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Hans-christoph Nuerk - One of the best experts on this subject based on the ideXlab platform.
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Mental Number Line in the preliterate brain the role of early directional experiences
Child Development Perspectives, 2016Co-Authors: Katarzyna Patro, Hans-christoph Nuerk, Ulrike CressAbstract:Numbers and space are strongly related in the human mind. In particular, small and large Numbers are Mentally linked to spatial directions, forming the so-called Mental Number Line. Traditionally, the direction of the Number Line was thought to emerge from cultural spatial experience with reading and writing. In this article, we review recent developMental data that put constraints on this traditional account and suggest that directional Number representation develops even before the acquisition of literacy. On the basis of these data, we argue that the link between Numbers and space is triggered by systematic involvement in directional actions of any kind rather than by reading and writing per se. Before school begins, children are exposed to many directional cues by observing the world around them and interacting with their parents. We propose a hypothetical mechanism through which this preliterate experience might activate spatially oriented numerical representation.
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computers in mathematics education training the Mental Number Line
Computers in Human Behavior, 2015Co-Authors: K. Orbinian Moeller, Hans-christoph Nuerk, Ursula Fischer, Ulrike CressAbstract:Mental Number Line representation associated with other numerical competencies.Successful computer-based Number Line trainings are reviewed.First focus on socially interactive and adaptive learning environments.Second focus on embodied interactions allowing for bodily experiences of numerical concepts.Latest developments in computer technology open up new directions for numerical trainings. Number magnitude is often described to be represented along a Mental Number Line. In children, the accuracy of this Mental Number Line seems to be associated with other basic numerical/arithmetic competencies. As a consequence, specific Number Line trainings have been developed. Evaluations indicated improvements not only in Number Line accuracy but also other numerical (e.g., magnitude comparison) and arithmetic tasks (e.g., Mental addition) not trained directly. Importantly, this was observed for both board games as well as first computer-supported Number Line trainings. However, computer technology progresses rapidly. In this literature review, we specifically focus on the issues of multi-player learning environments and embodied interactions as new opportunities for training the Mental Number Line. Regarding multi-player environments we discuss the adaptivity of learning environments needed to ensure balanced success rates in such trainings. As regards embodied interaction, we elaborate on new trainings allowing for bodily experiences of numerical concepts with new motion sensitive input devices and tangible user interfaces combining benefits of physical manipulatives with digitally provided symbolic information. We conclude that the latest developments in computer technology open up new directions for the training of the Mental Number Line in particular and numerical/arithmetical competencies in general.
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multiplication facts and the Mental Number Line evidence from unbounded Number Line estimation
Psychological Research-psychologische Forschung, 2015Co-Authors: Regina M Reinert, Hans-christoph Nuerk, Stefan Huber, K. Orbinian MoellerAbstract:A spatial representation of Number magnitude, aka the Mental Number Line, is considered one of the basic numerical representations. One way to assess it is Number Line estimation (e.g., positioning 43 on a Number Line ranging from 0 to 100). Recently, a new unbounded version of the Number Line estimation task was suggested: without labeled endpoints but a predefined unit, which was argued to provide a purer measure of spatial numerical representations. To further investigate the processes determining estimation performance in the unbounded Number Line task, we used an adapted version with variable units other than 1 to evaluate influences of (i) the size of a given unit and (ii) multiples of the units as target Numbers on participants' estimation pattern. We observed that estimations got faster and more accurate with increasing unit sizes. On the other hand, multiples of a predefined unit were estimated faster, but not more accurately than non-multiples. These results indicate an influence of multiplication fact knowledge on spatial numerical processing.
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on the relation between the Mental Number Line and arithmetic competencies
Quarterly Journal of Experimental Psychology, 2014Co-Authors: Tanja Link, Hans-christoph Nuerk, K. Orbinian MoellerAbstract:In this study, we aimed at investigating whether it is indeed the spatial magnitude representation that links Number Line estimation performance to other basic numerical and arithmetic competencies. Therefore, estimations of 45 fourth-graders in both a bounded and a new unbounded Number Line estimation task (with only a start-point and a unit given) were correlated with their performance in a variety of tasks including addition, subtraction, and Number magnitude comparison. Assuming that both Number Line tasks assess the same underlying Mental Number Line representation, unbounded Number Line estimation should also be associated with other basic numerical and arithmetic competencies. However, results indicated that children's estimation performance in the bounded but not the unbounded Number Line estimation task was correlated significantly with numerical and arithmetic competencies. We conclude that unbounded and bounded Number Line estimation tasks do not assess the same underlying spatial–numerical rep...
