A Portrait of Controversial Mathematics Problems and Students’ Metacognitive Awareness: A Case of Indonesia

Abstract

This study sheds light on the students' use of metacognitive strategies in solving controversial mathematical problems. This study involved 80 students. Data on metacognitive strategies were obtained through interviews and the results of students' work on test items. Data analysis and interpretation of the findings were carried out through text analysis on metacognitive strategy data obtained at the planning, monitoring, and evaluating stages. The results of data analysis depict that at the planning stage, students identify the aspect of the problems they have known and recognize the contradictory things. At the monitoring stage, students explore the elements that cause controversy. In the evaluating stage, students clarify, strengthen, improve, and conclude solutions to controversial mathematical problems. The results of this study indicate that it is necessary to apply metacognitive strategies to facilitate students to trace back the aspects inducing the controversy, eradicating the controversies among students. To this end, lecturers and students can develop mathematics learning models that involve metacognitive strategies for the success of learning mathematics in the future.

The Growth of Students' Function Limit Concepts Understanding in Solving Controversial Problems Based on Pirie Kieren's Theory

“…Controversial problems are problems that generate debate because of different points of view (Simic-Muller et al, 2015;Subanji et al, 2021). Controversy can occur when someone faces a problem that is different from normal problem Subanji et al (2021) and contrary to the existing scheme in mathematics (Walida et al, 2022). This problem arises due to an understanding of a problem that has not been resolved, causing conflict in one's mind (Subanji et al, 2021;Walida et al, 2022).…”

“…Controversy can occur when someone faces a problem that is different from normal problem Subanji et al (2021) and contrary to the existing scheme in mathematics (Walida et al, 2022). This problem arises due to an understanding of a problem that has not been resolved, causing conflict in one's mind (Subanji et al, 2021;Walida et al, 2022). Although this controversial problem can lead to conflict, it can make students' understanding of the problem deeper (Mueller & Yankelewitz, 2014).…”

“…Apart from that, students cannot explain the completion process well. Therefore, controversial problems can be given to students Walida et al (2022) to see the development of the students' mathematical understanding.…”

“…Research on controversial problems in mathematics is still focused on reasoning Simic-Muller et al (2015); Subanji et al (2021), higher-order thinking Rosyadi et al (2022); Suryawan et al (2023), metacognitive Walida et al (2022), and creative thinking (Subanji et al, 2023). The results of Subanji et al (2021) research are the characteristics of controversial mathematical reasoning which consists of three levels, namely initial, exploration, and clarification.…”

“…The results of their research showed that students reached the analysis and evaluation stage, but there was one student who was able to reach the creating stage. Walida et al (2022) researched students' metacognitive strategies when solving controversial mathematics problems. Meanwhile, Subanji et al (2023) research produced five levels of creative models by providing controversial questions, including: pre-imitation, imitation, modification, combination, and construction.…”