The authors have declared that no competing interests exist.
There has recently been an increasing focus on the development of automatic processing of numerical magnitude. However, little effort has been made to explore automatic access to non-symbolic numerical magnitude in preschool children. In experiment 1, we used a non-symbolic physical size comparison task in 3- to 6-year-olds to examine developmental changes and the effect of ratio and counting principle knowledge. Results showed that the existence of automatic non-symbolic numerical processing began at age 3–4 years and size congruity effects tended to reduce with increasing age from 4 years old. The study also found that non-counting-principle knowers had a larger congruity effect, and in low ratio conditions the size congruity effect was more easily found. In addition, symbolic number comparison ability was negatively related to size congruity effect. In experiment 2, we explored the relationship between inhibition skill and size congruity effects, as well as interference and facilitatory components in children aged 4 years old. Results showed no correlation between inhibition skills and the size congruity effect and only interference effects were found. We also found a larger interference effect in low ratio conditions than in high ratio conditions.
Numerosity is an important and useful abstract dimension in our lives. In recent decades there has been a growing amount of research into the developmental trajectories of automatic processing of numerical magnitude [
Children of early kindergarten age rarely use number symbols. They may be able to recognize numbers, but do not have automatic access to those number symbols yet [
The development of automatic access to numerosity may be related to the frequency of utilization of non-symbolic or symbolic magnitude information. Some researchers believe that children, without knowing symbolic numbers, mostly make use of non-symbolic notation [
The approximate number system (ANS) is a phylogenetic and ontogenetic system that represents large, approximate numerical magnitudes without the need to count or rely on numerical symbols [
In our study, we used the non-symbolic physical size comparisons paradigm in 3- to 6-year-old children to explore the developmental characteristics of automatic processing. To investigate the role of the ANS, we controlled the effect of ratio between the compared sets. We used a number comparison task that could measure symbolic number processing abilities, and selected children who had not yet acquired counting principles, to study the influence of mathematical language in the development of non-symbolic automatic processing.
This research was approved by the local ethical committee of Beijing Normal University. We obtained informed written consent from the next of kin, caretakers, or guardians on behalf of the minor/child participants involved in the study, according to the institutional guidelines of Beijing Normal University.
A total of 80 children participated in the study (mean age ± SD: 54.91 ± 11.47 months; range: 39–75 months; 34 boys), all from one kindergarten in Beijing, China. An additional 6 children were tested but were excluded as they did not complete the tasks. The kindergarten had 3 grades: Junior Class (34 participants; mean age ± SD: 43.09 ± 2.64 months, range: 39–48 months, 15 boys), Middle Class (23 participants, mean age ± SD: 58.23 ± 2.59 months, range: 52–60 months, 11 boys) and Senior Class (23 participants, mean age ± SD: 69.09 ± 4.21 months, range: 62–75 months, 8 boys). To test the effect of age, we also grouped the children into a 3-year-old group (
E-Prime 1.1 software installed on a 17-inch Dell computer was used to program the presentation of stimuli and to collect correct rate and reaction time (RT) data.
A. Congruent pair, 7 vs. 9 dots (high ratio), both numerically and physically larger compared with numerically and physically smaller dots which together have a smaller total surface area. B. Incongruent pair, 7 vs. 9 dots (high ratio), numerically larger but physically smaller dots compared with numerically smaller but physically larger dots which together have a larger total surface area. C. Congruent pair, 7 vs. 18 dots (low ratio). D. Incongruent pair, 7 vs. 18 dots (low ratio).
Participants were tested individually in a quiet room. First, the children completed the Give-a-Number task. The experimenter then put a 12-color card with different color squares on the table before the children, and asked them to choose the green, blue, and gray color. When they completed this correctly the color discrimination task was administered. Rest time between each task was approximately 2 minutes. Finally, the children completed the non-symbolic physical size comparison task and number comparison task. Half of participants completed the number comparison task first. The rest time between these 2 tasks was approximately 2 minutes. The entire procedure lasted approximately 25–30 minutes.