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unbounding the Mental Number Line new evidence on children s spatial representation of Numbers
Frontiers in Psychology, 2014Co-Authors: Tanja Link, Hans-christoph Nuerk, Stefan Huber, K. Orbinian MoellerAbstract:Number Line estimation (i.e., indicating the position of a given Number on a physical Line) is a standard assessment of children’s spatial representation of Number magnitude. Importantly, there is an ongoing debate on the question in how far the bounded task version with start and endpoint given (e.g., 0 and 100) might induce specific estimation strategies and thus may not allow for unbiased inferences on the underlying representation. Recently, a new unbounded version of the task was suggested with only the start point and a unit fixed (e.g., the distance from 0 to 1). In adults this task provided a less biased index of the spatial representation of Number magnitude. Yet, so far there are no children data available for the unbounded Number Line estimation task. Therefore, we conducted a cross-sectional study on primary school children performing both, the bounded and the unbounded version of the task. We observed clear evidence for systematic strategic influences (i.e., the consideration of reference points) in the bounded Number Line estimation task for children older than grade two whereas there were no such indications for the unbounded version for any one of the age groups. In summary, the current data corroborate the unbounded Number Line estimation task to be a valuable tool for assessing children's spatial representation of Number magnitude in a systematic and unbiased manner. Yet, similar results for the bounded and the unbounded version of the task for first- and second-graders may indicate that both versions of the task might assess the same underlying representation for relatively younger children - at least in Number ranges familiar to the children assessed. This is of particular importance for inferences about the nature and development of children's magnitude representation.
Marco Zorzi - One of the best experts on this subject based on the ideXlab platform.
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Neglect impairs explicit processing of the Mental Number Line
Frontiers in human neuroscience, 2012Co-Authors: Marco Zorzi, Roberto Marenzi, Mario Bonato, Barbara Treccani, Giovanni Scalambrin, Konstantinos PriftisAbstract:Converging evidence suggests that visuospatial attention plays a pivotal role in numerical processing, especially when the task involves the manipulation of numerical magnitudes. Visuospatial neglect impairs contralesional attentional orienting not only in perceptual but also in numerical space. Indeed, patients with left neglect show a bias towards larger Numbers when Mentally bisecting a numerical interval, as if they were neglecting its leftmost part. In contrast, their performance in parity judgements is unbiased, suggesting a dissociation between explicit and implicit processing of numerical magnitude. Here we further investigate the consequences of these visuospatial attention impairments on numerical processing and their interaction with task demands. Patients with right hemisphere damage, with and without left neglect, were administered both a Number comparison and a parity judgement task that had identical stimuli and response requirements. Neglect patients’ performance was normal in the parity task, when processing of numerical magnitude was implicit, whereas they showed characteristic biases in the Number comparison task, when access to numerical magnitude was explicit. Compared to patients without neglect, they showed an asymmetric distance effect, with slowing of the Number immediately smaller than (i.e., to the left of) the reference and a stronger SNARC effect, particularly for large Numbers. The latter might index an exaggerated effect of Number-space compatibility after ipsilesional (i.e., rightward) orienting in Number space. Thus, the effect of neglect on the explicit processing of numerical magnitude can be understood in terms of both a failure to orient to smaller (i.e., contralesional) magnitudes and a difficulty to disengage from larger (i.e., ipsilesional) magnitudes on the Number Line, which resembles the disrupted pattern of attention orienting in visual space.
