No abstract

The current study investigated whether children’s conformity to a majority testimony influenced their willingness to revise their own erroneous counting knowledge. The content of the testimonies focused on conventional rules of counting, by means of pseudoerrors (i.e., unconventional counts) occurring during a detection task. In this work measurements were taken at two different time points. At time 1 children aged 5 to 7 years ( N = 88) first made independent judgments on the correctness of unconventional counting procedures presented by means of a computerized detection task. Subsequently, they watched a video in which four teachers (unanimous majority) or three (non-unanimous majority) made correct claims about the counts and children had to decide whether the informants were right or not, and justify their answers. Our participants conformed significantly more when the correct testimony was provided by a unanimous majority than by a non-unanimous majority. In addition, in two of the three pseudoerrors presented, there was no difference in the children’s tendency to conform to unconventional counts as age increased. At time 2, which was taken to test whether the effect of the testimony was maintained over time, the responses of the 32 children (16 from each age group) who had endorsed the claims of the unanimous majority at time 1 revealed that teachers’ testimonies only had a lasting influence on elementary school children’s understanding of conventional counting rules.

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.

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.

The role of gender in mathematical abilities has caught the interest of researchers for several decades; however, their findings are not conclusive yet. Recently the need to explore its influence on the development of some foundational mathematic skills has been highlighted. Thus, the current study examined whether gender differentially affects young children’s performance in several basic numeracy skills, using a complex developmentally appropriate assessment that included not only standard curriculum-based measures, but also a non-routine task which required abstract thinking. Further, 136 children (68 girls) aged 6 to 8 years old completed: (a) the third edition of the standardized Test of Early Mathematical Ability (TEMA-3) to measure their mathematical knowledge; (b) the Kaufman Brief Intelligence Test (K-BIT), and (c) a non-routine counting detection task where children watched several characters performing different counts, had to judge their correctness, and justify their answers. Furthermore, frequentist and Bayesian analyses were combined to quantify the evidence of the null (gender similarities) and the alternative (gender differences) hypothesis. The overall results indicated the irrelevance or non-existence of gender differences in most of the measures used, including children’s performance in the non-routine counting task. This would support the gender similarity hypothesis in the basic numerical skills assessed.