scholarly journals Moving along the number line: Operational momentum in nonsymbolic arithmetic

2007 ◽  
Vol 69 (8) ◽  
pp. 1324-1333 ◽  
Author(s):  
Koleen McCrink ◽  
Stanislas Dehaene ◽  
Ghislaine Dehaene-Lambertz
Keyword(s):  
Number Line ◽  
Operational Momentum

scholarly journals Perceived Motion and Operational Momentum: How Speed, Distance, and Time Influence Two-Digit Arithmetic

2021 ◽  
Vol 12 ◽  
Author(s):  
Maciej Haman ◽  
Hubert Młodzianowski ◽  
Michał Gołȩbiowski
Keyword(s):  
Spatial Attention ◽  
Mental Arithmetic ◽  
Arithmetic Operation ◽  
Internal Representation ◽  
Representational Momentum ◽  
Number Line ◽  
Mental Number Line ◽  
Moving Object ◽  
Momentum Effect ◽  
Operational Momentum

Operational momentum was originally defined as a bias toward underestimating outcomes of subtraction and overestimating outcomes of addition. It was suggested that these estimation biases are due to leftward attentional shift along the mental number-line (spatially organized internal representation of number) in subtraction and rightward shift in addition. This assumes the use of “recycled” mechanisms of spatial attention, including “representational momentum” – a tendency to overestimate future position of a moving object, which compensates for the moving object’s shift during preparation of a reaction. We tested a strong version of this assumption directly, priming two-digit addition and subtraction problems with leftward and rightward motion of varied velocity, as velocity of the tracked object was found to be a factor in determining representational momentum effect size. Operands were subsequently moving across the computer screen, and the participants’ task was to validate an outcome proposed at the end of the event, which was either too low, correct, or too high. We found improved accuracy in detecting too-high outcomes of addition, as well as complex patterns of interactions involving arithmetic operation, outcome option, speed, and direction of motion, in the analysis of reaction times. These results significantly extend previous evidence for the involvement of spatial attention in mental arithmetic, showing movement of the external attention focus as a factor directing internal attention in processing numerical information. As a whole, however, the results are incompatible with expectations derived from the strong analogy between operational and representational momenta. We suggest that the full model may be more complex than simply “moving attention along the mental number-line” as a direct counterpart of attention directed at a moving object.

Moving on Down the (Mental Number) Line

2012 ◽  
Author(s):  
David Landy ◽  
Zachary J. Davis ◽  
Brian M. Guay ◽  
Megan L. Delaunay ◽  
Arthur Charlesworth ◽  
...  
Keyword(s):  
Number Line ◽  
Mental Number Line

The relationship between number line estimation and arithmetic competencies depends on age, operation and skill

2013 ◽  
Author(s):  
Julia Bahnmueller ◽  
Stefan Huber ◽  
Korbinian Moeller ◽  
Hans-Christoph Nuerk
Keyword(s):  
Number Line ◽  
Number Line Estimation ◽  
The Relationship

The Development of the Mental Representation of Numbers 0-10 in Elementary School Children

2020 ◽  
Author(s):  
Anat Feldman ◽  
Michael Shmueli ◽  
Dror Dotan ◽  
Joseph Tzelgov ◽  
Andrea Berger
Keyword(s):  
Sixth Grade ◽  
Number Line ◽  
Number Representation ◽  
Large Numbers ◽  
Position Task ◽  
Sigmoidal Curve ◽  
Anchor Points ◽  
The Right ◽  
Line P ◽  
Best Fit

In recent years, there has been growing interest in the development of mental number line (MNL) representation examined using a number-to-position task. In the present study, we investigated the development of number representation on a 0-10 number line using a computerized version of the number-to-position task on a touchscreen, with restricted response time; 181 children from first through sixth grade were tested. We found that the pattern of estimated number position on the physical number line was best fit by the sigmoidal curve function–which was characterized by underestimation of small numbers and overestimation of large numbers–and that the breakpoint changed with age. Moreover, we found that significant developmental leaps in MNL representation occurred between the first and second grades and again between the second and third grades, which was reflected in the establishment of the right endpoint and the number 5 as anchor points, yielding a more accurate placement of other numbers along the number line.

EXPRESS: Spatial-numerical associations from a novel paradigm support the Mental Number Line account

2021 ◽  
pp. 174702182110087
Author(s):  
Lauren Aulet ◽  
Sami R Yousif ◽  
Stella Lourenco
Keyword(s):  
Memory Task ◽  
Verbal Working Memory ◽  
Number Line ◽  
Mental Number Line ◽  
Task Demands ◽  
Numerical Magnitude ◽  
The Novel ◽  
Alternative Account ◽  
Subject Design ◽  
Multiple Tasks

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 product of a mental number line (MNL), in which numerical magnitude is intrinsically associated with spatial position. The alternative account is that d-SNAs reflect task demands, such as explicit numerical judgments and/or categorical responses. In the novel ‘Where was The Number?’ task, no explicit numerical judgments were made. Participants were simply required to reproduce the location of a numeral within a rectangular space. Using a between-subject design, we found that numbers, but not letters, biased participants’ responses along the horizontal dimension, such that larger numbers were placed more rightward than smaller numbers, even when participants completed a concurrent verbal working memory task. These findings are consistent with the MNL account, such that numbers specifically are inherently left-to-right oriented in Western participants.

Learning Improper Fractions with the Number Line and the Area Model

2021 ◽  
pp. 1-23
Author(s):  
Jing Tian ◽  
Victoria Bartek ◽  
Maya Z. Rahman ◽  
Elizabeth A. Gunderson
Keyword(s):  
Number Line ◽  
Area Model

Improving Struggling Fifth-Grade Students’ Understanding of Fractions: A Randomized Controlled Trial of an Intervention That Stresses Both Concepts and Procedures

2021 ◽  
pp. 001440292110088
Author(s):  
Madhavi Jayanthi ◽  
Russell Gersten ◽  
Robin F. Schumacher ◽  
Joseph Dimino ◽  
Keith Smolkowski ◽  
...  
Keyword(s):  
Randomized Controlled Trial ◽  
Explicit Instruction ◽  
Controlled Trial ◽  
Number Line ◽  
Randomized Controlled ◽  
Fifth Grade Students ◽  
Linear Representations ◽  
Mathematical Explanations ◽  
Grade 5 ◽  
Number Line Estimation

Using a randomized controlled trial, we examined the effect of a fractions intervention for students experiencing mathematical difficulties in Grade 5. Students who were eligible for the study ( n = 205) were randomly assigned to intervention and comparison conditions, blocked by teacher. The intervention used systematic, explicit instruction and relied on linear representations (e.g., Cuisenaire Rods and number lines) to demonstrate key fractions concepts. Enhancing students’ mathematical explanations was also a focus. Results indicated that intervention students significantly outperformed students from the comparison condition on measures of fractions proficiency and understanding ( g = 0.66–0.78), number line estimation ( g = 0.80–1.08), fractions procedures ( g = 1.07), and explanation tasks ( g = 0.68–1.23). Findings suggest that interventions designed to include explicit instruction, along with consistent use of the number line and opportunities to explain reasoning, can promote students’ proficiency and understanding of fractions.

Task beliefs and the voluntary use of the empty number line in third-grade subtraction and addition

2021 ◽  
Vol 106 (2) ◽  
pp. 231-249
Author(s):  
Jorine A. Vermeulen ◽  
Anton Béguin ◽  
Theo J. H. M. Eggen
Keyword(s):  
Number Line ◽  
Third Grade
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