Investigation of mathematical modeling to living reflection process

In recent years, applied mathematics has been playing an increasingly important role in other disciplines, such as engineering, nanotechnology, economics, and biology. Engineering fields are the areas where the integration of mathematical knowledge with skills is most distinguished and observed most intensively. In other words, engineering is an area where mathematical modeling is put to work and offered to the service of humanity. Education holds an important place in mathematics and engineering as an engineer who studied at the faculty of technology related to the modelling, what are the views of candidates, mathematical modeling, self-efficacy, and metacognitive instructional practices in the aftermath of the level of awareness that it is any different to them made elsewhere, and which is intended to determine what is the level of proficiency in mathematical modeling in this study a hybrid method is used where a combination of quantitative and qualitative methods is preferred. The "purposeful sampling" approach, which is one of the sample selection methods of the mixed research method, has been preferred. The study group consists of a total of 217 students of different levels of development studying at the Biomedical Engineering program of the Faculty of Technology of Kocaeli University in the academic year 2020-2021. Interviews with 45 engineer candidates from different classes, who stated that they would voluntarily participate in the interviews from 217 engineer candidates, and mathematical modeling practices were carried out with 12 groups formed by these candidates. In the research, firstly, the model and modeling, metacognitive awareness and mathematical modeling self-efficacy scale were applied to the study group and the pre-test and post-test data of the quantitative dimension were taken preliminary and final interview data of the qualitative dimension were obtained from the semi-structured interview form with a group of participants. At the next stage, to determine the mathematical modeling proficiency levels of engineer candidates, modeling activities were applied and evaluated by mathematics educator experts. The data collection with the applications made in the research process and the measurement tools used was carried out for a period of 11 weeks with the candidates of engineers between October 2020 and December 2020. It was found that the understanding of models and modeling, mathematical modeling self-efficacy and higher cognitive awareness of the candidates of engineers before and after the application were at a high level, and there was a statistically significant increase in favor of these levels after the applications. According to the research results, mathematical modeling Engineer candidates understanding of modelling and applications, mathematical modelling and metacognitive awareness it has been shown that statistically significant and positive effect on ozyeterlik. As a result of evaluating the responses of engineer candidates to mathematical modeling problems, it was concluded that they have a high level of mathematical modeling competencies, but some missing competencies should be developed. In addition, at the end of the application, it was determined that there was an improvement according to the initial situation according to the responses of the engineer candidates to the recent interviews in the interviews. Getting to know the process of learning and developing mathematical modeling in engineering education can give important tips for training engineers. In this context, it is expected that the research will produce results that can be used professionally both in engineer education and afterwards. It is proposed that the research on mathematical modeling education of engineers and their candidates should be disseminated in our country and that more comprehensive studies should be carried out in different engineering fields that are not examined within the scope of the study.