CP knowers | Non-CP knowers | |
---|---|---|
Congruent trails | 1057.07(319.53) | 1065.50 (178.19) |
Incongruent trails | 1137.80(315.52) | 1223.44 (223.80) |
3 years old | 4 years old | 5 years old | 6 years old | ||
---|---|---|---|---|---|
Low ratio | ACC | ||||
Mean congruity effect | 0.006 (0.082) | 0.066 (0.121) | 0.040 (0.067) | 0.011 (0.062) | |
Congruent trials | 0.955(0.062) | 0.982(0.056) | 0.997(0.016) | 0.989(0.029) | |
Incongruent trials | 0.949(0.071) | 0.916(0.141) | 0.957(0.067) | 0.978(0.049) | |
RT | |||||
Mean congruity effect | 133.22(228.48) | 188.71(201.51) | 174.96(134.84) | 83.50 (85.62) | |
Congruent trials | 1118.53(276.70) | 1014.92(207.08) | 850.62(199.67) | 797.97(298.06) | |
Incongruent trials | 1251.75(389.61) | 1203.63(308.19) | 1025.58(276.72) | 881.48(299.94) | |
High ratio | ACC | ||||
Mean congruity effect | 0.029 (0.082) | −0.001 (0.084) | 0.006 (0.03) | 0.006 (0.038) | |
Congruent trials | 0.967(0.053) | 0.962(0.057) | 0.994(0.022) | 0.994(0.022) | |
Incongruent trials | 0.938(0.067) | 0.963(0.061) | 0.988(0.030) | 0.989(0.029) | |
RT | |||||
Mean congruity effect | 61.34 (232.33) | 115.79 (129.33) | 64.846 (98.79) | 106.82(117.66) | |
Congruent trials | 1176.33(463.98) | 1019.57(219.90) | 890.63(222.31) | 749.32(219.35) | |
Incongruent trials | 1237.67(363.67) | 1135.37(277.35) | 955.47(232.75) | 856.14(322.28) |
ACC: accuracy; RT: reaction time.
We used a number comparison task that could measure symbolic number discrimination abilities. We calculated the mean reaction time and correct rate for this task as an indicator of mastering symbolic number knowledge. Mean percentage of correct responses was 87% (
In summary, we found that automatic non-symbolic numerical processing began at age 3- to 4-years old and size congruity effects tended to reduce with increasing age. The study also found a CP-knowledge effect and ratio effect.
However, some researchers have suggested that inhibitory control is necessary to resolve the conflict between visual and numerical parameters [
To directly test this hypothesis we conducted a second experiment in which we measured inhibition skill in 4-year-old children with stable size congruity effects. Additionally, we were also concerned about the interference and facilitatory components of the size congruity effect by using neutral condition (the number of dots is the same but the physical size differs). In the congruent trials, the RTs were shorter and accuracy was higher than in the neutral trials (facilitation effect); whereas in the incongruent trials, the RTs were longer and the accuracy lower than in the neutral trials (interference effect).
A total of 31 children participated in the study (mean age ± SD: 49.93 ± 2.03 months; range: 46–54 months; 15 boys), all from the same kindergarten as in Experiment 1.
Inhibition was assessed using the day-night task [
Tasks and stimuli were the same as in Experiment 1, except we added neutral trials to measure the facilitation and interference effects. A total of 68 trials were administered to each participant: 8 practice trials, 24 incongruent, 24 congruent, and 12 neutral trials (see Appendix). In the neutral condition 2 arrays containing the same number of dots were presented. The size of dots in one group was larger (radius: 0.9 cm) than the other (radius: 0.5 cm), similarly to Experiment 1.
Pearson correlations were calculated between day-night scores and the congruity, facilitation, and interference effects, and accuracy and RTs in each condition (
ACC-congruity effect (congruent—incongruent) | RT-congruity effect (incongruent—congruent) | ACC-facilitation effect (congruent—neutral) | ACC-interference effect (neutral—incongruent) | |
---|---|---|---|---|
Day-night scores | −0.258 ( |
0.308 ( |
−0.083 ( |
−0.159 ( |
ACC-congruent | ACC-incongruent | ACC-neutral | RT-congruent | |
Day-night scores | 0.098 ( |
0.287 ( |
−0.247 ( |
−0.326 ( |
RT-facilitation effect (neutral—congruent) | RT-interference effect (incongruent—neutral) | RT-incongruent | RT-neutral | |
Day-night scores | 0.195 ( |
0.149 ( |
−0.258 ( |
−0.247 ( |
The p-values of the correlations between day and night scores and the RT congruity effect, day and night scores and the RT-congruent, as well as day and night scores and the ACC-incongruent were marginal significant. We added bootstrapped 95% confidence intervals (1,000 bootstrapping samples) and calculated Bayes factors for the five largest correlation scores to verify this result. The results showed in the
RT congruity effect | RT-congruent | ACC-incongruent | ACC-congruity effect | RT-incongruent | |
---|---|---|---|---|---|
confidence intervals | 0.28 to 0.34 | -0.38 to -0.26 | 0.26 to 0.32 | -0.32 to -0.19 | -0.32 to -0.19 |
Bayes factors | B = 1.05 | B = 1.22 | B = 0.90 | B = 0.73 | B = 0.49 |
ACC of all trials reached 96.5%. A 3-way analysis of repeated measures ANOVA (conditions: congruent, neutral, incongruent) was conducted. Greenhouse–Geisser corrections for homogeneity of variance violations were implemented as determined by Mauchly’s test. The main effect was significant (
We conducted a 3-way analysis of repeated-measures ANOVA (condition: incongruent in low ratio, neutral, incongruent in high ratio). Mauchly's test of sphericity showed that homogeneity of variance was not violated. The main effect was significant (
Mean RTs from all correct trials were computed. Controlling for the RTs of the color discrimination task, a 3-way analysis of repeated-measures ANCOVA (conditions: congruent, neutral, incongruent) was conducted. Mauchly's test of sphericity showed that homogeneity of variance was not violated. The main effect was significant (
We conducted a 3-way (conditions: incongruent in low ratio, neutral, incongruent in high ratio) analysis of repeated-measures ANCOVA, controlling for the RTs of the color discrimination task. Mauchly's test of sphericity showed that homogeneity of variance was not violated. The main effect was significant (
We computed the RTs-interference effect (incongruent RTs—neutral RTs) respectively in the high ratio and low ratio conditions and used t-test to compare the effect. A larger RTs-interference effect was found for the low ratio condition (
We studied the development of automated non-symbolic magnitude and its influencing factors. We first explored the development of the size congruity effect in 3- to 6-year-old children. Second, whether the mastery of CP knowledge and number comparison ability related to the size congruity effect in children was investigated. Third, we questioned whether ratio affected the automatic processing of non-symbolic magnitude. Finally, we explored the relationship between the size congruity effect and inhibition skill, as well as interference and facilitatory components in children aged 4 years old.
