We first examined how effects of emotions on arithmetic performance change with participants’ age. Then, we investigated sequential modulations of effects of emotions on performance. In both analyses, latencies larger than the mean of the participant’s mean + 2.5 SDs were removed (mean: 0.5%).
Age-related changes in effects of emotion on arithmetic performance.
Effects of emotion on true and false problems. Effects of emotion on arithmetic performance and age-related differences therein were analyzed via mixed-design ANOVAs on mean response times for correct responses and percentages of errors (see Table 1), involving 4 (Age: 8, 10, 12, and 15 year-old children) x 2 (Problem Type: False, True) x 2 (Emotion: Neutral, Negative), with age as the only between-participants factor. We also analyzed z scores to control for potentially artifactual interactions due to increased speed of processing with age. Analyses of means and z scores showed similar patterns for effects of negative emotions on performance and for the Age x Emotion interaction. Therefore, only analyses of means are reported here. Also, the same age-related differences in effects of negative emotions came out significant when they were analyzed on proportional increased latencies in emotion condition relative to neutral condition (i.e., for each participant and each type of problem, the dependent variable was [(mean response times in the emotion condition – mean response times in the neutral condition)/mean response times in the neutral condition]. Finally, preliminary analyses examined effects of emotions during the first versus second half of the experiment. However, above and beyond general effects of block (i.e., children were faster during the second block than during the first block), no interaction involving the block factor came out significant. Therefore, we report analyses collapsed over blocks).
Analyses of mean verification times showed main effects of age (F(3,203) = 65.105, p < .001, ƞ2p =.490), problem type (F(1,203) = 4.912, p = .028, ƞ2p =.024), and emotion (F(1,203) = 112.112, p < .001, ƞ2p =.356). Children were faster as they grow older. Planned comparisons showed that 8 year olds (7559 ms) were slower than 10 year olds (3970 ms; F(1,203) = 104.59, p < .001, ƞ2p =.340), who were as fast as 12 year-olds (3646 ms; F < 1.0). Finally, 15 year-olds (3009 ms) were marginally faster than 12 year olds (F(1,203) = 2.992, p = .085, ƞ2p =.014). Moreover, participants were 105 ms faster on false problems than on true problems (4543 ms vs. 4648 ms), and 645 ms slower under emotion than under neutral condition (4918 ms vs. 4273 ms). Also, the significant Problem Type x Emotion interaction (F(1,203) = 8.551, p = .004, ƞ2p =.040) revealed that emotions led participants to slow down more while verifying true problems (+ 746 ms; F(1,203) = 105.49, p < .001, ƞ2p=.342) than false problems (+ 544 ms; F(1,203) = 65.35, p < .001, ƞ2p=.244). This Problem Type x Emotion interaction was found significant in all age groups (Fs > 8.503, ps < .005). Finally, and most interesting, emotion effects decreased as children grow older, although emotion effects were significant in all age groups (Fs > 19.272, ps < .001).
Table 1
Mean solution times and percentages of errors for true and false problems under neutral and emotion conditions as a function of children’s age.
Age Group x Problems | Latencies (in ms) | % Errors |
Neutral | Emotion | Differences | Neutral | Emotion | Differences |
8 year old. | | | | | | |
True Problems | 6698 | 8627 | 1930 | 8.5 | 8.8 | 0.3 |
False Problems | 7152 | 8558 | 1407 | 8.8 | 8.8 | 0.0 |
Means | 6925 | 8593 | 1668 | 8.7 | 8.8 | 0.2 |
10 year old. | | | | | | |
True Problems | 3646 | 4087 | 441 | 3.4 | 4.3 | 1.0 |
False Problems | 3918 | 4228 | 310 | 4.3 | 4.0 | -0.2 |
Means | 3782 | 4158 | 376 | 3.8 | 4.2 | 0.4 |
12 year old. | | | | | | |
True Problems | 3506 | 3827 | 321 | 5.9 | 6.4 | 0.5 |
False Problems | 3521 | 3729 | 209 | 5.8 | 5.4 | -0.4 |
Means | 3513 | 3778 | 265 | 5.8 | 5.9 | 0.0 |
15 year old. | | | | | | |
True Problems | 2831 | 3124 | 292 | 6.8 | 5.4 | -1.4 |
False Problems | 2915 | 3166 | 251 | 7.0 | 5.7 | -1.3 |
Means | 2873 | 3145 | 271 | 6.9 | 5.5 | -1.3 |
More specifically, emotions led 8 year olds to slow down by 1668 ms, 10 year olds by 376 ms, 12 year olds by 265 ms, and 15 year olds by 272 ms. Note that emotions increased latencies in 12 and 15 year-old participants to the same extent (F < 1.0). Analyses of errors showed that participants’ age was the only significant effect (F(3,203) = 7.652, p < .001, ƞ2p=.102). Larger error rates were made by the youngest group of 8 year-old children (F(1,203) = 22.734, p < .001, ƞ2p=101), and comparable error rates were found among the other three age groups (Fs < 3.623).
