An Exploration of Pre-service Mathematics Teachers’ Routine thinking in Solving Problems in Geometry: A Case Study of a University in Ghana
Ernest Larbi 
& Vimolan Mudaly
Issue: Vol.6 No.12 Article 16 pp. 3107 – 3122
DOI: https://doi.org/10.38159/ehass.202561216 | Published online 25th November, 2025
© 2025 The Author(s). This is an open access article under the CCBY license (http://creativecommons.org/licenses/by/4.0/).
Concerns have been raised that many mathematics classrooms follow a set of distinctive rules in solving mathematical tasks. Despite the impact of teachers’ knowledge on instructional design, and the critical role geometry plays in school mathematics curricula, research shows that pre-service mathematics teachers demonstrate more ritualised (procedural) knowledge in solving geometric problems than explorative (conceptual) knowledge. This study, therefore, explored the nature of eight Ghanaian pre-service mathematics teachers’ routine thinking in solving questions in geometry. A test consisting of 16 questions was administered to them. Those who solved 12 or more questions correctly were deemed to have performed well and were assigned to Group A, whilst those who solved fewer than 12 questions were deemed not to have performed so well and were assigned to Group B. The study used the interpretivist paradigm following the qualitative approach. The data was gathered through tests and semi-structured interviews. The results showed that the solution strategies of the three pre-service teachers in Group B were more ritualised, as they solved most of the tasks using a set of procedures. This ritualised thinking was evident in the solutions of those in Group B compared to those in Group A, whose routine strategies were more objectified and property-guided. Following these solution approaches, the study concluded that the Group B pre-service teachers demonstrated more ritualised thinking in solving geometric tasks than explorative thinking, which was more evident in the discourses of those in Group A. It was recommended that mathematics pre-service teachers should be equipped with an explorative sense or reasoning in addition to their ritualised or procedural reasoning. Findings will help develop pre-service mathematics teachers’ geometric reasoning by designing targeted instructional activities for learning geometry
Keywords: Commognition, Competence, Explorative, Pre-Service Teachers, Ritual
Akhter, Nasrin, and Nasreen Akhter. “Learning in Mathematics: Difficulties and Perceptions of Students.” Journal of Educational Research (1027-9776) 21, no. 1 (2018).
Al-Mutawah, Masooma Ali, Ruby Thomas, Abdulla Eid, Enaz Yousef Mahmoud, and Moosa Jaafar Fateel. “Conceptual Understanding, Procedural Knowledge and Problem-Solving Skills in Mathematics: High School Graduates Work Analysis and Standpoints.” International Journal of Education and Practice 7, no. 3 (2019): 258–73.
Alex, Jogymol, and Kuttikkattu J Mammen. “Students’ Understanding of Geometry Terminology through the Lens of Van Hiele Theory.” Pythagoras 39, no. 1 (2018): 1–8.
Armah, Robert Benjamin, Primrose Otokonor Cofie, and Christopher Adjei Okpoti. “The Geometric Thinking Levels of Pre-Service Teachers in Ghana.” Higher Education Research 2, no. 3 (2017): 98–106.
Bonyah, Ebenezer, and Ernest Larbi. “Assessing Van Hiele’s Geometric Thinking Levels among Elementary Pre-Service Mathematics Teachers.” African Educational Research Journal 9, no. 4 (2021): 844–51.
DeJonckheere, Melissa, and Lisa M Vaughn. “Semistructured Interviewing in Primary Care Research: A Balance of Relationship and Rigour.” Family Medicine and Community Health 7, no. 2 (March 8, 2019): e000057. https://doi.org/10.1136/fmch-2018-000057.
Dewi, I L K, and S Asnawati. “Relationship among Pre-Service Teacher Conception of Geometry and Teaching Skills.” In Journal of Physics: Conference Series, 1280:042042. IOP Publishing, 2019.
Erdogan, Ahmet. “Examining Pre-Service Mathematics Teachers’ Conceptual Structures about” Geometry”.” Online Submission 8, no. 27 (2017): 65–74.
Essack, Regina Miriam. Exploring Grade 11 Learner Routines on Function from a Commognitive Perspective. University of the Witwatersrand, Johannesburg (South Africa), 2015.
Gray, Clive. “Managing Cultural Policy: Pitfalls And Prospects.” Public Administration 87, no. 3 (September 27, 2009): 574–85. https://doi.org/10.1111/j.1467-9299.2008.01748.x.
Gutierrez, Pedro Antonio, Maria Perez-Ortiz, Javier Sanchez-Monedero, Francisco Fernandez-Navarro, and Cesar Hervas-Martinez. “Ordinal Regression Methods: Survey and Experimental Study.” IEEE Transactions on Knowledge and Data Engineering 28, no. 1 (January 1, 2016): 127–46. https://doi.org/10.1109/TKDE.2015.2457911.
Hurrell, Derek. “Conceptual Knowledge OR Procedural Knowledge or Conceptual Knowledge AND Procedural Knowledge: Why the Conjunction Is Important to Teachers.” Australian Journal of Teacher Education 46, no. 2 (February 2021): 57–71. https://doi.org/10.14221/ajte.2021v46n2.4.
Jentsch, Armin, and Lena Schlesinger. “Measuring Instructional Quality in Mathematics Education.” In CERME 10, 2017.
Keazer, Lindsay, and Jennifer Phaiah. “Analyzing Prospective Elementary Teachers’ Evidence of Conceptual Understanding and Procedural Fluency.” Investigations in Mathematics Learning 15, no. 2 (April 3, 2023): 135–48. https://doi.org/10.1080/19477503.2022.2139112.
