**Abstract**

With the rapidly developing technology, the labor force of the society has changed direction, and in the age of informatics, creative engineering applications have come to the forefront. Accordingly, the education levels of the labor force were also changed. The science, technology, engineering, and mathematics (STEM) education model in most countries aims to teach science, mathematics, technology, and engineering in relation to primary, secondary, high school, and higher education. STEM education, which has an impact in our country in recent years, has an important role in acquiring new skills, supporting creativity, innovation, and entrepreneurship, gaining the ability to transition between professions and adapting to new occupations. Nowadays, technology is expected to have different skills from individuals who will work in different fields with rapid development. Also, different teaching strategies play a major role in STEM integration and training. One of them, mathematical modeling, is the process of analyzing real-life or realistic situation using mathematical methods in the most general sense. The idea that mathematical modeling cycles should be used in STEM education at all levels from primary to tertiary education has gained importance in recent years, since it increases the students' motivation towards the lesson and they learn better by concentrating their attention.

**Keywords:** mathematical modeling cycle, STEM, real-life problems, metacognition, learning strategies

### **1. Introduction**

Because of the quality of teaching, students find mathematics very abstract and fear mathematics. Thus, there may be difficulties in transferring the information learned in the classroom to the daily life. The fact that the learning environments are teacher-centered and uniform can be one of the reasons why students have difficulty in implementing information in their daily lives. In this sense, the subjects taught in the course should be taught by different practices and activities in a way that is more meaningful and related to daily life. One of these activities, mathematical modeling activities, can be said to show the relationship between real life and its applicability to real life.

Mathematical modeling involves a complex process in which a problem state encountered in real life is formulated mathematically and solved with the help of mathematical models, and the solution is interpreted and evaluated in the real world [1]. In this process, mathematics is used to represent, analyze, predict, or otherwise make sense of real-world situations [2]. In mathematical modeling, the individual tries to create a mathematical model that will solve the problem that he/ she encounters in real life or in the future. The model in question includes not only mathematical structures but also estimates, assumptions, and strategies for solution [3, 4]. In other words, the solution plan including the assumptions, estimations, and mathematical tools used to solve the problem is the mathematical model for the problem. In addition to being mathematically correct, the model should be meaningful and adaptable for real life. While solving the problem, the individual should also evaluate the meaning of the solution for the real world. All these processes and all the stages of problem-solving in addition to the individual model are mathematical modeling [5].

Science, technology, engineering, and mathematics (STEM) education with technology age is appeared in the twenty-first century; it plays an important role in shaping cultural and economic development, embracing innovation, caring about creativity and problem-solving [6]. Due to the benefits of STEM education on the development of countries, intensive efforts are being made to reach the desired level between STEM and science education [7, 8].

The United States Bureau of Labor Statistics (2009) stated that 80% of the professions will need technology in 2018, and 8.5 million workforce will be needed in the STEM disciplines. STEM training can help students become problem-solvers and innovative and technologically literate citizens [9]. As the society becomes more dependent on technology, engineering, and mathematics, it is becoming increasingly important that students receive an integrated STEM education.

Due to global developments in the world demanding the thinking skills necessary to create a high workforce in the future, the curriculum for inter-curricular education in schools has been implemented. Initially, the implementation of STEM training was carried out with projects outside the formal classes. However, in the STEM education integrated with the direct curricula like Finland, there are also countries where many disciplines are taught.

STEM training has been implemented in many countries of the world (Korea, Japan, Germany, China, etc.), especially in the United States (USA) and in secondary schools and universities starting from primary schools. As STEM Education Coalition, there are organizations that undertake a roof in STEM education and direct STEM education and develop policy in this context [10].

STEM training, based on the integration of the disciplines of science, technology, engineering, and mathematics, has emerged as a result of the efforts of integrating separated parts in the real-world context [11], because, only by eliminating and integrating the boundaries between disciplines can the complex problems encountered in real life be understood and overcome. [12]. With STEM-oriented activities, the aim is to solve the real-life problems with the applications of technology and engineering disciplines by using the scientific knowledge which is the product of the basic sciences [12, 13]. For this purpose, it is necessary to remove the boundaries between disciplines [14–16]. In other words, STEM education understanding can be structured in the context of real-life problems by establishing a relationship between disciplines and focusing on a certain discipline.