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the spatial representation of Numbers evidence from neglect and pseudoneglect
Experimental Brain Research, 2009Co-Authors: Carlo Umiltà, Konstantinos Priftis, Marco ZorziAbstract:The aim of the present paper is to provide an overview of the evidence that links spatial representation with representation of Number magnitude. This aim is achieved by reviewing the literature concerning the Number interval bisection task in patients with left hemispatial neglect and in healthy participants (pseudoneglect). Phenomena like the Spatial Numerical Association of Response Codes (SNARC) effect and the shifts of covert spatial attention caused by Number processing are thought to support the notion that Number magnitude is represented along a spatially organized Mental Number Line. However, the evidence provided by chronometric studies is not univocal and is open to alternative, non-spatial interpretations. In contrast, neuropsychological studies have offered convincing evidence that humans indeed represent Numbers on a Mental Number Line oriented from left to right. Neglect patients systematically misplace the midpoint of a numerical interval they are asked to bisect (e.g., they say that 〈5〉 is halfway between 〈2〉 and 〈6〉) and their mistakes closely resemble the typical pattern found in bisection of true visual Lines. The presence of dissociations between impaired explicit knowledge and spared implicit knowledge supports the notion that neglect produces a deficit in accessing an intact Mental Number Line, rather than a distortion in the representation of that Line. Other results show that the existence of a strong spatial connotation constitutes a specific property of Number representations rather than a general characteristic of all ordered sequences.
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visuospatial priming of the Mental Number Line
Cognition, 2008Co-Authors: Ivilin Stoianov, Carlo Umiltà, Peter Kramer, Marco ZorziAbstract:It has been argued that Numbers are spatially organized along a "Mental Number Line" that facilitates left-hand responses to small Numbers, and right-hand responses to large Numbers. We hypothesized that whenever the representations of visual and numerical space are concurrently activated, interactions can occur between them, before response selection. A spatial prime is processed faster than a numerical target, and consistent with our hypothesis, we found that such a spatial prime affects non-spatial, verbal responses more when the prime follows a numerical target (backward priming) then when it precedes it (forward priming). This finding emerged both in a Number-comparison and a parity judgment task, and cannot be ascribed to a "Spatial-Numerical Association of Response Codes" (SNARC). Contrary to some earlier claims, we therefore conclude that visuospatial-numerical interactions do occur, even before response selection.
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Explicit versus Implicit Processing of Representational Space in Neglect: Dissociations in Accessing the Mental Number Line
Journal of cognitive neuroscience, 2006Co-Authors: Konstantinos Priftis, Francesca Meneghello, Marco Zorzi, Roberto Marenzi, Carlo UmiltàAbstract:The present study investigated the effects of left hemispatial neglect on two tasks activating the Mental Number Line (MNL). Six patients with left neglect performed a Mental Number bisection task and a modified version of the Spatial Numerical Association of Response Codes (SNARC) task. Effects of left neglect were observed in the Number bisection task, but not in the SNARC task. We argue that the dissociation between Number bisection and SNARC resembles, in the representational space of the MNL, previously reported dissociations on neglect between explicit knowledge (assessed by direct tasks) and implicit knowledge (assessed by indirect tasks).
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brain damage neglect disrupts the Mental Number Line
Nature, 2002Co-Authors: Konstantinos Priftis, Marco Zorzi, Carlo UmiltàAbstract:A popular metaphor for the representation of Numbers in the brain is the 'Mental Number Line', in which Numbers are represented in a continuous, quantity-based analogical format. Here we show that patients with hemispatial neglect misplace the midpoint of a numerical interval when asked to bisect it (for example, stating that five is halfway between two and six), with an error pattern that closely resembles the bisection of physical Lines. This new form of representational neglect constitutes strong evidence that the Mental Number Line is more than simply a metaphor, and that its spatial nature renders it functionally isomorphic to physical Lines.
Martin H. Fischer - One of the best experts on this subject based on the ideXlab platform.
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Ocular drift along the Mental Number Line
Psychological Research, 2016Co-Authors: Andriy Myachykov, Rob Ellis, Angelo Cangelosi, Martin H. FischerAbstract:We examined the spontaneous association between Numbers and space by documenting attention deployment and the time course of associated spatial-numerical mapping with and without overt oculomotor responses. In Experiment 1, participants maintained central fixation while listening to Number names. In Experiment 2, they made horizontal target-direct saccades following auditory Number presentation. In both experiments, we continuously measured spontaneous ocular drift in horizontal space during and after Number presentation. Experiment 2 also measured visual-probe-directed saccades following Number presentation. Reliable ocular drift congruent with a horizontal Mental Number Line emerged during and after Number presentation in both experiments. Our results provide new evidence for the implicit and automatic nature of the oculomotor resonance effect associated with the horizontal spatial-numerical mapping mechanism.
