Mathematical reflective thinking strategy in problem-solving viewed by cognitive style

Abstract

Mathematical reflective thinking is a mathematical thinking activity involving the persistent consideration process of the use of knowledge and decision making in solving a problem. This study aims to describe mathematical reflective thinking strategy of students based on impulsive and reflective cognitive styles in solving the mathematical problems. To do so, first, we developed three tasks about the linear programming problems. Next, 35 students of senior high school in the 11th grade (16-17 years-old), were given tasks and continued with the giving one set of Familiar Figures Figure Test (MFFT). Then four students were selected as representatives of the other students. In-depth interviews were conducted with students to confirm the findings of the task’s answers. Finally, the data were analyzed to explain the mathematical reflective thinking strategy of students based on cognitive styles. We found that students with impulsive cognitive styles have a tendency to think reflectively on the stage of understanding and reflection, using inefficient strategies, not completing answers, and give up easily in the face of a difficult task. Whereas the students with reflective cognitive style have a tendency to think reflectively on the stage of reflection and critical reflection, using expert strategies, concluding answers, and solving difficult problems in accordance with logic; and trial and error.

Students’ Mathematical Reflective Thinking Ability in Solving System of Linear Equations in Two Variables Problems

“…They experience difficulties when understanding the existing problems. Apart from that, it is also supported by research by (Salido, Suryadi, Dasari, & Muhafidin, 2020), which obtained research results, namely that students who have not thought reflectively in dealing with problems, use inefficient strategies, do not complete answers and quickly give up when facing complex tasks. Other research suggests that students with low abilities still experience difficulties in evaluating what they do (Mudakir et al, 2020).…”

Model DL Berbantuan Media Menemukan Pola Kemampuan Berpikir Kreatif dan Curiosity dengan Gaya Kognitif

“…Science curiosity merupakan faktor penting dalam gaya kognitif individu (Kahan, et al, 2017). Salah satu faktor yang mempengaruhi kemampuan pemecahan masalah siswa adalah karakteristik cara berpikir dan belajar individu di bidang kognitif (Mefoh, et al, 2017;Salido, et al, 2020). Jika siswa memiliki perbedaan gaya kognitif maka langkah pemecahan masalah berbeda pula.…”

“…Proses siswa menampilkan gagasan kreatifnya berbeda-beda, dikarenakan potensi dan pengalaman dimilikinya berbeda-beda pula (Rahmatina, Sumarmo, & Johar, 2014). Kreativitas digunakan untuk memberikan proses pemecahan masalah dikarenakan stimulus memiliki perspektif, kebaruan, keragaman, dan cerita yang berbeda (Aljarrah, 2020;Granberg & Olsson, 2015;Salido et al, 2020). Berpikir kreatif dapat dikembangkan menggunakan pemecahan masalah (Ayllon, Gomez, & Ballesta, 2016).…”

Students’ reflective thinking based on their levels of emotional intelligence in mathematical problem-solving

“…Problem-solving skills in mathematics learning are a means for students to develop and examine their ideas, transfer the skill to the uncommon situation, and take charge of their learning development (Das & Das, 2013). Salido et al (2020) explain that mathematical problem-solving can provide students with a chance to empower and develop their reflective thinking skills. This research, therefore, is set to Polya's problem-solving stages as it is equipped with a wellstructured framework to solve complex and sophisticated problems, making students more careful in following the steps and procedures for solving the problems.…”