## 2 Literature Review and Theoretical Foundation  
### Mathematical Problem-Solving Beliefs  
[PERSON] identified four key components that have an impact on mathematical problem solving [36]. These components can be conceptualized as mathematical knowledge, beliefs, metacognitive regulation, and metacognitive knowledge. In this study, the concept of belief, which is one of the components, was dealt with. [PERSON] and [PERSON] suggest that rather than a sole definition of the word \"belief\" that is accurate and true, there are several definitions that can be useful depending on the context [37]. Anglophone philosophers of mind often use the term \"belief\" to refer, roughly, to the attitude we have when we accept or regard something as true [38]. [PERSON] et al. defined beliefs as personal assumptions that learners use when determining what kind of action they will take [39]. They claimed that a belief is the source of the motivation that drives an action. This means that specific behaviors follow specific beliefs. For instance, students are more inclined to put in the effort to study if they believe it will help them in the long run [40]. Beliefs are becoming more and more important in mathematics education, and it is a good idea for students to understand so they can have a positive attitude toward the subject [41]. The process of learning is greatly aided by mathematical beliefs, which are subjective value judgments influenced by one's prior experiences [42]. Moreover, individuals' attitudes about mathematics have an effect on how they learn and solve problems [43].  
It is now well acknowledged that elements other than a person's knowledge also influence the procedures involved in solving mathematical problems [44]. [PERSON] stated that students' beliefs on the nature of mathematical knowledge and learning have an impact on certain aspects of the problem-solving process [45]. He noted, for instance, that students who struggled with problem solving thought math issues should be answered in ten minutes or less, that mathematicians were naturally talented people, and that students should have confidence in their mathematical understanding. Unsuccessful students may be unaware of their unfavorable attitudes toward mathematics. Additionally, these ideas might be harmful to their development and ability to learn [44]. As such, the development of students' mathematical beliefs is crucial [41]. An extremely significant portion of one's beliefs about mathematics are developed in school, and one's beliefs about mathematics shape how one interprets the mathematical world [46; 47]. Therefore, teachers' beliefs about mathematical problem solving also gain importance.  
[PERSON] outlined three generally accepted and utilized categories of teacher beliefs regarding the nature of mathematics [48]. The first is the instrumentalist perspective, which defines mathematics as a body of knowledge, abilities, and principles to be applied toward some external goal. Mathematics is a static body of preexisting, unified knowledge that is still in need of discovery, according to the Platonist approach, which makes up the second category. The third category identified by [PERSON] is the problem-solving perspective, which views mathematics as a process as opposed to a result and views it as a continually evolving and innovative human invention [48]. One of the first studies on this subject was [PERSON]'s pioneering investigation of secondary mathematics teachers' attitudes, which greatly influenced [PERSON]'s categories of beliefs regarding the nature of mathematics [48; 49]. Although there have been studies since then, it cannot be said that researchers have paid much attention to this issue [50]. Therefore, this study is important in that it will examine teachers' beliefs about mathematical problem solving in an up-to-date way. In addition, this investigation was carried out with artificial intelligence techniques, which are considered new for educational sciences.