scholarly journals Charting the role of the number line in mathematical development

2013 ◽  
Vol 4 ◽  
Author(s):  
Jo-Anne LeFevre ◽  
Carolina Jimenez Lira ◽  
Carla Sowinski ◽  
Ozlem Cankaya ◽  
Deepthi Kamawar ◽  
...  
Keyword(s):  
Number Line ◽  
Mathematical Development

scholarly journals How do different aspects of spatial skills relate to early arithmetic and number line estimation?

2017 ◽  
Vol 3 (2) ◽  
pp. 309-343 ◽  
Author(s):  
Véronique Cornu ◽  
Caroline Hornung ◽  
Christine Schiltz ◽  
Romain Martin
Keyword(s):  
Spatial Orientation ◽  
Verbal Working Memory ◽  
Number Line ◽  
Kindergarten Children ◽  
Hierarchical Regression ◽  
Spatial Skills ◽  
Estimation Task ◽  
Mathematical Development ◽  
Number Line Estimation

The present study investigated the predictive role of spatial skills for arithmetic and number line estimation in kindergarten children (N = 125). Spatial skills are known to be related to mathematical development, but due to the construct’s non-unitary nature, different aspects of spatial skills need to be differentiated. In the present study, a spatial orientation task, a spatial visualization task and visuo-motor integration task were administered to assess three different aspects of spatial skills. Furthermore, we assessed counting abilities, knowledge of Arabic numerals, quantitative knowledge, as well as verbal working memory and verbal intelligence in kindergarten. Four months later, the same children performed an arithmetic and a number line estimation task to evaluate how the abilities measured at Time 1 predicted early mathematics outcomes. Hierarchical regression analysis revealed that children’s performance in arithmetic was predicted by their performance on the spatial orientation and visuo-motor integration task, as well as their knowledge of the Arabic numerals. Performance in number line estimation was significantly predicted by the children’s spatial orientation performance. Our findings emphasize the role of spatial skills, notably spatial orientation, in mathematical development. The relation between spatial orientation and arithmetic was partially mediated by the number line estimation task. Our results further show that some aspects of spatial skills might be more predictive of mathematical development than others, underlining the importance to differentiate within the construct of spatial skills when it comes to understanding numerical development.

The role of visual experience for spatial numerical associations

2012 ◽  
Vol 25 (0) ◽  
pp. 222 ◽  
Author(s):  
Michael J. Proulx ◽  
Achille Pasqualotto ◽  
Shuichiro Taya
Keyword(s):  
Visual Experience ◽  
Opposite Effect ◽  
Random Number Generation ◽  
Number Line ◽  
Mental Number Line ◽  
Generation Task ◽  
Congenitally Blind ◽  
Left And Right ◽  
The Right

The topographic representation of space interacts with the mental representation of number. Evidence for such number–space relations have been reported in both synaesthetic and non-synaesthetic participants. Thus far most studies have only examined related effects in sighted participants. For example, the mental number line increases in magnitude from left to right in sighted individuals (Loetscher et al., 2008, Curr. Biol.). What is unclear is whether this association arises from innate mechanisms or requires visual experience early in life to develop in this way. Here we investigated the role of visual experience for the left to right spatial numerical association using a random number generation task in congenitally blind, late blind, and blindfolded sighted participants. Participants orally generated numbers randomly whilst turning their head to the left and right. Sighted participants generated smaller numbers when they turned their head to the left than to the right, consistent with past results. In contrast, congenitally blind participants generated smaller numbers when they turned their head to the right than to the left, exhibiting the opposite effect. The results of the late blind participants showed an intermediate profile between that of the sighted and congenitally blind participants. Visual experience early in life is therefore necessary for the development of the spatial numerical association of the mental number line.

scholarly journals Sharing a mental number line across individuals? The role of body position and empathy in joint numerical cognition

2018 ◽  
Vol 72 (7) ◽  
pp. 1732-1740 ◽  
Author(s):  
Matthias Hartmann ◽  
Martin H Fischer ◽  
Fred W Mast
Keyword(s):  
Numerical Cognition ◽  
Body Position ◽  
Random Number Generation ◽  
Number Line ◽  
Mental Number Line ◽  
Response Level ◽  
Spatial Reference ◽  
Mediating Role ◽  
Spatial Reference Frame

A growing body of research shows that the human brain acts differently when performing a task together with another person than when performing the same task alone. In this study, we investigated the influence of a co-actor on numerical cognition using a joint random number generation (RNG) task. We found that participants generated relatively smaller numbers when they were located to the left (vs. right) of a co-actor (Experiment 1), as if the two individuals shared a mental number line and predominantly selected numbers corresponding to their relative body position. Moreover, the mere presence of another person on the left or right side or the processing of numbers from loudspeaker on the left or right side had no influence on the magnitude of generated numbers (Experiment 2), suggesting that a bias in RNG only emerged during interpersonal interactions. Interestingly, the effect of relative body position on RNG was driven by participants with high trait empathic concern towards others, pointing towards a mediating role of feelings of sympathy for joint compatibility effects. Finally, the spatial bias emerged only after the co-actors swapped their spatial position, suggesting that joint spatial representations are constructed only after the spatial reference frame became salient. In contrast to previous studies, our findings cannot be explained by action co-representation because the consecutive production of numbers does not involve conflict at the motor response level. Our results therefore suggest that spatial reference coding, rather than motor mirroring, can determine joint compatibility effects. Our results demonstrate how physical properties of interpersonal situations, such as the relative body position, shape seemingly abstract cognition.

