Mathematical Modeling and Critical Thinking Analysis

In this review, the authors summarised studies related to Analysis of specific aspects of mathematical modelling skills, including problem-solving techniques and application to real-world situations, on critical thinking skills in higher institutions, and concentrated on engineering students or liberal arts colleges. The main aim is knowledge of cognition processes. to fill common knowledge gaps toward how mathematical modelling capabilities develop critical thinking in a variety of disciplinary settings. The objective of the review was to review the functions of problem-solving techniques, benchmarks pedagogical methods incorporating real world applications, cognitive processes that occur in modelling, reciprocity and autonomy learning outcomes, and metacognitive and affective factors. The selection of literature applied the methods of qualitative, quantitative and mixed methods analysis, offered mobile application, high relevance in high education and discursive focus of the literature. Results suggest that modelling techniques as problem solvers play a major role in developing critical thinking especially when individually facilitated by metacognitive strategies; educational innovations in the form of model prompting activities and project based learning can be effective in integrating real world context to enhance engagement and concept learning; cognitive processes involved in modelling tasks and development of essential thinking models are a priority; applying metacognitive strategies serve as scaffolds to modelling activities and development; and instruction; whereas; and instruction in metacognitive strategies mediate critical thinking benefits, yet affective aspects have not been well studied. These results step towards highlighting the pivotal position of cognitive and meta cognition structures in mathematical modelling pedagogy. The review emphasises the importance of longitudinal, comparative research and deeper investigation of the liberal arts set ups to guide curriculum development and instructional innovation that boost critical thinking by means of mathematical modelling.