated with reorienting after invalid cues. These results provide further evidence for a functional association between spatial attention and approximate arithmetic, as stipulated by the attentional shifts account of OM. They also suggest that the cognitive processes underlying multiplication and division are less prone to spatial biases compared to addition and subtraction, further underlining the involvement of differential cognitive processes.

Sign in / Sign up

Export Citation Format

Share Document