Children’s early mental number line: Logarithmic or decomposed linear?

Moeller, Korbinian; Pixner, Silvia; Kaufmann, Liane; Nuerk, Hans Christoph

doi:10.1016/j.jecp.2009.02.006

Cited by 157 publications

(235 citation statements)

References 36 publications

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“…Thereby, our results are hard to reconcile with the notion of an integrated holistic representation of numbers and measurement units in magnitude comparison tasks as suggested previously for two-digit numbers (e.g., Dehaene, Dupoux, & Mehler, 1990). Furthermore, the finding of such componential processing of physical quantities corresponds nicely with previous accounts of componential processing in arithmetic (e.g., as well as number line estimation (e.g., Moeller, Pixner, Kaufmann, & Nuerk, 2009 Second, our results not only generalize multi-symbol compatibility effects to units of measurement but also allow transfer of the string length congruity effect found for decimal fractions to measurement units (Huber et al, 2014b). Thus, not only the number of digits, but also the number of characters (i.e., digits plus letters indicating the scale units) seems to be processed and compared separately.…”

Section: Discussioncontrasting

confidence: 75%

Testing a model of componential processing of multi-symbol numbers—evidence from measurement units

Huber¹,

Bahnmueller

Klein

et al. 2015

Psychon Bull Rev

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Research on numerical cognition has addressed the processing of nonsymbolic quantities and symbolic digits extensively. However, magnitude processing of measurement units is still a neglected topic in numerical cognition research. Hence, we investigated the processing of measurement units to evaluate whether typical effects of multi-digit number processing such as the compatibility effect, the string length congruity effect, and the distance effect are also present for measurement units. In three experiments, participants had to single out the larger one of two physical quantities (e.g., lengths). In Experiment 1, the compatibility of number and measurement unit (compatible: 3 mm_6 cm with 3 < 6 and mm < cm; incompatible: 3 cm_6 mm with 3 < 6 but cm > mm) as well as string length congruity (congruent: 1 m_2 km with m < km and 2 < 3 characters; incongruent: 2 mm_1 m with mm < m, but 3 > 2 characters) were manipulated. We observed reliable compatibility effects with prolonged reaction times (RT) for incompatible trials. Moreover, a string length congruity effect was present in RT with longer RT for incongruent trials. Experiments 2 and 3 served as control experiments showing that compatibility effects persist when controlling for holistic distance and that a distance effect for measurement units exists. Our findings indicate that numbers and measurement units are processed in a componential manner and thus highlight that processing characteristics of multi-digit numbers generalize to measurement units. Thereby, our data lend further support to the recently proposed generalized model of componential multi-symbol number processing.

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Section: Discussioncontrasting

confidence: 75%

Testing a model of componential processing of multi-symbol numbers—evidence from measurement units

Huber¹,

Bahnmueller

Klein

et al. 2015

Psychon Bull Rev

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“…This understanding is important for the number line task in which participants are asked to locate a number on a number line. Successful performance requires verbal understanding of phonologicalorthographic relationships related to the Arabic place value system, as well as usage of verbal strategies, thus highlighting the common verbal skills required for both reading and numerical skills (Moeller, Pixner, Kaufmann, & Nuerk, 2009;Peeters, Degrande, Ebersbach, Verschaffel, & Luwel, 2016).Reading and mathematics both involve executive functions, entangling the relationship between RD, MD and ADHD further due to the central role of executive functions in ADHD (Barkley, 1997). Another related shared risk factor can be processing speed, for example, Peterson et al (2017) explored the unique and shared risk factors for RD, MD and ADHD and found that slower processing speed was a shared cognitive risk factor.…”

mentioning

confidence: 99%

Multiple skills underlie arithmetic performance: A large-scale structural equation modeling analysis

