scholarly journals Tracking the continuous dynamics of numerical processing: A brief review and editorial

2018 ◽  
Author(s):  
Thomas J. Faulkenberry ◽  
Matthias Witte ◽  
Matthias Hartmann
Keyword(s):  
Numerical Cognition ◽  
Mental Arithmetic ◽  
Special Section ◽  
Past Research ◽  
Number Processing ◽  
Hand Tracking ◽  
Single Digit ◽  
Future Directions ◽  
Numerical Processing ◽  
Computer Mouse

Many recent studies in numerical cognition have moved beyond the use of purely chronometric techniques in favor of methods which track the continuous dynamics of numerical processing. Two examples of such techniques include eye tracking and hand tracking (or computer mouse tracking). To reflect this increased concentration on continuous methods, we have collected a group of 5 articles that utilize these techniques to answer some contemporary questions in numerical cognition. In this editorial, we discuss the two paradigms and provide a brief review of some of the work in numerical cognition that has profited from the use of these techniques. For both methods, we discuss the past research through the frameworks of single digit number processing, multidigit number processing, and mental arithmetic processing. We conclude with a discussion of the papers that have been contributed to this special section and point to some possible future directions for researchers interested in tracking the continuous dynamics of numerical processing.

scholarly journals Tracking the continuous dynamics of numerical processing: A brief review and editorial

2018 ◽  
Vol 4 (2) ◽  
pp. 271-285 ◽  
Author(s):  
Thomas J. Faulkenberry ◽  
Matthias Witte ◽  
Matthias Hartmann
Keyword(s):  
Numerical Cognition ◽  
Mental Arithmetic ◽  
Special Section ◽  
Past Research ◽  
Number Processing ◽  
Hand Tracking ◽  
Single Digit ◽  
Future Directions ◽  
Numerical Processing ◽  
Computer Mouse

Many recent studies in numerical cognition have moved beyond the use of purely chronometric techniques in favor of methods which track the continuous dynamics of numerical processing. Two examples of such techniques include eye tracking and hand tracking (or computer mouse tracking). To reflect this increased concentration on continuous methods, we have collected a group of 5 articles that utilize these techniques to answer some contemporary questions in numerical cognition. In this editorial, we discuss the two paradigms and provide a brief review of some of the work in numerical cognition that has profited from the use of these techniques. For both methods, we discuss the past research through the frameworks of single digit number processing, multidigit number processing, and mental arithmetic processing. We conclude with a discussion of the papers that have been contributed to this special section and point to some possible future directions for researchers interested in tracking the continuous dynamics of numerical processing.

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.

The visual number world: A dynamic approach to study the mathematical mind

2018 ◽  
Vol 71 (1) ◽  
pp. 28-36 ◽  
Author(s):  
Matthias Hartmann ◽  
Jochen Laubrock ◽  
Martin H Fischer
Keyword(s):  
Numerical Cognition ◽  
Mental Arithmetic ◽  
Simultaneous Presentation ◽  
Language Research ◽  
On Line ◽  
Arithmetic Performance ◽  
Mathematical Mind ◽  
The Mind ◽  
Visual Number

In the domain of language research, the simultaneous presentation of a visual scene and its auditory description (i.e., the visual world paradigm) has been used to reveal the timing of mental mechanisms. Here we apply this rationale to the domain of numerical cognition in order to explore the differences between fast and slow arithmetic performance, and to further study the role of spatial-numerical associations during mental arithmetic. We presented 30 healthy adults simultaneously with visual displays containing four numbers and with auditory addition and subtraction problems. Analysis of eye movements revealed that participants look spontaneously at the numbers they currently process (operands, solution). Faster performance was characterized by shorter latencies prior to fixating the relevant numbers and fewer revisits to the first operand while computing the solution. These signatures of superior task performance were more pronounced for addition and visual numbers arranged in ascending order, and for subtraction and numbers arranged in descending order (compared to the opposite pairings). Our results show that the “visual number world”-paradigm provides on-line access to the mind during mental arithmetic, is able to capture variability in arithmetic performance, and is sensitive to visual layout manipulations that are otherwise not reflected in response time measurements.

scholarly journals Reversing the Manual Digit Bias in Two-Digit Number Comparison

2017 ◽  
Vol 64 (3) ◽  
pp. 191-204 ◽  
Author(s):  
Thomas J. Faulkenberry ◽  
Alexander Cruise ◽  
Samuel Shaki
Keyword(s):  
Numerical Cognition ◽  
Number Line ◽  
Number Representation ◽  
Digit Number ◽  
Computer Mouse ◽  
Number Comparison ◽  
Number Representations ◽  
Mouse Movements ◽  
Embodied Representation ◽  
Fixed Standard

