Children’s understandings of counting: Detection of errors and pseudoerrors by kindergarten and primary school children

Rodríguez, Purificación; Lago, María Oliva; Enesco, Ileana; Guerrero, Silvia

doi:10.1016/j.jecp.2012.08.005

Cited by 12 publications

(21 citation statements)

References 19 publications

(38 reference statements)

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“…Data suggest that the acquisition of logical and conventional rules appears to follow independent processes and different developmental trajectories. It is assumed that the comprehension of logical rules improves with age (see, e.g., Freeman, Antonucci, & Lewis, ; Le Corre, ; Sarnecka & Carey, ; Wynn, for a detailed analysis of children's early comprehension of cardinality); however, results from cross‐sectional and longitudinal studies have found distinct developmental patterns for the understanding of conventional rules (e.g., Briars & Siegler, ; Escudero, Rodríguez, Lago, & Enesco, ; LeFevre et al ., ; Rodríguez et al ., ).…”

Section: Introductionmentioning

confidence: 97%

“…In contrast to logical, unchangeable, and binding essential aspects, non‐essential aspects are modifiable and optional. They are conventional in the sense that these rules involve recommendations that vary depending on social contexts (e.g., Briars & Siegler, ; Laupa & Becker, ; Rodríguez, Lago, Enesco, & Guerrero, ). Examples include spatial adjacency, temporal adjacency, and spatial–temporal adjacency.…”

Section: Introductionmentioning

confidence: 99%

“…Another factor that has attracted the attention of researchers, either implicitly (LeFevre et al ., ) or explicitly (Escudero et al ., ; Rodríguez et al ., ), is the importance of the cardinal value in helping children realize that unconventional procedures also generate correct answers. The former authors proposed that children may become confused when presented with unconventional counts and that this may prevent children from establishing whether a puppet had counted correctly.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Detection of counting pseudoerrors: What helps children accept them?

Lago

Rodríguez

Escudero

et al. 2015

British J of Dev Psycho

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This study examines children's comprehension of non-essential counting features (conventional rules). The objective of the study was to determine whether the presence or absence of cardinal values in pseudoerrors and the type of conventional rule violated affects children's performance. A detection task with pseudoerrors was presented through a computer game to 146 primary school children in grades 2 through 4. The same pseudoerrors were presented both with and without cardinal values; the pseudoerrors violated conventional rules of spatial adjacency, temporal adjacency, spatial-temporal adjacency, and left-to-right direction. Half of the participants within each age group were randomly assigned to an experimental condition that included pseudoerrors with a cardinal value, and the other half were assigned to a condition that included pseudoerrors without a cardinal value. The results show that when presented with a cardinal value, children more easily recognize the optional nature of non-essential counting features. Likewise, the type of conventional rule transgressed significantly affected the children's acceptance of pseudoerrors as valid counts. Participants penalized breaches of temporal and spatial-temporal adjacency to a greater degree than breaches of spatial adjacency and left-to-right direction.

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Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Detection of counting pseudoerrors: What helps children accept them?

Lago

Rodríguez

Escudero

et al. 2015

British J of Dev Psycho

Self Cite

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“…Six-year-old kindergartners' estimations on a number line (1-100) were also shown to be more accurate when the number line was oriented SNARC congruently rather than SNARC incongruently (Ebersbach, 2014). Studies investigating preschoolers' understanding of counting and counting rules in particular have found that children are significantly better at detecting actual counting errors (e.g., counts resulting in the wrong cardinal value) than pseudo-errors (Briars & Siegler, 1984;Kamawar et al, 2010;LeFevre et al, 2006;Rodríguez, Lago, Enesco, & Guerrero, 2013). Pseudo-errors are correct counts that violate conventional (nonessential) counting rules, such as counting items sequentially, e.g., from left-to-right (order irrelevance principle; Gelman & Gallistel, 1978).…”

Section: Introductionmentioning

confidence: 99%

“…Pseudo-errors are correct counts that violate conventional (nonessential) counting rules, such as counting items sequentially, e.g., from left-to-right (order irrelevance principle; Gelman & Gallistel, 1978). However, whereas Briars and Siegler (1984) and LeFevre et al (2006) found that most kindergarteners know that counting items left-to-right is unessential and, therefore, are more willing to accept reverse direction counts, Rodríguez et al (2013) and Kamawar et al (2010) recently found that among children's main reasons for rejecting pseudo-errors was the violation of left-to-right direction of counting, with kindergarten children favoring a left-to-right or top-tobottom direction of counting. Finally, Shaki, Fischer, and Göbel (2012) documented a preschool preference to start counting of objects according to the culture-specific reading direction, which is subsequently enhanced by the acquisition of reading habits for English and Palestinian children and reduced for Israeli children due to an emerging directional conflict between reading text right-toleft and reading numbers left-to-right.…”

Section: Introductionmentioning

confidence: 99%

Development of spatial preferences for counting and picture naming

Knudsen

Fischer

Aschersleben

2014

Psychological Research

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The direction of object enumeration reflects children's enculturation but previous work on the development of such spatial preferences has been inconsistent. Therefore, we documented directional preferences in finger counting, object counting, and picture naming for children (4 groups from 3 to 6 years, N = 104) and adults (N = 56). We found a right-side preference for finger counting in 3-to 6-year-olds and a left-side preference for counting objects and naming pictures by 6 years of age. Children were consistent in their special preferences when comparing object counting and picture naming, but not in other task pairings. Finally, spatial preferences were not related to cardinality comprehension. These results, together with other recent work, suggest a gradual development of spatial-numerical associations from early non-directional mappings into culturally constrained directional mappings.

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The Development of Mathematical Reasoning

Nuñes

Bryant

2015

Handbook of Child Psychology and Developmental Science

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Psychological research on the development of children's mathematical reasoning has focused either on their understanding of quantities or on their knowledge of number. A synthesis between these two different kinds of theory can be achieved by acknowledging that numbers have two meanings: a representational meaning, defined by their use as signs for quantities or relations between quantities, and an analytical meaning, defined by the conventions in the number system. In the introduction, this chapter introduces these two meanings of numbers and explores the vital connections between them. The subsequent sections analyze how children's mathematical knowledge develops by their increasing ability to use different numerical representations (e.g., from the use of fingers to represent quantities to the use of conventional signs), by their growing understanding of invariant relations between quantities (e.g., realizing that, given a fixed number of cookies, the more people sharing the cookies, the less each one receives) and by their increasing awareness of the relevance of specific concepts to different situations (e.g., understanding the relevance of division to the solution of situations more readily connected to multiplication). Throughout the chapter, the connection between the nature of quantities and their numerical representations is explored. The final substantive section focuses on the use of numbers to quantify space and relations between spatial dimensions, and argues that understanding relations between different dimensions in space (e.g., length, width, and area) is crucial to quantifying space. The chapter ends with a brief discussion of directions for future research.

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Children’s understandings of counting: Detection of errors and pseudoerrors by kindergarten and primary school children

Cited by 12 publications

References 19 publications

Detection of counting pseudoerrors: What helps children accept them?

Detection of counting pseudoerrors: What helps children accept them?

Development of spatial preferences for counting and picture naming

The Development of Mathematical Reasoning

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