Holistic representation of negative numbers: Evidence from duration comparison tasks

2019 ◽  
Vol 193 ◽  
pp. 123-131 ◽  
Author(s):  
Jie Zhang ◽  
Wenfeng Feng ◽  
Zhijie Zhang
2010 ◽  
Vol 63 (10) ◽  
pp. 1969-1981 ◽  
Author(s):  
Dana Ganor-Stern ◽  
Michal Pinhas ◽  
Arava Kallai ◽  
Joseph Tzelgov

Author(s):  
Dana Ganor-Stern ◽  
Joseph Tzelgov

Abstract. The goal of the present study was to disentangle two possible representations of negative numbers - the holistic representation, where absolute magnitude is integrated with polarity; and the components representation, where absolute magnitude is stored separately from polarity. Participants' performance was examined in two tasks involving numbers from -100 to 100. In the numerical comparison task, participants had to decide which number of a pair was numerically larger/smaller. In the number line task, participants were presented with a spatial number line on which they had to place a number. The results of both tasks support the components representation of negative numbers. The findings suggest that processing of negative numbers does not involve retrieval of their meaning from memory, but rather the integration of the polarity sign with the digits' magnitudes.


Author(s):  
Dana Ganor-Stern

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.


2017 ◽  
Vol 58 (3) ◽  
pp. 313-342 ◽  
Author(s):  
Barbara S. Held

The positive/negative distinction works well in many fields—for example, in mathematics negative numbers hold their own, and in medical pathology negative results are usually celebrated. But in positive psychology negativity should be replaced with positivity for flourishing/optimal functioning to occur. That the designation of the psychological states and processes deemed positive (good/desirable) and negative (bad/undesirable) is made a priori, independent of circumstantial particularity, both intrapersonal and interpersonal, does not seem to bother positive psychologists. But it should, as it results in conceptual muddles and dead ends that cannot be solved within their conceptual framework of positivity and negativity. Especially problematic is an ambiguity I find in positive psychologists’ a priori and a posteriori understandings of positivity and negativity, an ambiguity about constitutive and causal relations that pervades their science and the conclusions drawn from it. By eliminating their a priori dichotomy of positivity and negativity, positive psychologists might well find themselves in a better position to put back together the psychological reality that they have fractured in their ontologically dubious move of carving up psychological reality a priori into positive and negative phenomena. They then might find themselves better placed to “broaden and build” their own science of flourishing.


2021 ◽  
Vol 39 (1) ◽  
pp. 65-82
Author(s):  
Stephen Phillippi ◽  
Casey L. Thomas ◽  
Yilin Yoshida ◽  
Hasheemah Afaneh

SAGE Open ◽  
2016 ◽  
Vol 6 (4) ◽  
pp. 215824401667137 ◽  
Author(s):  
Judah Paul Makonye ◽  
Josiah Fakude

The study focused on the errors and misconceptions that learners manifest in the addition and subtraction of directed numbers. Skemp’s notions of relational and instrumental understanding of mathematics and Sfard’s participation and acquisition metaphors of learning mathematics informed the study. Data were collected from 35 Grade 8 learners’ exercise book responses to directed numbers tasks as well as through interviews. Content analysis was based on Kilpatrick et al.’s strands of mathematical proficiency. The findings were as follows: 83.3% of learners have misconceptions, 16.7% have procedural errors, 67% have strategic errors, and 28.6% have logical errors on addition and subtraction of directed numbers. The sources of the errors seemed to be lack of reference to mediating artifacts such as number lines or other real contextual situations when learning to deal with directed numbers. Learners seemed obsessed with positive numbers and addition operation frames—the first number ideas they encountered in school. They could not easily accommodate negative numbers or the subtraction operation involving negative integers. Another stumbling block seemed to be poor proficiency in English, which is the language of teaching and learning mathematics. The study recommends that building conceptual understanding on directed numbers and operations on them must be encouraged through use of multirepresentations and other contexts meaningful to learners. For that reason, we urge delayed use of calculators.


Perception ◽  
1978 ◽  
Vol 7 (1) ◽  
pp. 91-96 ◽  
Author(s):  
Donald G Jamieson ◽  
William M Petrusic

The accuracy of many perceptual comparisons depends greatly on the order in which the to-be-compared stimuli are presented. With comparisons of durations around 300 ms, these presentation-order effects do not diminish, even with extended practice, when feedback about response accuracy is withheld. Providing such feedback greatly diminishes presentation-order effects and coincidentally produces substantial increases in response accuracy. The feedback acts in part through inducing response biases and in part through changes in sensitivity. The contradiction between studies which report time-order errors in duration comparison and those which do not is attributable to differences in the use of information feedback.


1968 ◽  
Vol 11 (1) ◽  
pp. 73-77 ◽  
Author(s):  
Cheng-Ming Lee

Let be a non-decreasing sequence of non-negative numbers, and let U∘=0. Then we haveYang [3] proved the following integral inequality:If y(x) is absolutely continuous on a≤x≤X, with y(a) = 0, then


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