How do students solve reversible thinking problems in mathematics?

Aneu Pebrianti, Sufyani Prabawanto, Elah Nurlaelah


Reversible thinking is a cognitive activity in finding a solution to a problem by arranging the direction of logical thinking from the end to the starting point. Reversible thinking requires a student to think logically in two ways. Therefore, reversible thinking influences students' success in solving problems. This study aims to identify students' thinking processes in solving problems that require reversible thinking ability. This research was conducted on junior high school students in Bandung, West Java, Indonesia, using test instruments, interviews, and documentation studies. The tests given consisted of two types of problems, including tests on forward-thinking problems and tests on reversible thinking problems. The research subjects were students with high average mathematics scores in their class. The study found that students could answer the tests on forward-thinking problem-solving very well but could not work on similar questions with the backward-thinking process. Based on the interview results, one of the causes for the need for more backward-thinking ability is the limited learning resources or context when students first learn the concept.


backward-thinking; forward-thinking; reversible-thinking

Full Text:



Abung, M., & Herman, T. (2023). Analysis of the flat sided volume of elementary mathematics textbook based on praxeology. Jurnal Pendidikan: Teori, Penelitian, dan Pengembangan, 8(3), 205–211.

Bungin, B. (2003). Analisa data penelitian kualitatif [qualitative research data analysis]. Raja Grafindo Persada.

Daulay, L. A., Hakim, H., & Sartikawati, L. D. (2019). The improvement of student’s mathematical communication ability by using cooperative learning: course review horay. Jurnal Tarbiyah, 26(1), 185-204.

Fitriati, F., Novita, R., & Johar, R. (2020). Exploring the usefulness of rich mathematical tasks to enhance students’ reflective thinking. Cakrawala Pendidikan, 39(2), 346–358.

Flanders, S. T. (2014). Investigating flexibility, reversibility, and multiple representations in a calculus environment. Gannon University.

Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2012). How to design and evaluate research in education (eight). McGraw-Hill.

Hackenberg, A. J. (2005). Construction of algebraic reasoning and mathematical caring relations. University of Georgia.

Hackenberg, A. J. (2010). Students’ reasoning with reversible multiplicative relationships. Cognition and Instruction, 28(4), 383–432.

Kajander, A., & Lovric, M. (2009). Mathematics textbooks and their potential role in supporting misconceptions. International Journal of Mathematical Education in Science and Technology, 40(2), 173–181.

Kandaga, T., Rosjanuardi, R., & Juandi, D. (2022). Epistemological obstacle in transformation geometry based on van hiele’s level. Eurasia Journal of Mathematics, Science and Technology Education, 18(4), 1-12.

Krutetskii, V. A., Teller, J., Kilptrick, J., & Wirszup, I. (1976). The psychology of mathematical abilities in schoolchildren. University of Chicago Press Chicago.

Maf’Ulah, S., Fitriyani, H., Yudianto, E., Fiantika, F. R., & Hariastuti, R. M. (2019). Identifying the reversible thinking skill of students in solving function problems. Journal of Physics: Conference Series, 1188(1), 012033.

Maf’ulah, S., & Juniati, D. (2019). Students’ strategies to solve reversible problems of function: the part of reversible thinking. Journal of Physics: Conference Series, 1417(1), 012051.

Maf’ulah, S., & Juniati, D. (2020). Exploring reversible thinking of preservice mathematics teacher students through problem-solving task in algebra. Journal of Physics: Conference Series, 1663(1), 012003.

Maf’ulah, S., Juniati, D., & Siswono, T. (2016). Pupils’ error on the concept of reversibility in solving arithmetic problems. Educational Research and Reviews, 11(18), 1775–1784.

Maf’ulah, S., Juniati, D., & Siswono, T. Y. E. (2017). The aspects of reversible thinking in solving algebraic problems by an elementary student winning national olympiad medals in science. World Transactions on Engineering and Technology Education, 15(2), 189–194.

Ministry of Education, Culture, Research and Technology, Decree of the Head of the Education Standards, Curriculum and Assessment Agency Number 008/H/Kr/2022 on Learning Outcomes in Early Childhood Education, Primary Education, and Secondary Educat (Issue 021). (2022). Kemendikbudritek.

Nova, T., Yunianta, H., & Dasari, D. (2023). Textbook praxeological-didactical analysis : Lessons learned from the Indonesian mathematics textbook. Journal on Mathematics Education, 14(3), 503–524.

Oakley, L. (2004). Cognitive development routledge modular psychology.

Piaget, J. (2005). Child’s conception of space: Selected works Vol 4. Routledge.’s+Conception+of+Space&ots=NI6aOum8nE&sig=appNZHZExbESstdWlVnaFbooahQ#v=onepage&q=The Child’s Conception of Space&f=false

Prabawanto, S. (2023). Improving prospective mathematics teachers’ reversible thinking ability through a metacognitive-approach teaching. Eurasia Journal of Mathematics, Science and Technology Education, 19(6), 1-13.

Ramful, A. (2014). Reversible reasoning in fractional situations: Theorems-in-action and constraints. Journal of Mathematical Behavior, 33, 119–130.

Ramful, A., & Olive, J. (2008). Reversibility of thought: An instance in multiplicative tasks. Journal of Mathematical Behavior, 27(2), 138–151.

Sangwin, C. J., & Jones, I. (2017). Asymmetry in student achievement on multiple-choice and constructed-response items in reversible mathematics processes. Educational Studies in Mathematics, 94(2), 205–222.

Saparwadi, L., Sa’dijah, C., As’ari, A. R., & Chandrad, T. D. (2020). The aspects and stages of reversible thinking of secondary school students in resolving the problems of fractional numbers. Systematic Reviews in Pharmacy, 11(6), 1302–1310.

Simon, M. A., Kara, M., Placa, N., & Sandir, H. (2016). Categorizing and promoting reversibility of mathematical concepts. Educational Studies in Mathematics, 93(2), 137–153.

Steffe, L. P. (2001). A new hypothesis concerning children’s fractional knowledge. Journal of Mathematical Behavior, 20(3), 267–307.

Steffe, L. P., & Olive, J. (2009). Children’s fractional knowledge. Springer Science & Business Media.

Sugiyono, D. (2010). Metode penelitian kuantitatif dan R&D [Quantitative and R&D research methods]. Alfabeta.

Suryadi, D. (2019). Landasan filosofis penelitian desain didaktis (DDR) [Philosophical foundation of didactic design research]. Pusat Pengembangan DDR Indonesia.

Sutiarso, S. (2020). Analysis of student reversible thinking skills on graph concept. Indonesian Journal of Science and Mathematics, 3(2), 185–195.

Syarah, F., Harahap, Y. N., & Putri, J. H. (2023). Kesulitan siswa dalam mempelajari materi aljabar [Student difficulties in learning algebra material]. Journal On Education, 5(4), 16067–16070.

Tzur, R. (2004). Teacher and students’ joint production of a reversible fraction conception. The Journal of Mathematical Behavior, 23, 93-114

Wahyuningrum, A. S., Suryadi, D., & Turmudi, T. (2019). Learning obstacles among Indonesian eighth graders on ratio and proportion. Journal of Physics: Conference Series, 1320(1), 012046.



  • There are currently no refbacks.

Copyright (c) 2023 Aneu Pebrianti, Sufyani Prabawanto, Elah Nurlaelah

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

 Creative Commons License
Jurnal Elemen is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

View My Stats