## 3 Results  
The test in the kindergarten setting allowed evaluation of the app functionality. The activities were highly appreciated by the children, who experimented with the device with curiosity and enthusiasm. A video illustrating various moments of the study, with the children performing different activities, is provided in the Supplementary Materials. Figure 3 depicts specific moments during activities, with virtual environments projected on the floor (Figure 3A,B) or on the wall (Figure 3C,D). A total of 58 filled grids were collected on a set of 31 total game sessions (each game session was devoted to one activity). The forms were filled by the different observers who participated in the activities (educators and psychologists). The number of observations for the various activities (9 different activities) ranged from 12 (What's hiding) to 2 (musical canon), with a mean of 6.44. The different numbers depended on the teachers' time schedules that allowed for participation in the activities, only at certain times of the day. At least one of the two psychologists was always present. First of all, ICC values computed among the raters for each activity were larger than 0.9, but for Musical Puzzle (ICC = 0.5). Therefore, the data from different observers, except for Musical Puzzle (for which ICC was deemed to low) and Canon (for which too few observations were collected to be considered reliable), were collapsed by averaging. Figure 4 shows the results about the variables rated at the different timepoints, T1 (Initial), T2 (Intermediate) and T3 (Final), considering the system as a whole (for this analysis, Musical Puzzle and Canon were not considered). As supported by the statistical analysis (Table 6), a significant increase in comprehension, strategy, enjoyment, participation, interaction and cooperation along timepoints was highlighted. A post hoc analysis stated that significant differences were mainly between T1-T2 and T1-T3, while they stabilized at T3, but for comprehension, that significantly increased also at T3. Figure 3: Moments of playful activities. (**A**) Sound environments: children have to find the trumpet with the sound corresponding to the central image (a storm). (**B**) the “Old MacDonald Had A Farm”: children have to jump on the animal in the correct instant during the song. (**C**) Musical Puzzle: children have to find the correct order of the trumpets to play the song (“La casa”—the house) correctly. (**D**) What’s hiding activity: children use feather clusters to discover what clouds are hiding (a ballpoint pen detail). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Friedman Test**} & \multicolumn{6}{c}{_Post Hoc_—Wilcoxon Test_} \\ \hline  & **T1** & **T2** & **T3** & **Chi-Squared** & \(p\)**-Value** & **T1 vs. T2** & **T1 vs. T3** & **T2 vs. T3** \\ \hline COMP & 1.00 & 2.13 & 2.88 & 15.20 & **0.001** & **0.012** & **0.012** & **0.028** \\ \hline CONF & 2.19 & 2.38 & 1.44 & 5.25 & 0.072 & & & \\ \hline STRAT & 1.00 & 2.38 & 2.63 & 13.07 & **0.001** & **0.012** & **0.012** & 0.674 \\ \hline ENJ & 1.31 & 2.19 & 2.50 & 6.69 & **0.035** & **0.043** & **0.035** & 0.173 \\ \hline PART & 1.25 & 2.25 & 2.50 & 8.00 & **0.018** & **0.021** & **0.017** & 0.144 \\ \hline INT & 1.19 & 2.13 & 2.69 & 10.14 & **0.006** & **0.017** & **0.018** & 0.092 \\ \hline COOP & 1.13 & 2.31 & 2.56 & 9.74 & **0.008** & **0.017** & **0.012** & 0.612 \\ \hline Q-DEV & 1.94 & 1.88 & 2.19 & 1.40 & 0.497 & & & \\ \hline Q-ACT & 2.44 & 1.63 & 1.94 & 3.91 & 0.142 & & & \\ \hline Q-ADU & 2.13 & 1.88 & 2.00 & 0.50 & 0.779 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison among timepoints for each variable. Data in T1, T2 and T3 are reported as mean ranks. Statistically significant correlations (\(p<0.05\)) are shown in bold. When the [PERSON] test was statistically significant, \(p\)-values of post hoc analysis (Wilcoxon test) are reported.