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Estimation abilities of large numerosities in Kindergartners.

Mejias S, Schiltz C - Front Psychol (2013)

Bottom Line: Additionally, children who presented better exact symbolic knowledge were also those with the most refined ANS.Our results support the view that approximate numerical representations are linked to exact number competence in young children before the start of formal math education and might thus serve as building blocks for mathematical knowledge.Since this core number system was also sensitive to external components such as the SEI this implies that it can most probably be targeted and refined through specific educational strategies from preschool on.

View Article: PubMed Central - PubMed

Affiliation: Educational Measurement and Applied Cognitive Science, Université du Luxembourg Walferdange, Luxembourg.

ABSTRACT
The approximate number system (ANS) is thought to be a building block for the elaboration of formal mathematics. However, little is known about how this core system develops and if it can be influenced by external factors at a young age (before the child enters formal numeracy education). The purpose of this study was to examine numerical magnitude representations of 5-6 year old children at 2 different moments of Kindergarten considering children's early number competence as well as schools' socio-economic index (SEI). This study investigated estimation abilities of large numerosities using symbolic and non-symbolic output formats (8-64). In addition, we assessed symbolic and non-symbolic early number competence (1-12) at the end of the 2nd (N = 42) and the 3rd (N = 32) Kindergarten grade. By letting children freely produce estimates we observed surprising estimation abilities at a very young age (from 5 year on) extending far beyond children's symbolic explicit knowledge. Moreover, the time of testing has an impact on the ANS accuracy since 3rd Kindergarteners were more precise in both estimation tasks. Additionally, children who presented better exact symbolic knowledge were also those with the most refined ANS. However, this was true only for 3rd Kindergarteners who were a few months from receiving math instructions. In a similar vein, higher SEI positively impacted only the oldest children's estimation abilities whereas it played a role for exact early number competences already in 2nd and 3rd graders. Our results support the view that approximate numerical representations are linked to exact number competence in young children before the start of formal math education and might thus serve as building blocks for mathematical knowledge. Since this core number system was also sensitive to external components such as the SEI this implies that it can most probably be targeted and refined through specific educational strategies from preschool on.

No MeSH data available.


Related in: MedlinePlus

Response-bias (RB) in the symbolic and non-symbolic tasks: children from 2nd and 3rd grade of Kindergarten overestimated the numerosity of the arrays.
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Figure 3: Response-bias (RB) in the symbolic and non-symbolic tasks: children from 2nd and 3rd grade of Kindergarten overestimated the numerosity of the arrays.

Mentions: Children of both testing times (i.e., 2nd and 3rd grade of Kindergarten) overestimated the numerosity of the arrays (Figure 3). To describe this tendency we computed the response-bias [RB = (child's response – target magnitude)/target magnitude] and tested it against zero using t-tests. A RB of zero indicates that estimates were accurate, a negative RB that target magnitudes were underestimated and a positive RB that target magnitudes were overestimated. Contrarily to the expected underestimation predicted by the bi-directional mapping hypothesis (e.g., Castronovo and Seron, 2007), preschool children overestimated target magnitude in the symbolic “Dots to AN” task [2nd grade children RB: M = 3.237; SD = 3.002; t(41) = 6.989, p < 0.001; 3rd grade children RB: M = 1.445; SD = 1.955; t(31) = 4.182, p < 0.001]. They also overestimated in the non-symbolic estimation task [2nd grade children RB: M = 2.075; SD = 2.024; t(41) = 6.645, p < 0.001; 3rd grade children RB: M = 0.786; SD = 1.359; t(31) = 3.270, p = 0.003]. This positive RB was shown by the preschool children of the 2nd grade on every target magnitudes of both estimation tasks. Preschool children of the 3rd grade also overestimated numerosities of all target magnitudes in the symbolic “dots to AN” task. But in the non-symbolic task only the two smallest target magnitudes were overestimated (see Figure 3).


