Abstract
Counting is a complex cognitive process that is paramount to arithmetical development at school. The improvement of counting skills of children depends on their understanding of the logical and conventional rules involved. While the logical rules are mandatory and related to one-to-one correspondence, stable order, and cardinal principles, conventional rules are optional and associated with social customs. This study contributes to unravel the conceptual understanding of counting rules of children. It explores, with a developmental approach, the performance of children on non-routine counting detection tasks, their confidence in their answers (metacognitive monitoring skills), and their ability to change a wrong answer by deferring to the opinion of a unanimous majority who justified or did not justify their claims. Hundred and forty nine children aged from 5 to 8 years were randomized to one of the experimental conditions of the testimony of teachers: with (n = 74) or without justification (n = 75). Participants judged the correctness of different types of counting procedures presented by a computerized detection task, such as (a) pseudoerrors that are correct counts where conventional rules are violated (e.g., first counting six footballs, followed by other six basketballs that were interspersed along the row), and (b) compensation errors that are incorrect counts where logical rules were broken twice (e.g., skipping the third element of the row and then labeling the sixth element with two number words, 5 and 6). Afterwards, children rated their confidence in their detection answer with a 5-point scale. Subsequently, they listened to the testimony of the teachers and showed either conformity or non-conformity. The participants considered both compensation errors and pseudoerrors as incorrect counts in the detection task. The analysis of the confidence of children in their responses suggested that they were not sensitive to their incorrect performance. Finally, children tended to conform more often after hearing a justification of the testimony than after hearing only the testimonies of the teachers. It can be concluded that the age range of the evaluated children failed to recognize the optional nature of conventional counting rules and were unaware of their misconceptions. Nevertheless, the reasoned justifications of the testimony, offered by a unanimous majority, promoted considerable improvement in the tendency of the children to revise those misconceptions.
Highlights
Current approaches assume that counting skills are a foothold in arithmetic performance and mathematical academic achievement during primary school (Chan et al, 2017; Chu et al, 2018; Geary et al, 2018)
Preliminary analyses showed that performance of the children was above the chance level on compensation errors (M = 2.17, SD = 0.88) and below the chance level on pseudoerrors (M = 0.91, SD = 0.73): compensation errors, t(148) = 9.32, p < 0.001, d = 0.76, 95% CI [0.53, 0,82]; pseudoerrors: t(148) = −9.94, p < 0.001, d = 0.81, 95% CI [−0.71, −0.48]
Based on the third goal of the study, we have found that a unanimous majority that do not provide arguments do not have the same influence on conformity of children, because the children considered the content of the testimony and the justification supporting it
Summary
Current approaches assume that counting skills are a foothold in arithmetic performance and mathematical academic achievement during primary school (Chan et al, 2017; Chu et al, 2018; Geary et al, 2018). In addition to domain-specific knowledge, other cognitive factors, such as metacognitive skills, which influence school performance of the children, should be explored (Roebers et al, 2012; De Neys et al, 2014; Lubin et al, 2015). To improve the understanding of the failures of children in the detection task, we measured other two abilities: the confidence in their own judgments (i.e., metacognitive monitoring), and the ability to change a wrong answer by deferring to the opinion of a unanimous majority. These are the issues we will cover
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