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newborn chicks need no Number tricks commentary Number space mapping in the newborn chick resembles humans Mental Number Line
Frontiers in Human Neuroscience, 2015Co-Authors: Samuel Shaki, Martin H. FischerAbstract:The study of numerical ordering abilities in chicks recently reported by Rugani et al. (2015) concluded that “similarly to humans, chicks associate smaller Numbers with the left space and larger Numbers with the right space.” (p. 534). But do their results really show that 3-day-old domestic chicks are aware of both relative and absolute quantities, map them from left to right, and have an “innate Number sense” (Rugani et al., 2015, p. 536)? Rugani et al. (2015) trained newborn chicks to expect food behind a centrally presented occluder and tested them by presenting two laterally displaced occluders (see their Figure Figure11 below). The key manipulation was the amount of black dots shown on both training and test occluders. After seeing five dots at training (in Experiment 1), when the chicks saw two dots on both lateralized test occluders they walked to the left; while seeing eight dots on either side at test biased walking choices to the right. Similarly, after seeing 20 dots at training (in Experiment 2), seeing eight vs. 32 dots at test induced walking to the left vs. right side. Thanks to controlling for non-numerical factors such as area, perimeter and density of the dot patterns (Experiment 3), the authors concluded that newborn chicks associate relatively small Numbers with left space and relatively larger Numbers with right space, in analogy with a vast literature of spatial-numerical associations (SNAs) in humans (recently reviewed by Fischer and Shaki, 2014). Figure 1 (Figure re-used by permission from Rugani et al., 2015): The panels (A,B) differ in numerosity as well as lightness, density, perceptual mass, saliency, and visual complexity. This finding is deemed important because it challenges the view that language is the foundation of symbolic thought, in particular our ability to represent quantities beyond the span of immediate apprehension (subitizing range of 3–4 items; cf. Kaufman et al., 1949). Moreover, it questions the well-established cultural origin of horizontal SNAs (Shaki et al., 2009; Shaki and Fischer, 2014). Despite the endorsement of these points by Brugger (2015) in his associated perspective, we have reason to doubt these conclusions. The authors acknowledged that the results of Experiments 1 and 2 could be accounted for by non-spatial cues as area, perimeter, or density of the displayed dots. They controlled for these confounds with numerosity in two conditions of their third experiment. Specifically, either perimeter and area were held constant, or perimeter and density were held constant, while numerosity varied. However, this means that numerosity co-varied either with density (in the first condition) or with area (in the second condition). Therefore, chicks in all control conditions responded to both numerosity and at least one uncontrolled dimension, as they were in the first and second experiments, too. This methodological detail contains the core of our concern because both density and area are indeed spatially effective cues. Whenever object density was uncontrolled, fewer black dots resulted in reduced perceptual mass or saliency (see Figure Figure1).1). Both of these features are known to be associated with space (Christman and Pinger, 1997; Heath et al., 2005; Friedrich et al., 2014): Denser displays attract attention to the right and this may explain why chicks turn to the left in the presence of fewer dots compared to their training. Similarly, whenever object area was uncontrolled, fewer black dots resulted in lighter occluders (see Figure Figure1).1). There is an established association of light with left (Elias and Robinson, 2005; McDine et al., 2011); this “left-light bias” may explain why chicks turn to the left in the presence of fewer dots compared to their training. Together, these concerns clarify that “current ways to control the visual cues of the Number stimuli are insufficient, as they control only a single variable at the [sic] time” (Gebuis and Reynvoet, 2012, p. 642). A further point of concern is that less and more visually complex patterns are associated with left and right space, respectively (Beaumont, 1985; Heath et al., 2005). This feature co-varied with numerosity and was not even controlled here but it also can explain why chicks turned left or right when they encountered fewer or more dots, respectively, when compared to their training. Therefore, we require replications with reversed contrast and with complexity dissociated from numerosity (cf. Heath et al., 2005)—Will Rugani et al.'s result replicate in the latter and reverse in the former case? Both outcomes would falsify their conclusions. To conclude, newborn chicks know no Number tricks: several non-numerical spatial associations can parsimoniously account for the choices of chicks without invoking the concept of a spatially oriented Mental Number Line. The considerable flexibility of SNAs in humans and their equivalent strength in either direction (Fischer and Shaki, 2014), the as well as some evidence from patients who neglect small Numbers regardless of the lateralization of their spatial deficit (van Dijck et al., 2011, 2012; Aiello et al., 2012, 2013; Pia et al., 2012), argue further against the proposal of Rugani et al. and indicate that SNAs may instead reflect cultural conventions. SNAs obtain with centrally presented numerical information and even in the absence of lateralized responses (Gevers et al., 2010; Fischer and Shaki, 2015), thus making the Mental Number Line a purely conceptual link between Number and space.