Estimation abilities of large numerosities in Kindergartners.

Mejias S, Schiltz C - Front Psychol (2013)

Response-bias (RB) in the symbolic and non-symbolic tasks: children from 2nd and 3rd grade of Kindergarten overestimated the numerosity of the arrays.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3756289&req=5

Figure 3: Response-bias (RB) in the symbolic and non-symbolic tasks: children from 2nd and 3rd grade of Kindergarten overestimated the numerosity of the arrays.
Mentions: Children of both testing times (i.e., 2nd and 3rd grade of Kindergarten) overestimated the numerosity of the arrays (Figure 3). To describe this tendency we computed the response-bias [RB = (child's response – target magnitude)/target magnitude] and tested it against zero using t-tests. A RB of zero indicates that estimates were accurate, a negative RB that target magnitudes were underestimated and a positive RB that target magnitudes were overestimated. Contrarily to the expected underestimation predicted by the bi-directional mapping hypothesis (e.g., Castronovo and Seron, 2007), preschool children overestimated target magnitude in the symbolic “Dots to AN” task [2nd grade children RB: M = 3.237; SD = 3.002; t(41) = 6.989, p < 0.001; 3rd grade children RB: M = 1.445; SD = 1.955; t(31) = 4.182, p < 0.001]. They also overestimated in the non-symbolic estimation task [2nd grade children RB: M = 2.075; SD = 2.024; t(41) = 6.645, p < 0.001; 3rd grade children RB: M = 0.786; SD = 1.359; t(31) = 3.270, p = 0.003]. This positive RB was shown by the preschool children of the 2nd grade on every target magnitudes of both estimation tasks. Preschool children of the 3rd grade also overestimated numerosities of all target magnitudes in the symbolic “dots to AN” task. But in the non-symbolic task only the two smallest target magnitudes were overestimated (see Figure 3).

Bottom Line: Additionally, children who presented better exact symbolic knowledge were also those with the most refined ANS.Our results support the view that approximate numerical representations are linked to exact number competence in young children before the start of formal math education and might thus serve as building blocks for mathematical knowledge.Since this core number system was also sensitive to external components such as the SEI this implies that it can most probably be targeted and refined through specific educational strategies from preschool on.

View Article: PubMed Central - PubMed

Affiliation: Educational Measurement and Applied Cognitive Science, Université du Luxembourg Walferdange, Luxembourg.

ABSTRACT
The approximate number system (ANS) is thought to be a building block for the elaboration of formal mathematics. However, little is known about how this core system develops and if it can be influenced by external factors at a young age (before the child enters formal numeracy education). The purpose of this study was to examine numerical magnitude representations of 5-6 year old children at 2 different moments of Kindergarten considering children's early number competence as well as schools' socio-economic index (SEI). This study investigated estimation abilities of large numerosities using symbolic and non-symbolic output formats (8-64). In addition, we assessed symbolic and non-symbolic early number competence (1-12) at the end of the 2nd (N = 42) and the 3rd (N = 32) Kindergarten grade. By letting children freely produce estimates we observed surprising estimation abilities at a very young age (from 5 year on) extending far beyond children's symbolic explicit knowledge. Moreover, the time of testing has an impact on the ANS accuracy since 3rd Kindergarteners were more precise in both estimation tasks. Additionally, children who presented better exact symbolic knowledge were also those with the most refined ANS. However, this was true only for 3rd Kindergarteners who were a few months from receiving math instructions. In a similar vein, higher SEI positively impacted only the oldest children's estimation abilities whereas it played a role for exact early number competences already in 2nd and 3rd graders. Our results support the view that approximate numerical representations are linked to exact number competence in young children before the start of formal math education and might thus serve as building blocks for mathematical knowledge. Since this core number system was also sensitive to external components such as the SEI this implies that it can most probably be targeted and refined through specific educational strategies from preschool on.

No MeSH data available.


Related in: MedlinePlus