## 5 Discussion and Conclusions  
We have used three artificial intelligence models that have allowed us to investigate how creative thinking dispositions and demographics may act in concert to influence the mathematical problem-solving beliefs of teachers. The aim of this study was actually to provide evidence on whether some teachers' educational characteristics can be determined without responding to any scale. For this purpose, the following process was implemented and the process is shown in Figure 8. If real data and artificial data are related to each other, it will be interpreted that the scores obtained with artificial intelligence predict the real scores correctly. \begin{table}
\begin{tabular}{c c c c c c} \hline \multicolumn{6}{c}{**Correlations**} \\ \hline  & & & **Real Scores** & \
\begin{tabular}{c} **Artificial ANFIS** \\ **Scores** \\ \end{tabular} &
\begin{tabular}{c} **Artificial ANN Scores** \\ \end{tabular} \\ \hline \multirow{8}{*}{Real scores} & \multicolumn{2}{c}{Correlation Coefficient} & 1.000 & 0.564 ** & 0.422 ** \\ \cline{2-5}  & \multicolumn{2}{c}{Sig. (2-tailed)} & \(\cdot\) & 0.000 & 0.000 \\ \cline{2-5}  & \multicolumn{2}{c}{N} & 133 & 133 & 133 \\ \cline{2-5}  & \multirow{4}{*}{Bootstrap c} & Bias & 0.000 & \(-\)0.003 & \(-\)0.004 \\ \cline{2-5}  & \multicolumn{2}{c}{Std. Error} & 0.000 & 0.081 & 0.078 \\ \cline{2-5}  & \multirow{4}{*}{Bootstrap c} & 95\% Confidence Interval & Lower & 1.000 & 0.397 & 0.254 \\ \cline{2-5}  & \multirow{4}{*}{Bootstrap c} & \multicolumn{2}{c}{Upper} & 1.000 & 0.718 & 0.559 \\ \cline{2-5}  & \multirow{4}{*}{Bootstrap c} & Correlation Coefficient & 0.564 ** & 1.000 & 0.357 ** \\ \cline{2-5}  & \multirow{4}{*}{Artificial ANFIS scores} & Sig. (2-tailed) & 0.000 & \(\cdot\) & 0.000 \\ \cline{2-5}  & \multirow{4}{*}{Bootstrap c} & Bias & \(-\)0.003 & 0.000 & 0.001 \\ \cline{2-5}  & \multirow{4}{*}{Bootstrap c} & Std. Error & 0.081 & 0.000 & 0.091 \\ \cline{2-5}  & & 95\% Confidence Interval & Lower & 0.397 & 1.000 & 0.171 \\ \cline{2-5}  & \multirow{4}{*}{Bootstrap c} & Interval & Upper & 0.718 & 1.000 & 0.523 \\ \cline{2-5}  & \multirow{4}{*}{Bootstrap c} & Correlation Coefficient & 0.422 ** & 0.357 ** & 1.000 \\ \cline{2-5}  & \multirow{4}{*}{Bootstrap c} & Sig. (2-tailed) & 0.000 & 0.000 & \(\cdot\) \\ \cline{2-5}  & & N & 133 & 133 & 133 \\ \cline{2-5}  & \multirow{4}{*}{Bootstrap c} & Bias & \(-\)0.004 & 0.001 & 0.000 \\ \cline{2-5}  & & Std. Error & 0.078 & 0.091 & 0.000 \\ \cline{2-5}  & & 95\% Confidence Interval & Lower & 0.254 & 0.171 & 1.000 \\ \cline{2-5}  & \multirow{4}{*}{Bootstrap c} & Hyper & 0.559 & 0.523 & 1.000 \\ \hline \end{tabular}  
* ** Correlation is significant at the 0.01 level (2-tailed). c Unless otherwise noted, bootstrap results are based on 1000 bootstrap samples.  
\end{table} 
Table 5: Correlation analyses. Firstly, Turkish teachers' MPSBs are modeled using three distinct artificial intelligence techniques: fuzzy logic, ANN, and ANFIS. In the study, it was explained with the support of the literature that teachers' MPSBs and CTDs [60; 64; 66] and their gender were related [40; 44; 69; 70; 71; 72; 73; 74]. No study has explicitly examined the impact of age on MPSBs. On the other hand, age has an impact on problem solving [78; 79], beliefs [77], and mathematics success [76]. Therefore, age was also included as an input variable because age was also related to experience and teachers' experience also affected their beliefs about mathematical problem solving. Individuals can solve problems more easily if they make appropriate and correct use of their experiences [57]. Results show that as individuals' education levels increase, their problem-solving skills increase [80; 81]. In addition, it is thought that working at different levels may be a variable in teachers' problem-solving beliefs. In conclusion, the inputs of the research were determined as students' CTD, gender, age, educational level, school level, and teaching experience, and the output was their MPSB.