Khaksar, Ramin, Traci Carlson, Donald W Schaffner, Mahni Ghorashi, Dieter Best, Srikanth Jandhyala, Julie Traverso, and Sasan Amini. “Unmasking Seafood Mislabeling in US Markets: DNA Barcoding as a Unique Technology for Food Authentication and Quality Control.” Food Control 56 (2015): 71–76.
Kivkovich, Nava. “A Tool for Solving Geometric Problems Using Mediated Mathematical Discourse (for Teachers and Pupils).” Procedia-Social and Behavioral Sciences 209 (2015): 519–25.
Llinares, Salvador. “Instructional Quality of Mathematics Teaching and Mathematics Teacher Education.” Journal of Mathematics Teacher Education 24, no. 1 (February 2021): 1–3. https://doi.org/10.1007/s10857-021-09488-2.
Mann, Manveer, and Mary C Enderson. “Give Me a Formula Not the Concept! Student Preference to Mathematical Problem Solving.” Journal for Advancement of Marketing Education 25, no. Special Issue on Teaching Innovations in Retailing Education (2017).
Mudaly, Ronicka, and Sebastian Sanjigadu. “Epistemic Journeying across Abyssal Lines of Thinking: Towards Reclaiming Southern Voices.” Education as Change 26, no. 1 (2022): 1–29.
Nahdi, D Salim, and M Gilar Jatisunda. “Conceptual Understanding and Procedural Knowledge: A Case Study on Learning Mathematics of Fractional Material in Elementary School.” In Journal of Physics: Conference Series, 1477:042037. IOP Publishing, 2020.
NCTM, À. “National Council of Teachers of Mathematics/2000/Principles and Standards for School Mathematics.” Council of Teachers of Mathematics, n.d.
Övez, Filiz Tuba Dikkartin, and Emine Özdemir. “An Examination of Pre-Service Teachers’ Van Hiele Levels of Geometric Thinking and Proof Perception Types in Terms of Thinking Processes.” Educational Research and Reviews 19, no. 1 (2024): 26–39.
Rittle-Johnson, Bethany, and Michael Schneider. “Developing Conceptual and Procedural Knowledge of Mathematics.” In The Oxford Handbook of Numerical Cognition, 1118–34. Oxford University Press, 2014. https://doi.org/10.1093/oxfordhb/9780199642342.013.014.
Rittle‐Johnson, Bethany. “Developing Mathematics Knowledge.” Child Development Perspectives 11, no. 3 (September 4, 2017): 184–90. https://doi.org/10.1111/cdep.12229.
Sabey, K. “Secondary Preservice Teachers’ Understanding of Euclidean Geometry.” University of Northern Iowa, 2009. https://scholarworks.uni.edu/etd/691.
Sfard, A. Thinking as Communicating: Human Development, the Growth of Discourses, and Mathematizing. New York, NY: Cambridge University Press, 2008.
———. “When the Rules of Discourse Change, but Nobody Tells You: Making Sense of Mathematics Learning from a Commognitive Standpoint.” The Journal of the Learning Science 16, no. 4 (2007): 567–615.
Sfard, Anna, Mel Sabella, Charles Henderson, and Chandralekha Singh. “Moving Between Discourses: From Learning-As-Acquisition To Learning-As-Participation.” In AIP Conference Proceedings, 55–58, 2009. https://doi.org/10.1063/1.3266753.
Shulman, Lee S. “Those Who Understand: Knowledge Growth in Teaching.” Educational Researcher 15, no. 2 (1986): 4–14.
Sugeng, S., and M. C. Nurhanurawati. “ The Effect of Various Media Scaffolding on Increasing Understanding of Students’ Geometry Concepts.” Journal on Mathematics Education 9, no. 1 (2018): 95–102.
Usta, Erdoğan, and Çiğdem Akkanat. “Investigating Scientific Creativity Level of Seventh Grade Students.” Procedia – Social and Behavioral Sciences 191 (June 2015): 1408–15. https://doi.org/10.1016/j.sbspro.2015.04.643.
Yi, Minju, Jian Wang, Raymond Flores, and Jaehoon Lee. “Measuring Pre-Service Elementary Teachers’ Geometry Knowledge for Teaching 2-Dimensional Shapes.” Eurasia Journal of Mathematics, Science and Technology Education 18, no. 8 (July 12, 2022): em2137. https://doi.org/10.29333/ejmste/12220.
Zuya, H. E., D. B. Matawal, and K. S. Kwalat. “ Conceptual and Procedural Knowledge of Pre-Service Teachers in Geometry.” International Journal of Innovative Education Research 5, no. 1 (2017): 30–38.
Prof. Vimolan Mudaly is a Full Professor at the University of KwaZulu-Natal and is in the Mathematics Education Department in the School of Education.
Dr. Ernest Larbi is a senior lecturer in the Mathematics Education Department of the Akenten Appiah-Menka University of Skills Training and Entrepreneurial Development, Kumasi, Ghana. He obtained his PhD from the University of KwaZulu-Natal, South Africa, supervised by Prof Mudaly.
Larbi , Ernest, and Vimolan Mudaly.“An Exploration of Pre-service Mathematics Teachers’ Routine thinking in Solving Problems in Geometry: A Case Study of a University in Ghana.” E-Journal of Humanities, Arts and Social Sciences 6, no. 12 (2025): 3107 – 3122, https://doi.org/10.38159/ehass.202561216.
© 2025 The Author(s). Published and Maintained by Noyam Journals. This is an open access article under the CCBY license (http://creativecommons.org/licenses/by/4.0/).
