scholarly journals Don’t eliminate the negative: Influences of negative number magnitude knowledge on algebra performance and learning.

2020 ◽  
Vol 112 (2) ◽  
pp. 384-396
Author(s):  
Laura K. Young ◽  
Julie L. Booth
Keyword(s):  
Negative Number ◽  
Number Magnitude

scholarly journals Student Magnitude Knowledge of Negative Numbers

2015 ◽  
Vol 1 (1) ◽  
pp. 38-55 ◽  
Author(s):  
Laura K. Young ◽  
Julie L. Booth
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Magnitude Estimation ◽  
Similar Pattern ◽  
Number Line ◽  
Negative Number ◽  
School Students ◽  
Negative Numbers ◽  
Number Magnitude ◽  
Linear Representations

Numerous studies have demonstrated the relevance of magnitude estimation skills for mathematical proficiency, but little research has explored magnitude estimation with negative numbers. In two experiments the current study examined middle school students’ magnitude knowledge of negative numbers with number line tasks. In Experiment 1, both 6th (n = 132) and 7th grade students (n = 218) produced linear representations on a -10,000 to 0 scale, but the 7th grade students’ estimates were more accurate and linear. In Experiment 2, the 7th grade students also completed a -1,000 to 1,000 number line task; these results also indicated that students are linear for both negative and positive estimates. When comparing the estimates of negative and positive numbers, analyses illustrated that estimates of negative numbers are less accurate than those of positive numbers, but using a midpoint strategy improved negative estimates. These findings suggest that negative number magnitude knowledge follows a similar pattern to positive numbers, but the estimation performance of negatives lags behind that of positives.

Exploring the Boundaries of the Number–Temporal Order Association

2015 ◽  
Vol 62 (3) ◽  
pp. 198-205 ◽  
Author(s):  
Dana Ganor-Stern
Keyword(s):  
Embodied Cognition ◽  
Mental Representation ◽  
Temporal Order ◽  
Past Research ◽  
Numerical Comparison ◽  
Negative Number ◽  
Comparison Task ◽  
Negative Numbers ◽  
The Past

Past research has shown that numbers are associated with order in time such that performance in a numerical comparison task is enhanced when number pairs appear in ascending order, when the larger number follows the smaller one. This was found in the past for the integers 1–9 ( Ben-Meir, Ganor-Stern, & Tzelgov, 2013 ; Müller & Schwarz, 2008 ). In the present study we explored whether the advantage for processing numbers in ascending order exists also for fractions and negative numbers. The results demonstrate this advantage for fraction pairs and for integer-fraction pairs. However, the opposite advantage for descending order was found for negative numbers and for positive-negative number pairs. These findings are interpreted in the context of embodied cognition approaches and current theories on the mental representation of fractions and negative numbers.

scholarly journals Number magnitude to finger mapping is disembodied and topological

2011 ◽  
Vol 209 (3) ◽  
pp. 395-400 ◽  
Author(s):  
Myrthe A. Plaisier ◽  
Jeroen B. J. Smeets
Keyword(s):  
Number Magnitude

What does the crowd think? How online comments and popularity metrics affect news credibility and issue importance

2017 ◽  
Vol 20 (8) ◽  
pp. 3068-3083 ◽  
Author(s):  
T Franklin Waddell
Keyword(s):  
News Media ◽  
Indirect Pathway ◽  
Negative Number ◽  
Study Results ◽  
Online Comments ◽  
News Credibility ◽  
Reader Comments ◽  
Construct Accessibility ◽  
Main Model ◽  
Issue Importance

Online comments hold the potential to promote positive deliberative outcomes, although past work has also shown that comments can have undesired effects when the sentiment of the crowd turns negative. Does the presence of comments possibly bolster or interfere with the reception and traditional functions of news media? Informed by the Modality-Agency-Interactivity-Navigability (MAIN) model, an online experiment tested the effect of reader comments (positive vs negative), number of “re-tweets” and “likes” (low vs high), and coverage frequency (infrequent vs frequent) on news credibility and issue importance. Negative reader comments (relative to positive comments) decreased message credibility and issue importance through the sequential indirect pathway of bandwagon perceptions, attention, and construct accessibility. Study results suggest that the traditional functions of news media may be hindered by audience incivility.