Ashkenazi

Silverman

2017

J. Numer. Cogn.

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Current theoretical approaches point to the importance of several cognitive skills not specific to mathematics for the etiology of mathematics disorders (MD). In the current study, we examined the role of many of these skills, specifically: rapid automatized naming, attention, reading, and visual perception, on mathematics performance among a large group of college students (N = 1,322) with a wide range of arithmetic proficiency. Using factor analysis, we discovered that our data clustered to four latent variables 1) mathematics, 2) perception speed, 3) attention and 4) reading. In subsequent structural equation modeling, we found that the latent variable perception speed had a strong and meaningful effect on mathematics performance. Moreover, sustained attention, independent from the effect of the latent variable perception speed, had a meaningful, direct effect on arithmetic fact retrieval and procedural knowledge. The latent variable reading had a modest effect on mathematics performance. Specifically, reading comprehension, independent from the effect of the latent variable reading, had a meaningful direct effect on mathematics, and particularly on number line knowledge. Attention, tested by the attention network test, had no effect on mathematics, reading or perception speed. These results indicate that multiple factors can affect mathematics performance supporting a heterogeneous approach to mathematics. These results have meaningful implications for the diagnosis and intervention of pure and comorbid learning disorders.Keywords: perception speed, mathematics performance, pure and comorbid mathematics disability Nobes, and Gabriel (2013) proposed that abnormalities in executive functions, specifically inhibition and visuospatial working memory, are the source of MD, rather than mathematics-specific quantitative understanding. Moreover, there is evidence that these cognitive skills affect individual differences in arithmetic abilities across the spectrum of mathematics proficiency. Szűcs, Devine, Soltesz, Nobes, and Gabriel (2014) demonstrated that individual differences in arithmetic abilities was predicted by phonological processing, verbal knowledge, visuospatial short-term and working memory, spatial ability and executive functioning. Journal of Numerical Cognitionjnc.psychopen.eu | 2363-8761The prevalence rate of MD is between 3-6% among children (Reigosa-Crespo et al., 2012;R. Shalev, Manor, Amir, & Gross-Tsur, 1993;von Aster, Schweiter, & Weinhold Zulauf, 2007;von Aster & Shalev, 2007) while there is less evidence in regard to prevalence rates among adults. However, the prevalence of the comorbidity of MD with other disorders that affect learning (such as reading and attention deficits) vary dramatically between studies, and range between 17-66% (Barbaresi, Katusic, Colligan, Weaver, & Jacobsen, 2005;Dirks, Spyer, van Lieshout, & de Sonneville, 2008;Gross-Tsur, Manor, & Shalev, 1996;Landerl & Moll, 2010;Lewis, Hitch, & Walker, 1994;R. Shalev et al., 1993;. Even the lowest reported comorbidit...

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“…To examine the two-linear model, we used the point that separates single-and two-digit numbers as the breakpoint on the 0-100 number line and the point that separates two-and three-digit numbers as the breakpoint on the 0-1000 number line. We followed the procedure used by Moeller (e.g., Moeller et al, 2009). As shown in Figs.…”

Section: Fit Of Two-linear Model and One-and Two-cycle Versions Of Prmentioning

confidence: 99%

“…This law is believed to describe representations of numerical as well as physical magnitudes (Bank & Hill, 1974;Dehaene, 1997). One of the widely used tasks to examine how the human mind represents numbers is the number line estimation task, in which participants are asked to place a given number on a straight line anchored with numbers at the two ends (e.g., 0 on the left end and 10 or 100 on the right end; Dehaene, Izard, Spelke, & Pica, 2008;Ebersbach, Luwel, Frick, Onghena, & Verschaffel, 2008;Geary, Hoard, Nugent, & Byrd-Craven, 2008;Moeller, Pixner, Kaufmann, & Nuerk, 2009;Muldoon, Simms, Towse, Menzies, & Yue, 2011;Opfer, Siegler, & Young, 2011;Siegler & Booth, 2004;Siegler & Opfer, 2003;Slusser, Santiago, & Barth, 2013;Whyte & Bull, 2008;.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, it would reexamine Muldoon and colleagues' (2011) conclusion about cross-cultural differences in line estimation based on Chinese and Scottish children who were matched on mathematical performance but not on age. Finally, given the ongoing debate on the best model that describes children's representation of number lines of 0-100 and 0-1000 Barth, Slusser, Cohen, & Paladino, 2011;Moeller et al, 2009;Opfer et al, 2011;Slusser et al, 2013;, we also attempted to fit our data from older preschoolers on those number lines to alternative models such as the one-cycle, two-cycle, and two-linear models. Given Chinese children's early advantage in mathematical cognition, we hypothesized that our data should fit a linear model at least for the 0-100 line but also possibly for the 0-1000 line.…”

Section: Introductionmentioning

confidence: 99%

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Development of numerical estimation in Chinese preschool children

Chen

Pan

et al. 2013

Journal of Experimental Child Psychology

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a b s t r a c tAlthough much is known about the development of mental representations of numbers, it is not clear how early children begin to represent numbers on a linear scale. The current study aimed to examine the development of numerical estimation of Chinese preschoolers. In total, 160 children of three age groups (51 3-and 4-year-olds, 50 5-year-olds, and 59 6-year-olds) were administered the numerical estimation task on three types of number lines (Arabic numbers, dots, and objects). All three age groups took the test on the 0-10 number lines, and the oldest group also took it on the 0-100 and 0-1000 Arabic number lines. Results showed that (a) linear representation of numbers increased with age, (b) representation of numbers was consistent across the three types of tasks, (c) Chinese participants generally showed earlier onset of various landmarks of attaining linear representations (e.g., linearity of various number ranges, accuracy, intercepts) than did their Western counterparts, as reported in previous studies, and (d) the estimates of older Chinese preschoolers on the 0-100 and 0-1000 symbolic number lines fitted the two-linear and linear models better than alternative models such as the one-cycle, two-cycle, and logarithmic models. These results extend the small but accumulating literature on the earlier development of number cognition among Chinese preschoolers compared with their Western counterparts, suggesting the importance of cultural factors in the development of early number cognition.

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Children’s early mental number line: Logarithmic or decomposed linear?

Cited by 157 publications

References 36 publications

Testing a model of componential processing of multi-symbol numbers—evidence from measurement units

Testing a model of componential processing of multi-symbol numbers—evidence from measurement units

Multiple skills underlie arithmetic performance: A large-scale structural equation modeling analysis

Development of numerical estimation in Chinese preschool children

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