**Selen Galiç, Bahadır Yıldız**

Hacettepe Üniversitesi

According to the OECD Report (2003), students should recognize the mathematical problems in their own real life, express them as mathematical problems, and interpret the results they have reached. It is a goal in all educational institutions for students to recognize mathematics in their lives and to use mathematics while solving problems in the world (NCTM, 2000). Many studies have been conducted to enable students to benefit from mathematical modeling in order to understand, interpret and finding different solutions to the problems related with their daily life situations, and the importance of mathematical modeling has been emphasized (Lesh & Zawojewski, 2007; Lingefjard 2006; English & Watters, 2004; Kasier, 2005; Mousoulides, Sriraman, and Christou, 2007). Modeling activities enable to students to better understand mathematical concepts, develop different perspectives on the problem situation, and develop mathematical thinking skills (Blum & Borromeo Ferri, 2009; Çavuş-Erdem & Gürbüz, 2019; Lesh & Doerr, 2003). While mathematical modeling which is used in the process of problem-solving is one of the special abilities in the National Mathematics Curriculum in Turkey (MEB, 2018), mathematical modeling is a part of the concepts and techniques National Mathematics Curriculum in Australia (Australian Curriculum , Assessment, and Reporting Authority, 2015).

Mathematical modeling is the expression of daily life situations as a mathematical problem by using a mathematical model. (Voskoglou, 2007). Based on this definition, mathematical models can be thought of as the mathematical formulation of daily life situations. On the other hand, Lingefjar (2007) defines mathematical modeling as an interdisciplinary approach that brings together many disciplines together and provides examples of how mathematics is used as a product and process. Looking at these definitions of mathematical modeling, it is seen that mathematical

modeling is handled in different ways. However it can be said that mathematical modeling is a process. According to NCTM (2000), students can begin to form elementary notions of mathematical modeling by learning that situations often can be described using mathematics. In this research, a daily life problem that students are familiar with will be used. The students’ process of generating mathematical models for the solution of the problem will be examined. Students will be asked to identify who is the first in line for COVID-19 vaccine. Students' mathematical modeling processes will be associated with students' academic achievement and students' views on the difficulty level of the problem solving process.

**Method**

In this case study research, one of the qualitative research designs was conducted. Case studies can be defined as processes, a unit of analysis, or as the output or product of the research (Merriam, 2009). Case studies research design was chosen because students’ mathematical modeling process is investigated in this study. This study was limited by participant students of a private school, students’ backward and the context. 8th-grade elementary school students’ mathematical modeling process was investigated in depth. This study was authorized by Hacettepe University's ethics

committee. This study was conducted with 56 8th-grade students that voluntarily enrolled in a private elementary school in Turkey. This study was performed in four sessions. There were 14 students in each session and students were carried out with groups that had 3 or 4 students. The group session was formed by the academic success of students.

This study was conducted during COVID-19 and after preparing the vaccine. Hence the mathematical modeling in this study was about who is the first in line for COVID-19 Vaccine, which is produced in a limited number and whose first trial will be made. Activity sheets were prepared for the age of the research group as understandable and clear. The paper was given to each student to read individually. And then, researchers explained what they should do. It was important that students were limited to the website which was given to students in the activity sheet. The problem

statement for this study was given to the students by a researcher. They would like to have to find a model to express the order of the COVID-19 vaccine. Students researched globalmag.wordpress.com, were prepared for this study, to find data about COVID-19 and any clue to get a solution. Using a digital note-taking document or pen-pencil was used

according to the group's opinion. In this study, an observation form was used by the researcher to take note of the students’ approaches, and their mathematical words during the process. After all, groups completed the activity, students were asked to examine their process on the opinion form individually. In this form, students were answered how they reached the result, where they had difficulties, and possible reasons for their difficulties.

Students are expected to generate mathematical modeling to solve the given daily life problem collaboratively. In this process, students will be asked to use their media literacy and research skills. It is expected of students to access the data on the given web-site, to interpret the data, to express these data mathematically and to generate a mathematical model for the problem situation. Because the problem does not have an exact solution, it is expected that students will have difficulty. A rubric was formed by the researchers for evaluation of the students’ mathematical modeling.

Moreover, students will be asked to evaluate their own processes. It is expected that while there will be a negative correlation between their difficulty level during the process and their mathematical modeling, a positive correlation will be expected between students' academic success and their mathematical modeling.

**Keywords:** Mathematical modeling, middle school students, COVID-19 vaccine, mathematics education

**References**

Australian Curriculum, Assessment and Reporting Authority (2015). [online]Available at: http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1

Blum, W., & Ferri, R. B. (2009). Mathematical modelling: Can it be taught and learnt?. Journal of mathematical modelling and application, 1(1), 45-58.

Doğan, M. F., Gürbüz, R., Erdem, Z. Ç., & Şahin, S. (2019). Using mathematical modeling for integrating STEM disciplines: A theoretical framework. Türk Bilgisayar ve Matematik Eğitimi Dergisi, 10(3), 628-653.

English, L. D. ve Watters, J. J. (2004). Mathematical Modeling in the Early School Years. Mathematics Education Research Journal. 16(3), 59-80.

Kaiser, G. (2005). Mathematical modelling in school–examples and experiences. Mathematikunterricht I'm Spannungsfeld von Evolution und Evaluation. Festband für Werner Blum, 99-108.

Lingefjärd, T. (2006). Faces of Mathematical Modeling. Zentralblatt für Didaktik der Mathematik-ZDM. 38(2), 96-112.

Lingefjärd, T., 2007. Mathematical modelling in teacher education- Necessity or unnecessarily, Ed: W. Blum, P.L.

Galbraith, H.W. Henn, M. Niss, Modelling and Applications in Mathematics Education: 14 th ICMI Study, New York: Springer, 333- 340.

Mousoulides, N., Sriraman, B. ve Christou, C. (2007). From Problem Solving to Modelling: The Emergence of Models and Modelling Perspectives. Nordic Studies in Mathematics Education. 12(1), 23-47.

National Council of Teachers of Mathematics [NCTM], (2002). Principles and Standards for School Mathematics : An Overview. Reston: NCTM.

Lesh, R. ve Doerr, H. M. (2003). (Eds.). Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning and Teaching. Mahwah, NJ:Lawrence Erlbaum.

Lesh, R. and Zawojewski, J.S. (2007) Problem Solving and Modeling. In: Lester, F., Ed., Second Handbook of Research on Mathematics Teaching and Learning, Information Age Publishing, Greenwich, CT, 763-802.

Merriam, S. B. (2009). Qualitative research: A guide to design and implementation. San Francisco, CA: John Wiley & Sons.

Voskoglou, M. (2007). A stochastic model for the modeling process. In C. Haines P. Galbraith W. Blum and S. Khan (Eds.),

Mathematical modeling: education, engineering and economics (pp. 149–157). ICTMA12, Chichester: HorwoodPub.

Galiç, S. ve Yıldız B. (2021). Mathematical Modeling With 8th Grade Students: Who is The First In Line For Covid-19 Vaccine?, VIII th Internatıonal Eurasian Educational Research Congress (EJER2021), 07- 10 Temmuz 2021, Aksaray

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