What is the room for guessing in metacognition? Findings in mathematics problem solving based on gender differences

Abstract

Introduction. Understanding the interaction of metacognitive strategies with guessing in problem-solving is a focus point in educational psychology, especially in mathematics education, especially with gender differences. These provide different nuances in understanding students' cognitive dynamics in guessing and metacognitive strategies. These interactions must be explained in depth to understand the unique phenomenon of second-guessing that sometimes arises in metacognitive activities based on students' gender. This research aims to reveal the process of metacognition and students' guessing thinking in solving mathematical problems. This research seeks to contribute to an empirical of metacognitive processes and their practical implications for educators and curriculum designers by uncovering these activities. Study participants and methods. The participants in this study were (30) 12th-grade high school students, consisting of (16) female students and (14) male students who had studied mathematics with statistical material. The primary method in this research is a case study with a qualitative descriptive approach. The indepth interview technique using the MAI protocol is based on the results of mathematical problem-solving to explore information about students' natural metacognitive processes according to what they think when working on problems. Semi-structured interviews used the Indonesian language to eliminate the influence of differences in regional language proficiency levels as much as possible. Results. The results of interviews on mathematical problem-solving tasks show a 'guessing' strategy in students' metacognitive activities. However, there is a striking difference between female and male students' use of the 'guessing' strategy when solving mathematical problems. Female students use the 'guessing' method more often than male students; even the 'guessing' method used by male students cannot solve the problem, thus changing the guessing strategy to estimation. This means that most of the students' answers used the guessing method. These findings underscore the dynamic nature of the cognitive processes used by students, revealing diverse interactions between metacognitive strategies and guessing during problem-solving efforts. Conclusion. This research shows that rather than standing in isolation, guessing has a place within metacognitive processes, with metacognitive regulation guiding and shaping the deliberate application of guessing in mathematical problem-solving contexts. This can be a factor for reconsidering the perceived dichotomy between precision-driven methodologies and intuitive guessing.