Defragmenting students’ reflective thinking levels for mathematical problem solving: does it work?

ABSTRACT

Study on fragmentation and defragmentation of reflective thinking structures has never been conducted. Therefore, the purpose of this study was threefold: (1) to identify the types and forms of fragmentation of students’ reflective thinking structures in solving mathematical problems, (2) to describe attempts to defragment students’ reflective thinking structures in each type and form of fragmentation, and (3) to find out if such defragmentation attempts can work for reflective thinkers who experience fragmentation. This research was qualitative, exploratory, and descriptive. The subjects included in this study were students who thought reflectively and experienced fragmentation at each level of reflective thinking when solving mathematical problems. Data collection was conducted using tests, interviews, think-aloud protocols, and observation. Data analysis was conducted using constant comparative method. Data validity was established using method and source triangulation. The results showed: (1) Scanning Defragmentation work for Less-Strict Fragmentation, (2) Schema Emergence Defragmentation work for Pseudo-True Fragmentation, (3) Schema Activation work for Pseudo-False Fragmentation, (4) Connection Emergence Defragmentation work for Nonexistent-Connection Fragmentation, (5) Compare-Reflect Defragmentation work for Confidence-False Fragmentation. The results of this study can be reference for mathematics researchers and educators to develop learning models that can prevent the occurrence of fragmentation of reflective thinking structures.

KEYWORDS:

• Defragmentation
• fragmentation
• limited intervention
• mathematical problem-solving
• reflective thinking
• thinking structure

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Muhammad Noor Kholid

Dr. Muhammad Noor Kholid is both lecturer and researcher in Mathematics Department – Universitas Muhammadiyah Surakarta – Indonesia. In recent years, his focus on reflection in mathematics learning and implementation of TPACK. He has a personal research roadmap on reflection until 2031. His research papers contribute in both journal indexed by Scopus and WoS.

Yoga Tegar Santosa

Yoga Tegar Santosa was born in Wonosobo, Indonesia. He is a final year undergraduate student of Mathematics Education at the Universitas Muhammadiyah Surakarta. During his study, he has been employed in lecturer researches that focus on mathematical reflection. He has plans to continue his studies at the master’s and doctoral levels with a consistent research focus on mathematical reflection.

Tin Lam Toh

Dr Toh Tin Lam is an Associate Professor and currently the Head of the Mathematics & Mathematics Education Academic Group in the Singapore National Institute of Education, Nanyang Technological University. He was a school teacher and head of mathematics department in a Singapore school before joining the university in 2001. He graduated with a PhD in mathematics and starts his mathematics education research after joining the university. He publishes both in mathematics and mathematics education in international refereed academic journals.

Agung Putra Wijaya

Dr. Agung Putra Wijaya was born in Seputih Raman, Lampung, Indonesia. He has been working as a lecturer since 2012 in Universitas Lampung, Indonesia. He graduated from Department of Mathematics Education, FKIP Universitas Lampung, Indonesia in 2009., master degree from Department of Mathematics Education, Universitas Sebelas Maret, 835 Indonesia in 2011, and doctoral degree in Department of Mathematics Education, Universitas Negeri Malang, Indonesia in 2023.

Imam Sujadi

Imam Sujadi is a Doctor of Mathematics Education who currently works at Sebelas Maret University (UNS) in Surakarta, Indonesia. His research interests are students’ thinking processes in solving mathematical problems and differentiated mathematics learning. Apart from being a lecturer, he is also actively involved in learning and assessment activities at the Directorate General of Primary and Secondary Education, Ministry of Education and Culture. He can be contacted via [email protected].

Heris Hendriana

Prof. Dr. Heris Hendriana, M.Pd. is a professor in the Mathematics Education – IKIP Siliwangi – Indonesia. He was promoted as a professor in 2019. His research interest is in mathematics education, Ethno-Metaphorical Humanist, and Metaphorical Thinking. In addition, he is also the Chairman of the Indonesian Mathematics Educators Society (I-MES), it is a professional organization of mathematics educators.