Determination of Psychometric Characteristics of Mathematical Modeling Competencies Scale: Gifted and Talented Youth

Abstract

Introduction: It can be claimed that mathematical modeling, which is a key concept in terms of creating original projects with the developed models, is important in the education of gifted youth. Determining their modeling competencies and identifying the stages that they need to develop will provide essential data in terms of deciding on what kind of educational practices and program differentiation will be carried out. The study aims to develop a scale for mathematical modeling competencies and to determine its psychometric properties.Method: This is a descriptive study which was carried out with the participation of gifted students in two different groups. Exploratory factor analysis (EFA) was performed on the data obtained from 301 participants in the first group, and confirmatory factor analysis (CFA) was performed on the data obtained from 185 participants in the second group.Findings: The scale includes items to be rated on a level of agreement including “Strongly agree”, “Agree”, “Moderately agree”, “Disagree” and “Strongly disagree”, and there are no items that need reverse coding. The sub-factors of the scale were determined as ‘identifying the real-life problem’, ‘understanding and simplifying the problem’, ‘mathematizing’, ‘working mathematically’ and ‘interpretation and validation’. Cronbach's alpha internal consistency coefficients were calculated as 0.958 for the scale and .811, .900, .883, .820 and .927 for the sub-factors, respectively. Fit indices of the scale (χ2 / df = 2.00, GFI = .90, RMSEA = .075, SRMR = .063, IFI = .97, NNFI = .97, CFI = .97, NFI = .94, PNFI = .86) determined.Discussion: The developed scale is a 5-point Likert-type scale and there are no items that need to be reverse coded. According to the findings obtained from the analysis, it was concluded that the 31-item scale with a 5-factor structure is a valid and reliable scale. As a result of the research, it was concluded that the 31-item scale with a five-factor structure had sufficient psychometric properties to be used in future studies. The scale helps to measure both as a whole in the modeling process and partially in its stages. In this context, the scale developed within the scope of this research can be used for determining the stages that students are best at and those that require improvement.

Effects of mathematical modelling based project production and management program on gifted students’ mathematical modelling and reflective thinking for real-life problem solving

“…The internal consistency coefficients, Cronbach's alpha, were α = 0.958 for the whole scale and 0.811, 0.900, 0.883, 0.820, and 0.927 respectively for each sub-factor of IP, US, M, WM, and IV respectively. Fit indices (χ 2=df = 2.00, GFI = 0.90, RMSEA = 0.075, SRMR = 0.063, IFI = 0.97, NNFI = 0.97, CFI = 0.97, NFI = 0.94, PNFI = 0.86) demonstrated that the instrument has a valid structure ( Özbek & Köse, 2022). The Content Validity Index, which represents the mean value of the items' Content Validity Ratio, was found to be very high with 0.95 ( Özbek & Köse, 2022).…”

“…It simplifies and expresses real-life problems mathematically to solve, interpret, and validate the real-life problems through developing interdisciplinary models (Borromeo Ferri, 2006;Maaß, 2006;Tekin Dede, 2017). This study is grounded on the theoretical framework (Borromeo Ferri, 2006) of mathematical modelling cycle (see Figure 1) and competencies based on multi-steps of the modelling process ( Özbek & Köse, 2022). It starts project with the 'identifying the real-life problem', continues with the 'understanding and simplifying the problem', 'mathematizing', 'working mathematically' and culminates project with 'interpretation and validation'.…”

“…Reviewing literature on the theoretical framework both reflective thinking in the problem-solving context (Kızılkaya & As ¸kar, 2009) and mathematical modelling (Borromeo Ferri, 2006;Özbek & Köse, 2022) revealed they both share a similar cyclical structured thinking which allows to progress practically along their stages and also questioning what is done and why. They seem to share a related structure in terms of being a solution-generating producing process which starts with real-life problem.…”

“…Creative productivity in STEM domain requires motivation, general knowledge and skills and knowledge and skills in STEM domain (Cho, 2003(Cho, , 2007Sternberg, 1988;Urban, 2003) These components have been found to be critical predictor of creative productivity of scientifically talented students Kim et al, 2021) at the secondary schools. Reflective thinking (Lia, 2020;Özbek & Köse, 2019;Sternberg, 1988;Urban, 2003) is one of the main components of general knowledge and skills needed for creative productivity, meanwhile mathematical modelling is another main component of knowledge and skills in STEM domain (Blum & Niss, 1991;Cho, 2003Cho, , 2007Özbek & Köse, 2022;Sternberg, 1988;Urban, 2003). There have been studies on the relationship between creative productivity and academic achievements in general.…”

Project productions with real-life problems in the STEM domain of gifted youths according to their program evaluations

“…In the previous studies, it was found that gifted youth might be successful in project production by solving competitional global problems, and integrating into virtual environments (Çetinkaya, 2020). There have been studies on the examination of gifted youth views on the effectiveness of education program, their views were found to be positive, (Kayişdağ & Melekoğlu, 2019) and project productions on how they transformed their talents, skills, knowledge and competencies such as mathematical modelling (Özbek & Köse, 2022) and reflective thinking into creative production. Also, innovative approaches such as mathematical modelling-based PPMP and project-based activities were examined in terms of project qualifications of gifted youth and positive changes resulted in project production (Çetinkaya, 2020; Özbek & Cho, 2022).…”