Our experiment documented that automatic access to non-symbolic magnitude began at 3- to 4-years-old and size congruity effects tended to reduce with increasing age from 4 years old. This developmental trend is in agreement with previous research in school children [
It may also be necessary to consider the role of inhibitory mechanisms in automatic processing; however, previous research suggests the development of inhibiting ability is independent of automatic numerical processing [
We investigated the CP-knowledge effect. Negen and Sarnecka (2015) found that children at the non-CP-knower level performed by chance in numerosity comparison tasks (standard ANS task), indicating that they may not have understood the task [
Our study found that CP knowledge had relationship with the size congruity effect and the non-CP knowers had a larger congruity effect with low ratio. In addition, the ability to process symbolic magnitude was negatively correlated with congruity effect. These findings suggest developmental change occurs and support the hypothesis that increased utilization of symbolic numerosity processing may result in the reduction of non-symbolic size congruity effects, which index the ability to automatically process non-symbolic numerosities. It is well-known that training and practice can enhance automatized performance in different cognitive processing [
We also found the size congruity effect more easily and a larger interference effect in low ratio conditions, providing evidence that children used approximate number representation when performing the physical size comparisons task. These results add to a growing body of evidence that ratio or distance effects exist in automatic numerical processing and are consistent with previous reports on both symbolic and non-symbolic stimuli in school children and adults [
However, not all studies have shown ratio/distance effect in automatic processing of number magnitude information [
On the contrary, these results are inconsistent with Dehaene and Akhavein’s (1995) model of single representations of number magnitude [
In the present study, we also found the size congruity effect more easily in low ratio conditions. Our non-symbolic task was different from Tzelgov et al. (1992) and Rubinsten et al. (2002), with the number of dots larger than 5. The classification of digits as large or small was mainly memory-based, as the previous studies mentioned. In the non-symbolic numerosity task, because of imprecision of large numerical magnitude representation, subjects had difficulty retrieving from memory to judge the whether the number of dots was large or small. Therefore, our finding of a ratio effect supports an algorithmic-based process which maps magnitude onto an analogical number line, at least in automatic non-symbolic large numerosity processing.
The ratio effect finding suggested that subjects detected a smaller difference between 2 non-symbolic stimuli with greater difficultly, resulting in less numerosity activation in the high ratio. Children responded more correctly in the incongruent trials of low ratio than in neutral trials (ratio: 1). Children responded more slowly in the incongruent trials of low ratio than in high ratio, and more sequentially than in neutral trials. The larger interference effect in the low ratio condition indicated that the precision of discriminating the numerical difference between 2 sets of dots decreased with the ratio. Thus, young children might use approximate number representation when automatically processing large numerical magnitude. Because the ANS is active early in infancy, children mostly rely on it before learning symbolic representation, when representing large cardinal values [
Our results demonstrated the presence of a significant interference effect but no facilitation effect for non-symbolic processing in 4-year-old children. The finding was consistent with Rousselle and Noël (2008) who also only found an interference effect in non-symbolic processing in 4- to 6-year olds [
To conclude, this study traced the development and explored the influencing factors of automatic numerical processing of non-symbolic stimuli in preschool children. By the age of 3 to 4 years, children can automatically process numerosities and sensitivity to numerical cues decreases with age. The ratio effect and a larger interference effect in a low ratio suggested that the ANS plays a role in non-symbolic physical size comparison tasks. The effect of CP knowledge and its relationship with number comparison tasks indicated that the increased utilization of symbolic representation may have a negative correlation with automatic non-symbolic numerical processing. Only significant interference effects were present in 4-year-old children. The correlation between inhibition skills and size congruity effect need further study with a larger sample.
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