Relating magnitudes: the brain's code for proportions

Jacob, Simon N.; Vallentin, Daniela; Nieder, Andreas

doi:10.1016/j.tics.2012.02.002

Cited by 110 publications

(114 citation statements)

References 68 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In fact, many students who are competent with whole numbers stmggle with fractions (NMAP, 2008). Even so, fmding that proficiency with whole-number addition and subtraction calculations did not moderate intervention effects is surprising given prior descriptive research (Hecht & Vagi, 2010;Seethaler et al, 2011), and some evidence indicates that fractions and whole numbers are processed in similar areas of the brain (Jacob, Vallentin, & Nieder, 2012). Given that fraction knowledge is more highly correlated with whole number division than addition or subtraction (Siegler et al, in press), additional study is warranted beyond fourth grade, as the curricular focus on multiplication and division grows.…”

Section: Did Skill With Whole-numher Calculations Moderate Interventimentioning

confidence: 99%

Improving at-risk learners’ understanding of fractions.

Fuchs

Schumacher

Long

et al. 2013

Journal of Educational Psychology

231

243

View full text Add to dashboard Cite

Metropolitan-Nashville Public Schools, Nashville, TennesseeThe purposes of this study were to investigate the effects of an intervention designed to improve at-risk 4th graders' understanding of fractions and to examine the processes by which effects occurred. The intervention focused more on the measurement interpretation of fractions; the control condition focused more on the part-whole interpretation of fractions and on procedures. Intervention was also designed to compensate for at-risk students' limitations in the domain-general abilities associated with fraction leaming. At-risk students (n = 259) were randomly assigned to intervention and control. Whole-number calculation skill, domaingeneral abilities (working memory, attentive behavior, processing speed, listening comprehension), and fraction proficiency were pretested. Intervention occurred for 12 weeks, 3 times per week, 30 min per session, and then fraction performance was reassessed. On each conceptual and procedural fraction outcome, effects favored intervention over control (effect sizes = 0.29 to 2.50), and the gap between at-risk and low-risk students narTowed for the intervention group but not the control group. Improvement in the accuracy of children's measurement interpretation of fractions mediated intervention effects. Also, intervention effects were moderated by domain-general abilities, but not whole-number calculation skill.

show abstract

Section: Did Skill With Whole-numher Calculations Moderate Interventimentioning

confidence: 99%

Improving at-risk learners’ understanding of fractions.

Fuchs

Schumacher

Long

et al. 2013

Journal of Educational Psychology

231

243

View full text Add to dashboard Cite

show abstract

“…Hence the preferred procedure for evaluating a decimal as a match to a partitioned perceptual display would be estimation of a relative magnitude. People (and perhaps other animals) appear to be able to estimate proportions based on their system for approximate magnitude (Jacob, Vallentin, & Nieder, 2012;Nieder & Dehaene, 2009;Halberda & Fiegenson, 2008). However, by their very nature, approximate magnitudes will be more error-prone than exact calculations (assuming the reasoner is competent in counting).…”

Section: Relational Structure Of Rational Numbersmentioning

confidence: 99%

From rational numbers to algebra: Separable contributions of decimal magnitude and relational understanding of fractions

DeWolf

Bassok

Holyoak

2015

Journal of Experimental Child Psychology

View full text Add to dashboard Cite

“…Although previous work indicates that magnitude representations for fractions involve roughly the same general neural area (the IPS) as do magnitude representations for symbolic integers (and non-symbolic numerosities; see Jacob and Nieder, 2009b;Jacob et al, 2012), the extent to which processing and representation of magnitude is the same or different for fractions relative to other number types has not been examined. Furthermore, the more general question of whether different symbolic formats for numbers evoke the same or different abstract magnitude representations remains unanswered.…”

Section: Using Fmri To Investigate Magnitude Representationmentioning

confidence: 99%

Neural representations of magnitude for natural and rational numbers

et al. 2016

View full text Add to dashboard Cite

a b s t r a c t a r t i c l e i n f oArticle history: Received 12 January 2016 Accepted 26 July 2016 Available online 26 July 2016 Humans have developed multiple symbolic representations for numbers, including natural numbers (positive integers) as well as rational numbers (both fractions and decimals). Despite a considerable body of behavioral and neuroimaging research, it is currently unknown whether different notations map onto a single, fully abstract, magnitude code, or whether separate representations exist for specific number types (e.g., natural versus rational) or number representations (e.g., base-10 versus fractions). We address this question by comparing brain metabolic response during a magnitude comparison task involving (on different trials) integers, decimals, and fractions. Univariate and multivariate analyses revealed that the strength and pattern of activation for fractions differed systematically, within the intraparietal sulcus, from that of both decimals and integers, while the latter two number representations appeared virtually indistinguishable. These results demonstrate that the two major notations formats for rational numbers, fractions and decimals, evoke distinct neural representations of magnitude, with decimals representations being more closely linked to those of integers than to those of magnitude-equivalent fractions. Our findings thus suggest that number representation (base-10 versus fractions) is an important organizational principle for the neural substrate underlying mathematical cognition.

show abstract

Relating magnitudes: the brain's code for proportions

Cited by 110 publications

References 68 publications

Improving at-risk learners’ understanding of fractions.

Improving at-risk learners’ understanding of fractions.

From rational numbers to algebra: Separable contributions of decimal magnitude and relational understanding of fractions

Neural representations of magnitude for natural and rational numbers

Contact Info

Product

Resources

About