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random walks on the Mental Number Line
Experimental Brain Research, 2014Co-Authors: Samuel Shaki, Martin H. FischerAbstract:The direction of influence between conceptual and motor activation, and its relevance for real-life activities, is still unclear. Here, we use the frequently reported association between small/large Numbers and left/right space to investigate this issue during walking. We asked healthy adults to generate random Numbers as they made lateral turns and found that (1) lateral turn decisions are predicted by the last few Numbers generated prior to turning; (2) the intention to turn left/right makes small/large Numbers more accessible; and (3) magnitude but not order of auditorily presented Numbers influences the listener’s turn selection. Our findings document a bidirectional influence between conceptual and motor activation and point to a hierarchically organized conceptual–motor activation.
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Mental Number Line
The Encyclopedia of Cross-Cultural Psychology, 2013Co-Authors: Martin H. FischerAbstract:The speed of processing in simple Number tasks, such as magnitude comparison (“which Number is larger?”), reveals much about the cognitive representation of Numbers. Three effects, in particular, point to a “Mental Number Line” as the universal representation of Number meaning in our minds. First, we usually find that the time to discriminate two Numbers decreases with increasing numerical distance between them: we know that 8 is larger than 2 before we know that 4 is larger than 2. This distance effect holds regardless of Number format (digits, words, dot patterns, Roman numerals), stimulus modality (visual, auditory), or response modality (verbal, button press). Second, if we hold the distance between Numbers constant (as in the pairs 4 − 2 vs. 8 − 6) we need less time to process small than large Numbers, and are also more accurate (the size effect). Finally, varying their spatial arrangement (4 − 2 vs. 2 − 4) often reveals faster responses with smaller Numbers on the left and larger Numbers on the right side. This spatial-numerical association of response codes (SNARC) effect does, however, depend on cultural factors. Keywords: cognition; problem solving
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cultural effects on the Mental Number Line
Journal of Cross-Cultural Psychology, 2011Co-Authors: Silke M. Göbel, Samuel Shaki, Martin H. FischerAbstract:This special issue is the result of a workshop on the cultural effects on the Mental Number Line held in York (U.K.) in July 2009. The workshop was funded by the ExperiMental Psychology Society (www.eps.ac.uk) and the European Society for Cognitive Psychology (www.escop.eu), and we thank both organisations for sponsoring the event. The aims of the workshop were to bring together experiMental psychologists who study effects of cultural variables on numerical cognition, to facilitate insights into the development and flexibility of numerical cognition by comparing across cultures, and to provide an up-to-date cross-disciplinary overview of research into cultural aspects of numerical cognition that encompasses behavioural, observational, Internet-based, and neuroscientific methods. This special issue gives a lively and accurate representation of the breadth and depth of the workshop contributions. Humans are intrinsically driven to represent numerosity in many ways. The “Mental Number Line” in our title is a metaphor for Number representations that are not linguistically mediated but spatial in nature. The most common spatial representation of Numbers in Western societies is a left-to-right arrangement for Numbers of increasing magnitude (such as on rulers). While this is not the only spatial representation of Numbers (think of thermometers, hands, clocks, ...), it seems to have a profound effect on our numerical cognition. This has led to the discovery of the SNARC effect and to the relative neglect of other spatial mappings. Several articles in this special issue illustrate the variety of interactions that emerge between Number representations and cultural preferences over the time course of our enculturation (see Figure 1). Finger counting, for example, is ontogenetically one of the first methods used to represent numerosity. Lindemann, Alipour, and Fischer show cultural differences in finger counting that persist well into adulthood. The question about what causes those differences is at the heart of this special issue. Evidence for two potential causes is presented: Cultural differences might be driven by the direction of reading or by differences in the existence, structure, or use of Number words. Bender and Beller investigate the variability in linguistic structures used in Polynesian and Micronesian languages by documenting the development of those numeration systems and suggest how this development might have influenced spatial representations. Data by Helmreich et al. juxtaposing Germanand Italianspeaking children show that the structure of the numeration system used in a particular language can indeed influence the accuracy of spatial-numerical mappings. And it does not only affect spatial representations: Krinzinger et al., comparing children speaking French, German, or Flemish, show clearly that the consistency of the numeration system has an effect on children’s ease of acquisition of Number words and Number transcoding. Furthermore, Butterworth et al. show that in a culture that has no Number words children use spatial strategies very effectively to solve numerical tasks. They investigated Number processing in aboriginal children in Australia and also report the curious lack of finger counting in this population.
