AI-Driven Predictions of Mathematical Problem-Solving Beliefs: Fuzzy Logic, Adaptive Neuro-Fuzzy Inference Systems, and Artificial Neural Networks

Abstract

Featured Application: This study demonstrates the applicability of artificial intelligence methods, such as fuzzy logic, artificial neural network (ANFIS), and adaptive neuro-fuzzy inference system (ANN), in predicting mathematical problem-solving beliefs (MPSBs). The proposed models can be utilized in educational settings to identify and support teachers or students with specific belief patterns, thereby enabling tailored interventions to enhance problem-solving skills. Additionally, the integration of AI techniques into educational research paves the way for innovative approaches to studying cognitive and behavioral traits. Considering that creative thinkers are individuals who can think outside of the box, exhibit original thoughts, and demonstrate problem-solving skills, it is likely that there is a relationship between mathematical problem-solving beliefs (MPSBs) and creative thinking dispositions (CTDs). This study aimed to predict teachers' MPSBs with their CTDs and some demographic features. Three different artificial intelligence models (fuzzy logic, artificial neural network (ANN), and adaptive neuro-fuzzy inference system (ANFIS)) were developed, and artificial data were obtained. The inputs of the research were determined as CTD, gender, age, educational level, school level, and teaching experiences, and the output was determined as MPSBs. Afterward, whether there was a relationship between real and artificial results was examined with statistical analysis. The research results show that there is a statistically significant, positive, and moderate relationship between artificial ANN MPSB scores and real MPSB scores (r = 0.422; p < 0.05), as well as artificial ANFIS MPSB scores and real MPSB scores (r = 0.564; p < 0.05). These results are important sources of evidence indicating that artificial intelligence methods accurately predict teachers' MPSB scores.