This study investigates the relationship between metacognition and achievement goals which may influence mathematical modeling competency in students of mathematics education programs. The current study employs 538 students of mathematics education program; 483 (89.8%) of whom are male and 55 (10.2%) are aged from 18 years old to 22 years old. The study follows a correlational research design to investigate and measure the degree of relationship amongst mathematical modeling competencies, achievement goals and metacognition. Results indicate that achievement goals and metacognition positively influence mathematical modeling competency. Moreover, four metacognition dimensions including awareness, planning, cognitive strategy and self-checking are positive partial mediators because they increase the association between achievement goals and mathematical modeling competency. In conclusion, metacognition and achievement goals positively affect students' mathematical modeling competency.
Guided by a model promoted by Biccard and Wessels (2011) and empirical evidence, this work aims to examine a model that includes meta-cognitive behaviour and mathematical modelling competency with the indirect effects of two performance goal sub-constructs, namely, other-approach and other-avoidance goals. The study investigates the correlation between meta-cognitive behaviour and performance goals that may affect mathematical modelling competency. A total of 538 mathematics education programme students (89.8% female and 10.2% male) in Indonesia are considered. A correlational study is performed to examine the level of the link amongst mathematical modelling competency, performance goals and meta-cognitive behaviour. Results show that meta-cognitive behaviour positively affects mathematical modelling competency, but no significant direct relationship is observed between performance goals and mathematical modelling competency. Furthermore, other-approach and other-avoidance goals are significant mediators between meta-cognitive behaviour and mathematical modelling competency. We conclude that meta-cognitive behaviour positively influences the mathematical modelling competency of students, which is unaffected by other-approach and other-avoidance goals.
The idea of linear Diophantine fuzzy sets (LDFs) is a novel tool for analysis, soft computing, and optimization. Recently, the concept of a linear Diophantine fuzzy graph has been proposed in 2022. The aim of this research is to extend topological numbers to LDFSs. A real value assigned to a particular graph is known as a topological graph theoretic parameter. We extend the bound of the crisp graph toward the linear Diophantine fuzzy graph (LDFG), including the edge and vertex deletion operations via LDFG theoretic parameters. We also investigate the interesting bound of the LDFGs via LDFG theoretic parameters. Finally, for decision-making problems, we developed an algorithm by exploiting the relationship between LDFG theoretic parameters and LDFSs. Based on the established approach, we discussed a numerical example of an application of a medical diagnosis using the linear Diophantine fuzzy Sombor graph parameter and the first, fifth, and sixth versions of the linear Diophantine fuzzy Sombor graph parameters.