K. Orbinian Moeller - One of the best experts on this subject based on the ideXlab platform.
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computers in mathematics education training the Mental Number Line
Computers in Human Behavior, 2015Co-Authors: K. Orbinian Moeller, Hans-christoph Nuerk, Ursula Fischer, Ulrike CressAbstract:Mental Number Line representation associated with other numerical competencies.Successful computer-based Number Line trainings are reviewed.First focus on socially interactive and adaptive learning environments.Second focus on embodied interactions allowing for bodily experiences of numerical concepts.Latest developments in computer technology open up new directions for numerical trainings. Number magnitude is often described to be represented along a Mental Number Line. In children, the accuracy of this Mental Number Line seems to be associated with other basic numerical/arithmetic competencies. As a consequence, specific Number Line trainings have been developed. Evaluations indicated improvements not only in Number Line accuracy but also other numerical (e.g., magnitude comparison) and arithmetic tasks (e.g., Mental addition) not trained directly. Importantly, this was observed for both board games as well as first computer-supported Number Line trainings. However, computer technology progresses rapidly. In this literature review, we specifically focus on the issues of multi-player learning environments and embodied interactions as new opportunities for training the Mental Number Line. Regarding multi-player environments we discuss the adaptivity of learning environments needed to ensure balanced success rates in such trainings. As regards embodied interaction, we elaborate on new trainings allowing for bodily experiences of numerical concepts with new motion sensitive input devices and tangible user interfaces combining benefits of physical manipulatives with digitally provided symbolic information. We conclude that the latest developments in computer technology open up new directions for the training of the Mental Number Line in particular and numerical/arithmetical competencies in general.
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multiplication facts and the Mental Number Line evidence from unbounded Number Line estimation
Psychological Research-psychologische Forschung, 2015Co-Authors: Regina M Reinert, Hans-christoph Nuerk, Stefan Huber, K. Orbinian MoellerAbstract:A spatial representation of Number magnitude, aka the Mental Number Line, is considered one of the basic numerical representations. One way to assess it is Number Line estimation (e.g., positioning 43 on a Number Line ranging from 0 to 100). Recently, a new unbounded version of the Number Line estimation task was suggested: without labeled endpoints but a predefined unit, which was argued to provide a purer measure of spatial numerical representations. To further investigate the processes determining estimation performance in the unbounded Number Line task, we used an adapted version with variable units other than 1 to evaluate influences of (i) the size of a given unit and (ii) multiples of the units as target Numbers on participants' estimation pattern. We observed that estimations got faster and more accurate with increasing unit sizes. On the other hand, multiples of a predefined unit were estimated faster, but not more accurately than non-multiples. These results indicate an influence of multiplication fact knowledge on spatial numerical processing.