Nowadays, both the training and applications related to STEM have been widely used in the world. On the one hand, many people now agree on what STEM means, interdisciplinary studies, and the common uses of science, technology, engineering, and mathematics. However, Clark-Wilson and Ahmed [17] emphasized that mathematics was included in an integrated curriculum on how M should be interpreted. Therefore, mathematics educators have said that mathematics in STEM should be used more, not as a servant. Coad [18] emphasizes that the use of mathematics

**153**

way (**Figure 2**).

skills and teamwork [31].

*The Role of Mathematical Modeling in STEM Integration and Education*

situation in order to make the real-life situation meaningful.

as a data presentation tool with its study may lead to discrediting mathematics. Although mathematics is an inevitable component of STEM activities, it is also emphasized in this study that it is important to evaluate mathematical success and

One of the most important tools for transition to STEM education is mathematical modeling [19]. Model-eliciting activities (MEA) are mathematical modeling applications. Mathematical modeling applications are composed of concepts related to different disciplines by their nature [20]. There is not a single definition of mathematical modeling agreed in the literature [21]. Instead, there are definitions, explanations, or shared assumptions made by individual authors. According to Kaiser [22], mathematical modeling is seen as a creative process to interpret the results and make changes to the model in order to define, control, or optimize the

One of the many challenges faced by educators is the ways in which complex solutions to unusual problems can be taught to the student in the context of STEM education. One of the tools for transition to STEM training is the MEA [23].

MEAs, which are integrated into curricula for students to solve complex and difficult real-life problems, force students to build models and encourage them to test their established models, and their theoretical structure is known as a kind of open-ended problem-solving activities based on mathematical modeling perspective [24]. In school mathematics, MEAs have the potential to allow students to use mathematics in a flexible, creative, and powerful way in the STEM field because MEAs support the development of mathematical literacy [25], productive trends in mathematics [26], and a deep and integrated understanding of mathematical content and practices [27]. In MEAs, students clearly document their thought processes, consider their limitations, and use science and mathematics knowledge in the solution of the problem [28, 29]. MEAs offer students the opportunity to work on complex real-life problems involving model development. A framework for quality STEM integration curriculum is linked to the structure of MEAs [30]. According to the framework, the curricula (a) will serve a meaningful purpose and an engaging context, (b) enable students to develop problem-solving skills and engineering designs, (c) allow students to have the opportunity to redesign

and learn if they fail, (e) support student-centered pedagogy, facilitator, and cooperative learning, including teacher, and (f) are designed to promote communication

One of the first schemes presented as an approach to mathematical modeling is Blum [32]. The mathematical modeling cycle here consists of the real situation and the real world, the mathematical model, and the results in two parallel sections. In the loop, problem-solving is often perceived as a guide for the real situation.

According to Lesh and Doerr [3], it is the basic elements that must be included in a mathematical modeling cycle. There are three basic elements in mathematical modeling (**Figure 1**). According to them, a real-world problem must be started in mathematical modeling. The students generally act in the framework of mathematics and logic with ideas that involve mathematical assumptions and approaches. Then, the mathematics used should be accurate and also in a logical

The mathematical modeling cycle commonly used in literature is developed by Blum and Leiß [33]. Similar to other models, a distinction is made between the real world and mathematics in this model. A prerequisite for this model is that students

**2. Real-life problems, mathematical modeling cycles, and STEM**

*DOI: http://dx.doi.org/10.5772/intechopen.88615*

participation.

*Theorizing STEM Education in the 21st Century*

between STEM and science education [7, 8].

countries where many disciplines are taught.

direct STEM education and develop policy in this context [10].

relationship between disciplines and focusing on a certain discipline.

cal modeling [5].

world [1]. In this process, mathematics is used to represent, analyze, predict, or otherwise make sense of real-world situations [2]. In mathematical modeling, the individual tries to create a mathematical model that will solve the problem that he/ she encounters in real life or in the future. The model in question includes not only mathematical structures but also estimates, assumptions, and strategies for solution [3, 4]. In other words, the solution plan including the assumptions, estimations, and mathematical tools used to solve the problem is the mathematical model for the problem. In addition to being mathematically correct, the model should be meaningful and adaptable for real life. While solving the problem, the individual should also evaluate the meaning of the solution for the real world. All these processes and all the stages of problem-solving in addition to the individual model are mathemati-

