Students' Responses to the Implementation of a Mathematical Problem-Solving Model Based on Mathematization and Mathematical Modeling in Integral Calculus

Abstract

Mathematical problem-solving is an essential competency in mathematics education, particularly in Integral Calculus, which requires students to understand problems, construct mathematical representations, develop mathematical models, interpret results, and reflect on solution processes. Although mathematical problem-solving models have been widely implemented, studies investigating students' responses to each stage of the model remain limited. This study aimed to describe students' responses to the implementation of a mathematization- and mathematical modeling-based problem-solving model in Integral Calculus. A quantitative descriptive design was employed involving 37 undergraduate students in the Mathematics Education Study Program at Universitas Muhammadiyah Semarang, Indonesia. Data were collected using a questionnaire based on the model's five stages and analyzed using descriptive statistics. The findings showed that the model received a very positive response, with an overall mean score of 4.42. The highest response was observed in the Understanding the Problem and Identifying Information stage (M = 4.58), whereas Constructing Initial Representations received the lowest mean score (M = 4.14). Students' responses improved in the subsequent stages, indicating that mathematization remained the most challenging phase, while reflection was perceived very positively. These findings provide empirical evidence that analyzing students' responses across each stage offers valuable insights for evaluating and improving the implementation of mathematical problem-solving models in Integral Calculus.