Order and Magnitude Share a Common Representation in Parietal Cortex

2009 ◽  
Vol 21 (11) ◽  
pp. 2114-2120 ◽  
Author(s):  
Michael S. Franklin ◽  
John Jonides
Keyword(s):  
Distance Effect ◽  
Number Line ◽  
Judgment Task ◽  
Mental Number Line ◽  
Numerical Magnitude ◽  
Intraparietal Sulcus ◽  
Ordinal Information ◽  
Common Representation ◽  
Distance Effects

The role of the intraparietal sulcus (IPS) in the representation of numerical magnitude is well established. Recently, there has also been speculation that the IPS is involved in the representation of ordinal information as well. These claims, however, overlook the fact that all neuroimaging paradigms in which participants make judgments about either magnitude and/or order result in a behavioral distance effect (i.e., the comparison is easier when the stimuli span a greater distance). This leaves open two possibilities: It may be that activation of the IPS is due to the mechanism that yields distance effects, or it may be that the IPS is involved in the representation of information about both magnitude and order. The current study used fMRI to compare a magnitude task in which participants show distance effects to an order-judgment task that yields reverse-distance effects. The results reveal activation of the IPS for both the magnitude and order tasks that is based on participants' strategies as opposed to the actual distance between the numbers. This leads to the conclusion that the IPS represents a mental number line, and that accessing this line can lead to distance effects when participants compare magnitudes and to reverse-distance effects when participants check for order.

scholarly journals Cognitive processes underlying arithmetical skills in primary school: the role of fluency, handwriting, number line and number acuity

2018 ◽  
pp. 115-138
Author(s):  
Paolo Stievano ◽  
Davide M. Cammisuli ◽  
Silvia Michetti ◽  
Chiara Ceccolin ◽  
Giovanni Anobile
Keyword(s):  
Primary School ◽  
Cognitive Processes ◽  
Number Line

scholarly journals EXPRESS: The Association of Basic Numerical Abilities and Math Achievement: The Mediating Role of Visuospatial and Arithmetical Abilities

2021 ◽  
pp. 174702182110400
Author(s):  
Franziska Rebholz ◽  
Jessika Golle ◽  
Korbinian Moeller
Keyword(s):  
Number Line ◽  
Mathematical Achievement ◽  
School Students ◽  
Mediating Role ◽  
Solution Strategies ◽  
Domain Specific ◽  
Numerical Abilities ◽  
Visuospatial Abilities ◽  
Number Line Estimation

Basic numerical abilities such as number line estimation have been observed repeatedly to be associated with mathematical achievement. Recently, it was argued that the association between basic numerical abilities and mathematical achievement is fully mediated by visuospatial abilities. However, arithmetical abilities have not yet been considered as influencing this association, even though solution strategies in number line estimation as well as mathematical achievement often involve arithmetical procedures. Therefore, we investigated the mediating role of arithmetical and visuospatial abilities on the association between number line estimation and mathematical achievement in a sample of n = 599 German elementary school students. Results indicated that arithmetical abilities as well as visuospatial abilities mediated the association between number line estimation and mathematical achievement. However, neither visuospatial nor arithmetical abilities fully mediated the association between number line estimation and mathematical achievement when considered in isolation. This substantiates the relevance of the intertwined development of visuospatial and arithemtical abilities as well as basic numerical abilities such as number line estimation (i.e. the combination of domain-specific numerical and domain-general abilities) driving mathematical achievement.

A Case of Units

2003 ◽  
Vol 9 (7) ◽  
pp. 397-399
Author(s):  
Christopher M. Kribs-Zaleta ◽  
D'Lynn Bradshaw
Keyword(s):  
Young Children ◽  
Learning Opportunities ◽  
School Mathematics ◽  
Learning Potential ◽  
Mathematical Development ◽  
Great Learning ◽  
The World ◽  
Principles And Standards ◽  
Children’S Work

Young children learn by playing, and they first learn mathematics through exploration that develops naturally from their curiosity and experiences. They count, build, draw, model, and measure the world around them. The informal origins of their first mathematical insights remain an important link to the role of context in learning at any age. It is especially important for teachers to know this, in order to be alert to learning opportunities that arise. By paying attention to the details in students' conversations, we can develop the habit of listening to their mathematical discoveries. Encouraging and focusing these discoveries often releases the great learning potential inside students. Principles and Standards for School Mathematics (NCTM 2000) elaborates on the idea of play being children's work by observing, “Adults support young children's diligence and mathematical development when they direct attention to the mathematics children use in their play, challenge them to solve problems, and encourage their persistence” (p. 74).

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