## 4 Discussion  
Our objective of the study was to analyze the effectiveness of the game and the efficacy of game mechanic factors affecting attention span and executive function in the elderly. Regarding attention span, from the data of the two attention assessments (D-CAT and SAT), we used a paired sample \(t\)-test to compare the pre-test and post-test results of the game training. This showed that there is a significant difference between D-CAT (\(p\) < 0.001) and SAT (\(p\) < 0.001), which indicates that the game is effective. With the advancement of technology, individuals can improve their attention span by training with the serious mental calculation game in this study. This also proves that this game design can successfully turn traditional mental calculation into a new game on smartphones and with attention-span-improvement outcomes. Moreover, many individuals have smartphones and use them daily; it is more convenient for them to undergo cognitive training with mobile technology devices. Regarding executive function, other studies have shown that traditional arithmetic calculation does not enhance executive function [91,92]. However, by using this serious smartphone game on mental calculation, participants can improve their attention span and executive function. According to the data of two executive function assessments (TMT-A and TMT-B), we used the paired sample \(t\)-test to compare the results of the pre-test and post-test scores of the game. This showed that there is a significant difference between TMT-A (\(p\) < 0.001) and TMT-B (\(p\) < 0.001). This might be because the process of the traditional \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{6}{c}{**Game Mechanic Factors**} & \multicolumn{4}{c}{**Assessment Tests**} \\ \hline
**Participants** & **Difficulty** & **Pressure** & **Competition** & **D-CAT** & **SAT** & **TMT-A** & **TMT-B** \\ \hline Group 1 & With & Without & With & 0.95 & 0.87 & 0.63 & 0.76 \\ Group 2 & With & With & With & 0.83 & 0.80 & 0.85 & 0.63 \\ Group 3 & With & Without & Without & 0.95 & 0.89 & 0.65 & 0.97 \\ Group 4 & With & With & Without & 0.88 & 0.46 & 0.70 & 0.70 \\ Group 5 & Without & Without & With & 0.94 & 0.90 & 0.96 & 0.81 \\ Group 6 & Without & With & With & 0.98 & 0.62 & 0.85 & 0.93 \\ Group 7 & Without & Without & Without & 0.77 & 0.82 & 0.96 & 0.70 \\ Group 8 & Without & With & Without & 0.99 & 0.82 & 0.41 & 0.96 \\ \hline \hline \end{tabular}
\end{table} 
Table 26: Test–retest reliability (intraclass correlation coefficient). arithmetic calculation during training is straightforward. Subjects either verbally answer an examiner or write down the answer on paper. However, the game requires both the use of the brain and the movement of the hands and fingers. Players need to mentally calculate the question, choose cards, use their fingers to select them, and then execute commands by moving the correct answer into the target position. After that, players removed their finger from the screen for the final answering process. This combination of mental and physical operation activity on a smartphone is more complicated than a traditional arithmetic calculation. Therefore, this could be the reason that this game can improve both attention span and executive function. Difficulty is an important game mechanic factor. The mixed repeated-measure ANOVA showed that there are significant differences between D-CAT (\(p<0.001\)), SAT (\(p<0.001\)), TMT-A (\(p<0.001\)), and TMT-B (\(p<0.001\)). In the theory of flow, a moderate difficulty level can increase performance, where a suitable level of difficulty means that a game is moderately difficult, which is an effective result in this experiment. The difficulty level might provide a challenge for individuals. They want to overcome a challenge and feel successful. This makes the game more attractive and makes players focus on it, thus improving attention span and executive function.