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on the relation between the Mental Number Line and arithmetic competencies
Quarterly Journal of Experimental Psychology, 2014Co-Authors: Tanja Link, Hans-christoph Nuerk, K. Orbinian MoellerAbstract:In this study, we aimed at investigating whether it is indeed the spatial magnitude representation that links Number Line estimation performance to other basic numerical and arithmetic competencies. Therefore, estimations of 45 fourth-graders in both a bounded and a new unbounded Number Line estimation task (with only a start-point and a unit given) were correlated with their performance in a variety of tasks including addition, subtraction, and Number magnitude comparison. Assuming that both Number Line tasks assess the same underlying Mental Number Line representation, unbounded Number Line estimation should also be associated with other basic numerical and arithmetic competencies. However, results indicated that children's estimation performance in the bounded but not the unbounded Number Line estimation task was correlated significantly with numerical and arithmetic competencies. We conclude that unbounded and bounded Number Line estimation tasks do not assess the same underlying spatial–numerical rep...
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unbounding the Mental Number Line new evidence on children s spatial representation of Numbers
Frontiers in Psychology, 2014Co-Authors: Tanja Link, Hans-christoph Nuerk, Stefan Huber, K. Orbinian MoellerAbstract:Number Line estimation (i.e., indicating the position of a given Number on a physical Line) is a standard assessment of children’s spatial representation of Number magnitude. Importantly, there is an ongoing debate on the question in how far the bounded task version with start and endpoint given (e.g., 0 and 100) might induce specific estimation strategies and thus may not allow for unbiased inferences on the underlying representation. Recently, a new unbounded version of the task was suggested with only the start point and a unit fixed (e.g., the distance from 0 to 1). In adults this task provided a less biased index of the spatial representation of Number magnitude. Yet, so far there are no children data available for the unbounded Number Line estimation task. Therefore, we conducted a cross-sectional study on primary school children performing both, the bounded and the unbounded version of the task. We observed clear evidence for systematic strategic influences (i.e., the consideration of reference points) in the bounded Number Line estimation task for children older than grade two whereas there were no such indications for the unbounded version for any one of the age groups. In summary, the current data corroborate the unbounded Number Line estimation task to be a valuable tool for assessing children's spatial representation of Number magnitude in a systematic and unbiased manner. Yet, similar results for the bounded and the unbounded version of the task for first- and second-graders may indicate that both versions of the task might assess the same underlying representation for relatively younger children - at least in Number ranges familiar to the children assessed. This is of particular importance for inferences about the nature and development of children's magnitude representation.
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Extending the Mental Number Line A Review of Multi-Digit Number Processing
Zeitschrift für Psychologie, 2011Co-Authors: Hans-christoph Nuerk, K. Orbinian Moeller, Elise Klein, Klaus Willmes, Martin H. FischerAbstract:Multi-digit Number processing is ubiquitous in our everyday life - even in school, multi-digit Numbers are computed from the first year onward. Yet, many problems children and adults have are about the relation of different digits (for instance with fractions, decimals, or carry effects in multi-digit addition). Cognitive research has mainly focused on single-digit processing, and there is no comprehensive review of the different multi-digit Number processing types and effects. The current review aims to fill this gap. First, we argue that effects observed in single- digit tasks cannot simply be transferred to multi-digit processing. Next, we list 16 effect types and processes which are specific for multi-digit Number processing. We then discuss the development of multi-digit Number processing, its neurocognitive correlates, its cultural or language- related modulation, and finally some models for multi-digit Number processing. We finish with conclusions and perspectives about where multi- digit Number processing research may or should be heading in following years.
Stella F Lourenco - One of the best experts on this subject based on the ideXlab platform.
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spatial numerical associations from a novel paradigm support the Mental Number Line account
Quarterly Journal of Experimental Psychology, 2021Co-Authors: Lauren S Aulet, Sami R Yousif, Stella F LourencoAbstract:Multiple tasks have been used to demonstrate the relation between Numbers and space. The classic interpretation of these directional spatial–numerical associations (d-SNAs) is that they are the pro...
