The unique and shared contributions of arithmetic operation understanding and numerical magnitude representation to children’s mathematics achievement

2017 ◽  
Vol 164 ◽  
pp. 68-86 ◽  
Author(s):  
Terry Tin-Yau Wong
Keyword(s):  
Mathematics Achievement ◽  
Arithmetic Operation ◽  
Numerical Magnitude ◽  
Magnitude Representation ◽  
Numerical Magnitude Representation

The case for a notation-independent representation of number

2009 ◽  
Vol 32 (3-4) ◽  
pp. 333-335 ◽  
Author(s):  
Stanislas Dehaene
Keyword(s):  
Empirical Evidence ◽  
Numerical Magnitude ◽  
Subliminal Priming ◽  
Magnitude Representation ◽  
Modality Effects ◽  
Automatic Activation

AbstractCohen Kadosh & Walsh (CK&W) neglect the solid empirical evidence for a convergence of notation-specific representations onto a shared representation of numerical magnitude. Subliminal priming reveals cross-notation and cross-modality effects, contrary to CK&W's prediction that automatic activation is modality and notation-specific. Notation effects may, however, emerge in the precision, speed, automaticity, and means by which the central magnitude representation is accessed.

scholarly journals Relational quantitative reasoning in kindergarten predicts mathematical achievement in third grade

2016 ◽  
Vol 2 (2) ◽  
pp. 77-90 ◽  
Author(s):  
Lennart Schalk ◽  
Henrik Saalbach ◽  
Roland H. Grabner ◽  
Elsbeth Stern
Keyword(s):  
Elementary School ◽  
Mathematical Achievement ◽  
Quantitative Reasoning ◽  
Third Grade ◽  
Outcome Variable ◽  
Numerical Magnitude ◽  
Long Term Effects ◽  
Domain Specific ◽  
Reading Abilities ◽  
Numerical Magnitude Representation

Tremendous variation in elementary school children’s mathematical achievement can partly be traced back to differences in early domain-specific quantitative competencies. While previous research mainly focused on numerical magnitude representation and counting, we tested the long-term effects of relational quantitative reasoning. Before children (N = 51) entered school (i.e. at age 5-6), we assessed this competence with a test that required no knowledge about Arabic numerals. Two and a half years later, when children were in third grade of elementary school, we gauged mathematical achievement, general reasoning ability, and reading skills. A multiple regression analysis with mathematical achievement as outcome variable revealed a small but unique impact of children’s relational quantitative reasoning in kindergarten on their later mathematical achievement after controlling for general reasoning and reading abilities. Thus, a considerable amount of individual differences in mathematics achievement in elementary school results from differences in early relational quantity understanding that emerge before systematic instruction starts.

scholarly journals Is Order the Defining Feature of Magnitude Representation? An ERP Study on Learning Numerical Magnitude and Spatial Order of Artificial Symbols

PLoS ONE ◽  
2012 ◽  
Vol 7 (11) ◽  
pp. e49565 ◽  
Author(s):  
Hui Zhao ◽  
Chuansheng Chen ◽  
Hongchuan Zhang ◽  
Xinlin Zhou ◽  
Leilei Mei ◽  
...  
Keyword(s):  
Numerical Magnitude ◽  
Spatial Order ◽  
Magnitude Representation

scholarly journals Representation of numerical magnitude in math-anxious individuals

2018 ◽  
Vol 72 (3) ◽  
pp. 424-435 ◽  
Author(s):  
Àngels Colomé
Keyword(s):  
Stroop Task ◽  
Size Effects ◽  
Math Anxiety ◽  
Group Differences ◽  
Numerical Magnitude ◽  
Magnitude Representation ◽  
Distance Effects ◽  
Equivalent Distance

Larger distance effects in high math-anxious individuals (HMA) performing comparison tasks have previously been interpreted as indicating less precise magnitude representation in this population. A recent study by Dietrich, Huber, Moeller, and Klein limited the effects of math anxiety to symbolic comparison, in which they found larger distance effects for HMA, despite equivalent size effects. However, the question of whether distance effects in symbolic comparison reflect the properties of the magnitude representation or decisional processes is currently under debate. This study was designed to further explore the relation between math anxiety and magnitude representation through three different tasks. HMA and low math-anxious individuals (LMA) performed a non-symbolic comparison, in which no group differences were found. Furthermore, we did not replicate previous findings in an Arabic digit comparison, in which HMA individuals showed equivalent distance effects to their LMA peers. Lastly, there were no group differences in a counting Stroop task. Altogether, an explanation of math anxiety differences in terms of less precise magnitude representation is not supported.

Relations of different types of numerical magnitude representations to each other and to mathematics achievement

2014 ◽  
Vol 123 ◽  
pp. 53-72 ◽  
Author(s):  
Lisa K. Fazio ◽  
Drew H. Bailey ◽  
Clarissa A. Thompson ◽  
Robert S. Siegler
Keyword(s):  
Mathematics Achievement ◽  
Numerical Magnitude ◽  
Different Types

The Flip Side of the Auditory Spatial Selection Benefit

2015 ◽  
Vol 62 (1) ◽  
pp. 66-74 ◽  
Author(s):  
Iring Koch ◽  
Vera Lawo
Keyword(s):  
Task Switching ◽  
Auditory Task ◽  
Numerical Magnitude ◽  
Attention Shifting ◽  
Gender Selection ◽  
Spatial Selection ◽  
Number Words ◽  
Switch Costs ◽  
Mixing Costs ◽  
Experimental Group

In cued auditory task switching, one of two dichotically presented number words, spoken by a female and a male, had to be judged according to its numerical magnitude. One experimental group selected targets by speaker gender and another group by ear of presentation. In mixed-task blocks, the target-defining feature (male/female vs. left/right) was cued prior to each trial, but in pure blocks it remained constant. Compared to selection by gender, selection by ear led to better performance in pure blocks than in mixed blocks, resulting in larger “global” mixing costs for ear-based selection. Selection by ear also led to larger “local” switch costs in mixed blocks, but this finding was partially mediated by differential cue-repetition benefits. Together, the data suggest that requirements of attention shifting diminish the auditory spatial selection benefit.

Sign in / Sign up

Export Citation Format

Share Document