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.