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the developing Mental Number Line does its directionality relate to 5 to 7 year old children s mathematical abilities
Frontiers in Psychology, 2018Co-Authors: Lauren S Aulet, Stella F LourencoAbstract:Spatial representations of Number, such as a left-to-right oriented Mental Number Line, are well documented in Western culture. Yet the functional significance of such a representation remains unclear. To test the prominent hypothesis that a Mental Number Line may support mathematical development, we examined the relation between spatial-numerical associations (SNAs) and math proficiency in 5- to 7-year-old children. We found evidence of SNAs with two tasksparadigms: a non-symbolic magnitude comparison task, and a symbolic ‘Where was The Number?’ (WTN) task. Further, we found a significant correlation between these two tasks, demonstrating convergent validity of the directional Mental Number Line across numerical format. Although there were no significant correlations between children’s SNAs on the WTN task and math ability, children’s SNAs on the magnitude comparison task were negatively correlated with their performance on a measure of cross-modal arithmetic, suggesting that children with a stronger left-to-right oriented Mental Number Line were less competent at cross-modal arithmetic, an effect that held when controlling for age and a set of general cognitive abilities. Despite some evidence for a negative relation between SNAs and math ability in adulthood, we argue that the effect here may reflect task demands specific to the magnitude comparison task, not necessarily an impediment of the Mental Number Line to math performance. We conclude with a discussion of the different properties that characterize a Mental Number Line and how these different properties may relate to mathematical ability.
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probing the Mental Number Line a between task analysis of spatial numerical associations
Cognitive Science, 2015Co-Authors: Chingai Cheung, Vladislav Ayzenberg, Rachel F L Diamond, Sami R Yousif, Stella F LourencoAbstract:The Mental Number Line (MNL) hypothesis is that Numbers are Mentally represented in spatial format, particularly in leftto-right orientation among Westerners. The MNL has received support from various paradigms, but it remains controversial as it is challenged by alternative models. Here we used an individual differences approach to assess spatialnumerical associations (SNAs) across a variety of tasks. The MNL hypothesis predicts correlations across SNA tasks because they should tap a common MNL representation. Control tasks were included to account for effects not specific to SNAs. Correlation analyses revealed significant associations across several SNA tasks, even when controlling for general cognitive abilities or individual differences in response time (RT). These findings provide unique support for the MNL hypothesis, and begin to shed insight on potential explanations that may contribute to variation in the strength of the correlations among SNA tasks.
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when Numbers get heavy is the Mental Number Line exclusively numerical
PLOS ONE, 2013Co-Authors: Kevin J Holmes, Stella F LourencoAbstract:The Mental Number Line, with its left-to-right orientation of increasing numerical values, is often regarded as evidence for a unique connection between space and Number. Yet left-to-right orientation has been shown to extend to other dimensions, consistent with a general magnitude system wherein different magnitudes share neural and conceptual resources. Such observations raise a fundaMental, yet relatively unexplored, question about spatial-numerical associations: What is the nature of the information represented along the Mental Number Line? Here we show that this information is not exclusive to Number, simultaneously accommodating numerical and non-numerical magnitudes. Participants completed the classic SNARC (Spatial-Numerical Association of Response Codes) task while sometimes wearing wrist weights. Weighting the left wrist–thereby linking less and more weight to right and left, respectively–worked against left-to-right orientation of Number, leaving no behavioral trace of the Mental Number Line. Our findings point to the dynamic integration of magnitude dimensions, with spatial organization instantiating representational currency (i.e., more/less relations) shared across magnitudes.
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bisecting the Mental Number Line in near and far space
Brain and Cognition, 2010Co-Authors: Matthew R Longo, Stella F LourencoAbstract:Much evidence suggests that common posterior parietal mechanisms underlie the orientation of attention in physical space and along the Mental Number Line. For example, the small leftward bias (pseudoneglect) found in paper-and-pencil Line bisection is also found when participants "bisect" Number pairs, estimating (without calculating) the Number midway between two others. For bisection of physical Lines, pseudoneglect has been found to shift rightward as Lines are moved from near space (immediately surrounding the body) to far space. We investigated whether the presentation of stimuli in near or far space also modulated spatial attention for the Mental Number Line. Participants bisected physical Lines or Number pairs presented at four distances (60, 120, 180, 240cm). Clear rightward shifts in bias were observed for both tasks. Furthermore, the rate at which this shift occurred in the two tasks, as measured by least-squares regression slopes, was significantly correlated across participants, suggesting that the transition from near to far distances induced a common modulation of lateral attention in physical and numerical space. These results demonstrate a tight coupling between Number and physical space, and show that even such prototypically abstract concepts as Number are modulated by our on-Line interactions with the world.