Abstract. Though recent work in numerical cognition has supported a strong tie between numerical and spatial representations (e.g., a mental number line), less is known about such ties in multi-digit number representations. Along this line, Bloechle, Huber, and Moeller (2015) found that pointing positions in two-digit number comparison were biased leftward toward the decade digit. Moreover, this bias was reduced in unit-decade incompatible pairs. In the present study, we tracked computer mouse movements as participants compared two-digit numbers to a fixed standard (55). Similar to Bloechle et al. (2015) , we found that trajectories exhibited a leftward bias that was reduced for unit-decade incompatible comparisons. However, when positions of response labels were reversed, the biases reversed. That is, we found a rightward bias for compatible pairs that was reduced for incompatible pairs. This result calls into question a purely embodied representation of place value structure and instead supports a competition model of two-digit number representation.

scholarly journals Digital culture

2021 ◽  
Author(s):  
Alberto Acerbi
Keyword(s):  
Digital Media ◽  
Cultural Evolution ◽  
Cultural Transmission ◽  
Past Research ◽  
Digital Culture ◽  
Cultural Dynamics ◽  
Cumulative Culture ◽  
Future Directions

Cultural evolution can provide a useful framework to understand how information is produced, transmitted, and selected in contemporary online, digital, media. The diffusion of digital technologies triggered a radical departure from previous modalities of cultural transmission but, at the same time, general characteristics of human cultural evolution and cognition influence these developments. In this chapter, I will explore some areas where the links between cultural evolution research and digital media seem more promising. As cultural evolution-inspired research on internet phenomena is still in its infancy, these areas represent suggestions and links with works in other disciplines more than reviews of past research in cultural evolution. These include topics such as how to characterise the online effects of social influence and the spread of information; the possibility that digital, online, media could enhance cumulative culture; and the differences between online and offline cultural transmission. In the last section I will consider other possible future directions: the influences of different affordances in different media supporting cultural transmission; the role of producers of cultural traits; and, finally, some considerations on the effects on cultural dynamics of algorithms selecting information.

scholarly journals IEEE Access Special Section Editorial: Biologically Inspired Image Processing Challenges and Future Directions

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 147459-147462
Author(s):  
Jiachen Yang ◽  
Qinggang Meng ◽  
Maurizio Murroni ◽  
Shiqi Wang ◽  
Feng Shao
Keyword(s):  
Image Processing ◽  
Special Section ◽  
Biologically Inspired ◽  
Future Directions

When adding is right: Temporal order judgements reveal spatial attention shifts during two-digit mental arithmetic

2020 ◽  
Vol 73 (7) ◽  
pp. 1115-1132 ◽  
Author(s):  
Maria Glaser ◽  
André Knops
Keyword(s):  
Spatial Attention ◽  
Task Difficulty ◽  
Temporal Order ◽  
Mental Arithmetic ◽  
Stimulus Onset ◽  
Arithmetic Problem ◽  
Single Digit ◽  
Arithmetic Task ◽  
Addition And Subtraction ◽  
Attention Shifts

Recent research suggests that addition and subtraction induce horizontal shifts of attention. Previous studies used single-digit (1d) problems or verification paradigms that lend themselves to alternative solution strategies beyond mental arithmetic. To measure spatial attention during the active production of solutions to complex two-digit arithmetic problems (2d) without manual motor involvement, we used a temporal order judgement (TOJ) paradigm in which two lateralised targets were sequentially presented on screen with a varying stimulus onset asynchrony (SOA). Participants verbally indicated which target appeared first. By varying the delay between the arithmetic problem presentation and the TOJ task, we investigated how arithmetically induced attention shifts develop over time (Experiment 1, n = 31 and Experiment 2, n = 58). In Experiment 2, we additionally varied the carry property of the arithmetic task to examine how task difficulty modulates the effects. In the arithmetic task, participants were first presented with the arithmetic problem via headphones and performed the TOJ task after the delay before responding to the arithmetic task. To account for spontaneous attentional biases, a baseline TOJ was run without arithmetic processing. Both experiments revealed that addition induces shifts of spatial attention to the right suggesting that visuospatial attention mechanisms are recruited during complex arithmetic. We observed no difference in spatial attention between the carry and noncarry condition (Experiment 2). No shifts were observed for subtraction problems. No common and conclusive influence of delay was observed across experiments. Qualitative differences between addition and subtraction and the role of task difficulty are discussed.

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