The effectiveness of a mathematical modeling based project production and management program within the context of project production of gifted students

Even though gifted youth might have the potential to produce creative solution models for real-life problems, not all their talents, skills, and knowledge may be transformed into original products and projects. This study aims to determine gifted youths' mathematical modeling project production competencies and structure, to examine the impact of a modeling-based project production and management program on these competencies and project production, and to identify the triggers and contributing factors of project production. In this mixed method study, both quantitative and qualitative procedures were employed. In the first phase, a correlational study, one of the quantitative research methods, was used. The next phase covers the planning and designing of the project production and management program based on the data obtained. In the last phase, qualitative data were also obtained in order to deeply analyze the process along with the experimental design. The study group of the first phase consisted of 300 randomly selected gifted youths who were registered in the Project Production and Management Program (PPMP) in the field of Mathematics in Science and Art Centers (SACs) throughout Türkiye. In the experimental phase, the study group of the research comprised 60 participants who were purposively selected from among the 300 participants that took part in the first phase of the study. The data sources used in the study include the Mathematical Modelling Competences Scale, interview form, modeling diary, project form, peer suggestion form, and expert suggestion form. The implementation and the collection of simultaneous data covered a 41-week period. The scale developed by the researcher was administered as a pre-test, post-test and retention test and interviews were held before, mid and after the process. Participants recorded entries in the modeling diary, project form, peer suggestion form, and expert suggestion form on a weekly basis. The SPSS 26 and Mplus 8.5 programs was used to analyze the data obtained. Structural equation modeling, ANCOVA and Bonferroni multiple comparison test were performed. Friedman, Wilcoxon signed ranks, and Mann-Whitney U tests were employed to analyze the scores obtained from the factors. Qualitative data analysis was conducted using the grounded theoretical framework. Validity was ensured in the study through expert opinion, external reviewer, participant confirmation, detailed description, long-term experience in the field, and variation. Reliability was ensured through inter-rater agreement, intra-rater agreement, provision of a detailed description, inclusion of direct quotations, and analysis of data based on a theoretical framework. Inter-rater reliability and intra-rater reliability were calculated as .82 and .95, respectively, and it was decided that the rating was reliable. It was concluded that the mathematical modeling-based project production of the gifted students had a five-factor structure: identifying the real-life problem, understanding and simplifying, mathematizing, working mathematically, and interpreting and validation, and that this structure was cyclical, since interpretation and validation require the evaluation of the process by returning to the second factor. It was concluded that the modeling-based project production and management program positively affected the mathematical modeling levels and project productions of the gifted youths and that this development was maintained. A positive and lasting effect was determined on all factors partially. It was also concluded that for the factor of identifying the real-life problem, they were able to identify real-life problems for which they could produce solutions by using their potential. In addition, for the factor of understanding and simplifying the real-life problem, they could transform the problem into a mathematical problem. For the mathematizing factor, they could use appropriate mathematical methods to build models that would represent real-life situations. Moreover, for the factor of working mathematically, by solving the model that represented the real-life problem, they were able to obtain mathematical results by using mathematical relationships, knowledge, and structures. For the interpretation factor, they could explain what the solution of the mathematical model meant in real life, interpret to what extent the model explained the real-life situation and show its applicability in real life, clarify its necessity for real life, analyze its benefits in real life. For the validation factor, they could determine the accuracy of the assumptions necessary for the solution, check the steps they followed, determine the accuracy of the mathematical model they developed, correct the errors if there were any in its solution, correct the errors if there were any in the mathematical model. It was concluded that there were fifteen reflection categories for the mathematical modeling project production and it was also concluded that participants had the greatest difficulty in mathematization and validation, and that they overcame the difficulties they faced by making reflection decisions. The triggers of the mathematical modeling projects production of gifted youths were grouped in seven categories, and it was seen that focusing on universal, real-life and popular science problems in the field they were interested in was most important factor. It was indicated that there were 15 factors contributing to mathematical modeling projects production, and some of these factors are; being guided by expert suggestions, sharing suggestions and experience by making peer presentations, cyclical progress in the process, evaluating the results of planning and designing decisions on a weekly basis and experiencing in practice. It is suggested that the results obtained should be considered in the context of ensuring the project production. Key words: Project production and management program, gifted and talented youth, mathematical modelling, reflective thinking.