The Development of Ordinal Numerical Competence in Young Children

Brannon, Elizabeth M.; Walle, Gretchen A. Van de

doi:10.1006/cogp.2001.0780

Cited by 38 publications

(58 citation statements)

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“…Second, two details of our data confirm other reports that the acquisition of numerals affects performance on nonverbal numerical tasks. First, as Brannon & Van de Walle (2001) had found in their study of non-verbal ordinal judgments, "one"-knowers were the only ones who completely failed to order any of the pairs. Since pre-verbal infants can order both small (Feigenson & Carey, 2003, 2005Feigenson & Halberda, 2004) and large (Brannon, 2002) sets, it seems unlikely that "one"-knowers' failure was caused by representational limits on their core systems.…”

Section: Summary: Experimentsmentioning

confidence: 88%

One, two, three, four, nothing more: An investigation of the conceptual sources of the verbal counting principles

2007

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Section: Summary: Experimentsmentioning

confidence: 88%

One, two, three, four, nothing more: An investigation of the conceptual sources of the verbal counting principles

2007

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“…Specifically, in most of the studies in the field of ordinal processing, participants were presented with pairs of items (e.g., numbers, letters, months, etc.) and were asked to decide whether the presentation of these pairs followed an ascending or a descending order [21,26] or to decide which one of the items appeared earlier/later in a sequence (e.g., [17,27]). All of these tasks required manipulation of quantity, magnitude or semantic information before extracting order information and arriving at a decision.…”

Section: Ordinalitymentioning

confidence: 99%

“…Although it is less commonly discussed in the scientific literature, other research studies have shown quite clearly that processing ordinal information may be considered a core cognitive ability (just like the core quantity system) (e.g., [17,27,37,61,62]). …”

Section: Ordinality and Quantitymentioning

confidence: 99%

Processing Ordinality and Quantity: The Case of Developmental Dyscalculia

Rubinsten¹

2011

PsycEXTRA Dataset

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In contrast to quantity processing, up to date, the nature of ordinality has received little attention from researchers despite the fact that both quantity and ordinality are embodied in numerical information. Here we ask if there are two separate core systems that lie at the foundations of numerical cognition: (1) the traditionally and well accepted numerical magnitude system but also (2) core system for representing ordinal information. We report two novel experiments of ordinal processing that explored the relation between ordinal and numerical information processing in typically developing adults and adults with developmental dyscalculia (DD). Participants made ''ordered'' or ''non-ordered'' judgments about 3 groups of dots (non-symbolic numerical stimuli; in Experiment 1) and 3 numbers (symbolic task: Experiment 2). In contrast to previous findings and arguments about quantity deficit in DD participants, when quantity and ordinality are dissociated (as in the current tasks), DD participants exhibited a normal ratio effect in the non-symbolic ordinal task. They did not show, however, the ordinality effect. Ordinality effect in DD appeared only when area and density were randomized, but only in the descending direction. In the symbolic task, the ordinality effect was modulated by ratio and direction in both groups. These findings suggest that there might be two separate cognitive representations of ordinal and quantity information and that linguistic knowledge may facilitate estimation of ordinal information.Citation: Rubinsten O, Sury D (2011) Processing Ordinality and Quantity: The Case of Developmental Dyscalculia. PLoS ONE 6(9): e24079.

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“…One task, used primarily with nonhuman primates, involves judgments between two sets of items (e.g., Beran, 2004;Brannon & Terrace, 2000;Call, 2000;Judge, Evans, & Vias, 2005). This task also sometimes is used with human children (e.g., Brannon & Van de Walle, 2001;Feigenson, Carey, & Hauser, 2003). The second task is the bisection task that has been used extensively with rats and pigeons (e.g., Emmerton & Renner, 2006;Fetterman, 1993;Meck & Church, 1983;Roberts, 2005Roberts, , 2006 and occasionally with nonhuman primates and human children (e.g., Beran, Smith, Redford, & Washburn, 2006;Droit-Volet, Clement, & Fayol, 2003;Jordan & Brannon, 2006a, 2006b).…”

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confidence: 99%

Quantity representation in children and rhesus monkeys: Linear versus logarithmic scales

Beran

Johnson-Pynn

Ready

2008

Journal of Experimental Child Psychology

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The performance of 4-and 5-year-old children and rhesus monkeys was compared using a computerized task for quantity assessment. Participants first learned two quantity anchor values and then responded to intermediate values by classifying them as either similar to the large anchor or the small anchor. Of primary interest was an assessment of where the point of subjective equality (PSE) occurred for each species across four different sets of anchors to determine whether the PSE occurred at the arithmetic mean or the geometric mean. Both species produced PSEs that were closer to the geometric mean for three of four anchor sets. This indicates that monkeys and children access either a logarithmic scale for quantity representation or a linear scale that is subject to scalar variability, both of which are consistent with Weber's law and representation of quantity that takes the form of analog magnitudes. KeywordsQuantity Judgments; Representational Scale; Children; Monkeys; Bisection TaskThe quantity discriminations made by many species are restricted in their accuracy on the basis of the ratio between those sets (e.g., Barth, Kanwisher, & Spelke, 2003;Beran, 2007;Beran, Taglialatela, Flemming, James, & Washburn, 2006;Brannon, Cantlon, & Terrace, 2006;Brannon & Terrace, 2000;Call, 2000;Huntley-Fenner, 2001). Comparisons with larger ratios (as determined by dividing the smaller quantity by the larger quantity) lead to lower performance levels, even when the distance between sets is constant (e.g., 8 versus 10 is more difficult than 2 versus 4). This suggests that an analog magnitude system produces discriminable representations of sets, and this system is consistent with Weber's law, which states that discrimination of sets becomes more difficult for a fixed difference as the magnitude of those sets increases.Correspondence to: Michael Beran, Language Research Center, Georgia State University, University Plaza, Atlanta, GA 30303, Telephone -404-244-2469, Fax -404-244-5829, E-mail -mjberan@yahoo.com. Publisher's Disclaimer: This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Evidence for discrimination performance being modulated by Weber's Law comes from differing sources. One task, used primarily with nonhuman primates, involves judgments between two sets of items (e.g., Beran, 2004;Brannon & Terrace, 2000;Call, 2000; Judge, Evans, & Vias, 2005). This task also sometimes is used with human children (e.g., Brannon & Van de Walle, 2001; Feigenson, Carey, & Hauser, 2003). The second task is the bisection task that has been used extensively with rats and pigeons (e.g., Emmerton & Renner, 2006;Fetterm...

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The Development of Ordinal Numerical Competence in Young Children

Cited by 38 publications

References 0 publications

One, two, three, four, nothing more: An investigation of the conceptual sources of the verbal counting principles

One, two, three, four, nothing more: An investigation of the conceptual sources of the verbal counting principles

Processing Ordinality and Quantity: The Case of Developmental Dyscalculia

Quantity representation in children and rhesus monkeys: Linear versus logarithmic scales

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