Internal number magnitude representation is not holistic, either

2009 ◽  
Vol 21 (5) ◽  
pp. 672-685 ◽  
Author(s):  
K. Moeller ◽  
H.-C. Nuerk ◽  
K. Willmes
Keyword(s):  
Magnitude Representation ◽  
Number Magnitude

scholarly journals The association between number magnitude and space is dependent on notation: Evidence from an adaptive perceptual orientation task

2019 ◽  
Vol 5 (1) ◽  
pp. 38-54
Author(s):  
Tianwei Gong ◽  
Baichen Li ◽  
Limei Teng ◽  
Zijun Zhou ◽  
Xuefei Gao ◽  
...  
Keyword(s):  
Judgment Task ◽  
Snarc Effect ◽  
Number Word ◽  
Reaction Time Difference ◽  
Number Words ◽  
Number Magnitude ◽  
Spatial Response ◽  
Orientation Task ◽  
Arabic Digits ◽  
Perceptual Orientation

Research on adults' numerical abilities suggests that number representations are spatially oriented. This association of numbers with spatial response is referred to as the SNARC (i.e., spatial–numerical association of response codes) effect. The notation-independence hypothesis of numeric processing predicts that the SNARC effect will not vary with notation (e.g., Arabic vs. number word). To test such assumption, the current study introduced an adaptive experimental procedure based on a simple perceptual orientation task that can automatically smooth out the mean reaction time difference between Arabic digits and traditional Chinese number. We found that the SNARC effect interacted with notation, showing a SNARC effect for Arabic digits, but not for verbal number words. The results of this study challenged the commonly held view that notation does not affect numerical processes associated with spatial representations. We introduced a parallel model to explain the notation-dependent SNARC effect in the perceptual orientation judgment task.

scholarly journals Beyond Natural Numbers: Negative Number Representation in Parietal Cortex

2012 ◽  
Vol 6 ◽  
Author(s):  
Kristen P. Blair ◽  
Miriam Rosenberg-Lee ◽  
Jessica M. Tsang ◽  
Daniel L. Schwartz ◽  
Vinod Menon
Keyword(s):  
Parietal Cortex ◽  
Number Representation ◽  
Natural Numbers ◽  
Negative Number

The large-scale structure of homogeneous turbulence

1967 ◽  
Vol 27 (3) ◽  
pp. 581-593 ◽  
Author(s):  
P. G. Saffman
Keyword(s):  
Large Scale ◽  
Isotropic Turbulence ◽  
Homogeneous Turbulence ◽  
Wave Number ◽  
Initial Instant ◽  
Force System ◽  
Correlation Tensor ◽  
Number Magnitude ◽  
Small Wave Number ◽  
Conservation Of Momentum

A field of homogeneous turbulence generated at an initial instant by a distribution of random impulsive forces is considered. The statistical properties of the forces are assumed to be such that the integral moments of the cumulants of the force system all exist. The motion generated has the property that at the initial instant\[ E(\kappa) = C\kappa^2 + o(\kappa^2), \]whereE(k) is the energy spectrum function,kis the wave-number magnitude, andCis a positive number which is not in general zero. The corresponding forms of the velocity covariance spectral tensor and correlation tensor are determined. It is found that the terms in the velocity covarianceRij(r) areO(r−3) for large values of the separation magnituder.An argument based on the conservation of momentum is used to show thatCis a dynamical invariant and that the forms of the velocity covariance at large separation and the spectral tensor at small wave number are likewise invariant. For isotropic turbulence, the Loitsianski integral diverges but the integral\[ \int_0^{\infty} r^2R(r)dr = \frac{1}{2}\pi C \]exists and is invariant.

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