Science, technology, engineering, and mathematics (STEM) education with technology age is appeared in the twenty-first century; it plays an important role in shaping cultural and economic development, embracing innovation, caring about creativity and problem-solving [6]. Due to the benefits of STEM education on the development of countries, intensive efforts are being made to reach the desired level

The United States Bureau of Labor Statistics (2009) stated that 80% of the professions will need technology in 2018, and 8.5 million workforce will be needed in the STEM disciplines. STEM training can help students become problem-solvers and innovative and technologically literate citizens [9]. As the society becomes more dependent on technology, engineering, and mathematics, it is becoming increasingly important that students receive an integrated STEM education.

Due to global developments in the world demanding the thinking skills necessary to create a high workforce in the future, the curriculum for inter-curricular education in schools has been implemented. Initially, the implementation of STEM training was carried out with projects outside the formal classes. However, in the STEM education integrated with the direct curricula like Finland, there are also

STEM training has been implemented in many countries of the world (Korea, Japan, Germany, China, etc.), especially in the United States (USA) and in secondary schools and universities starting from primary schools. As STEM Education Coalition, there are organizations that undertake a roof in STEM education and

STEM training, based on the integration of the disciplines of science, technology, engineering, and mathematics, has emerged as a result of the efforts of integrating separated parts in the real-world context [11], because, only by eliminating and integrating the boundaries between disciplines can the complex problems encountered in real life be understood and overcome. [12]. With STEM-oriented activities, the aim is to solve the real-life problems with the applications of technology and engineering disciplines by using the scientific knowledge which is the product of the basic sciences [12, 13]. For this purpose, it is necessary to remove the boundaries between disciplines [14–16]. In other words, STEM education understanding can be structured in the context of real-life problems by establishing a

Nowadays, both the training and applications related to STEM have been widely used in the world. On the one hand, many people now agree on what STEM means, interdisciplinary studies, and the common uses of science, technology, engineering, and mathematics. However, Clark-Wilson and Ahmed [17] emphasized that mathematics was included in an integrated curriculum on how M should be interpreted. Therefore, mathematics educators have said that mathematics in STEM should be used more, not as a servant. Coad [18] emphasizes that the use of mathematics

**152**

as a data presentation tool with its study may lead to discrediting mathematics. Although mathematics is an inevitable component of STEM activities, it is also emphasized in this study that it is important to evaluate mathematical success and participation.

One of the most important tools for transition to STEM education is mathematical modeling [19]. Model-eliciting activities (MEA) are mathematical modeling applications. Mathematical modeling applications are composed of concepts related to different disciplines by their nature [20]. There is not a single definition of mathematical modeling agreed in the literature [21]. Instead, there are definitions, explanations, or shared assumptions made by individual authors. According to Kaiser [22], mathematical modeling is seen as a creative process to interpret the results and make changes to the model in order to define, control, or optimize the situation in order to make the real-life situation meaningful.

One of the many challenges faced by educators is the ways in which complex solutions to unusual problems can be taught to the student in the context of STEM education. One of the tools for transition to STEM training is the MEA [23].

MEAs, which are integrated into curricula for students to solve complex and difficult real-life problems, force students to build models and encourage them to test their established models, and their theoretical structure is known as a kind of open-ended problem-solving activities based on mathematical modeling perspective [24]. In school mathematics, MEAs have the potential to allow students to use mathematics in a flexible, creative, and powerful way in the STEM field because MEAs support the development of mathematical literacy [25], productive trends in mathematics [26], and a deep and integrated understanding of mathematical content and practices [27]. In MEAs, students clearly document their thought processes, consider their limitations, and use science and mathematics knowledge in the solution of the problem [28, 29]. MEAs offer students the opportunity to work on complex real-life problems involving model development. A framework for quality STEM integration curriculum is linked to the structure of MEAs [30]. According to the framework, the curricula (a) will serve a meaningful purpose and an engaging context, (b) enable students to develop problem-solving skills and engineering designs, (c) allow students to have the opportunity to redesign and learn if they fail, (e) support student-centered pedagogy, facilitator, and cooperative learning, including teacher, and (f) are designed to promote communication skills and teamwork [31].