Distributional analyses of emotion effects. We used the so-called Vincentization technique42 to characterize the dynamics of the emotion effects and to compare these dynamics across age groups. We analyzed distributions of the emotion effects (i.e., latencies for emotion trials – latencies for neutral trials) as a function of the overall distribution of latencies43,44. The latencies for correct responses were sorted in ascending order and binned in four classes of equal size (N = 24 observations maximum). The mean of each bin (henceforth referred to as quartiles) was computed separately for each participant and each emotion condition. Average distributions of latencies were obtained by computing the mean values of quartiles by emotion condition (neutral, emotion), and age group separately. Preliminary analyses revealed similar distributions of emotion effects for true and false problems. Therefore, we report analyses collapsed over problem type.
Emotion effects were analyzed with an ANOVA with 4 (Age: 8, 10, 12, and 15 year-old children) x 4 (Quartile: 1st, 2nd, 3rd, and 4th ), with age as the only between-participants factor. The main effects of age (F(3,609) = 28.925, p < .001, ƞ2p =.299) and of quartile (F(3,609) = 54.192, p < .001, ƞ2p =.211) were significant. The effects of quartiles were significant in all age groups (Fs > 3.55), showing that the longer the latencies, the larger the emotion effects (linear trends, Fs > 4.451; see Fig. 1).
Mediation analyses. We tested whether arithmetic fluency mediated age-related changes in how emotions influence arithmetic performance. A simple mediation analysis on emotion effects (differences in latencies between emotion and neutral conditions) was carried out. Using the Medmod 1.1.0 module for JAMOVI (10000 boostrapped resamples; Model 445), we regressed emotion effects on age (coded in years) and entered arithmetic fluency as the mediator. As can be seen in Fig. 2, emotion effects decreased with increasing age (a=-69.49), and the higher arithmetic fluency the smaller the effects of emotions (b=-13.78). The confidence interval of the indirect effect through arithmetic fluency did not include zero (ab= -112.30; CI95%=(-169.00 — -66.60). Arithmetic fluency was thus a significant mediator that accounted for 61.8% of the total age-related changes in effects of emotion on children’s arithmetic performance. Note however that age had a unique influence on emotional effects (c’=-69.49, p = .010).
Age-related changes in sequential modulations of effects of emotions
The goal of this series of analyses was to determine whether the emotion effects found on latencies on current trials were modulated by the type of immediately preceding trials (neutral vs. emotion) and to determine how such modulations change with age. Mean latencies on current trials (Table 2) were analyzed using 4 (Age: 8, 10, 12, and 15 year-old children) x 2 (Previous Trials: neutral, emotion) x 2 (Current Trials: neutral, emotion) ANOVAs, with age as the only between-participants factors.
The effects of age (F(3,203) = 64.399, p < .001, ƞ2p =.869), previous trials (F(1,203) = 6.050, p < .015, ƞ2p =.029), current trials (F(1,203) = 132.442, p < .001, ƞ2p =.395), and Age x Previous Trials (F(3,203) = 27.075, p = .286, ƞ2p =.002) were significant. Most importantly, the Previous Trials x Current Trials interaction (F(3,203) = 9.733, p = .002, ƞ2p =.046) was significant. The Grade x Previous Trials x Current Trials interaction (F < 1.5) was not significant. In each age group, emotion effects on current trials were smaller after emotion trials than after neutral trials. Emotion effects went from 1574 ms after emotion trials down to 1215 ms after neutral trials in 8 year-old children, from 430 ms to 386 ms in 10 year-old children, from 428 ms to 77 ms in 12 year-old children, and from 363 ms to 231 ms in 15 year-old children. All these emotion effects were significant (ts > 3.929, ps>..001), except after neutral trials in 12 year-old children (t < 1.190).
In sum, in addition to significant emotion effects in all age groups, we found that deleterious effects of negative emotion on performance were larger on true than on false problems, increased with problems solved more slowly, and decreased with participants’ increasing age. Moreover, we found that emotion effects were sequentially modulated by emotional valence of previous trials in all age groups, such that they were larger on current trials following emotion trials than after neutral trials.
Table 2
Mean solution times (in ms) and percentages of errors for current neutral or emotion trials following neutral or emotion trials.
Age x Previous Trials | Latencies (in ms) | % Errors |
Current Trials |
Neutral | Emotion | Differences | Neutral | Emotion | Differences |
8 year old | | | | | | |
Neutral | 6915 | 8130 | 1215 | 9.2 | 8.5 | 0.7 |
Emotion | 6670 | 8244 | 1574 | 8.4 | 9.0 | -0.7 |
10 year old. | | | | | | |
Neutral | 3724 | 4109 | 386 | 3.9 | 4.2 | 0.3 |
Emotion | 3820 | 4250 | 430 | 3.8 | 4.1 | 0.3 |
12 year old. | | | | | | |
Neutral | 3507 | 3584 | 77 | 6.1 | 5.9 | 0.2 |
Emotion | 3505 | 3933 | 428 | 5.5 | 5.9 | 0.3 |
15 year old. | | | | | | |
Neutral | 2815 | 3046 | 231 | 7.1 | 6.4 | 0.7 |
Emotion | 2904 | 3267 | 363 | 6.6 | 4.4 | 2.2 |