The Impact of Inductive Teaching on Pre-Tertiary Students’ Academic Performance in Solving Circle Theorem Problems

Main Article Content

Thomas Gona Akwasi Dimaweh
Ebenezer Bonyah
Benjamin Adu Obeng

Abstract

Purpose – This study was motivated by the persistent challenges students face in solving geometry problems, particularly circle theorems. It aimed to investigate how an inductive teaching approach affects pre-tertiary students’ performance in solving circle theorem problems.


Methodology – A mixed-methods approach grounded in the pragmatist paradigm was used, adopting a quasi-experimental pre-test–post-test control-group design. Using purposive and stratified sampling, 84 second-year students were selected and assigned to experimental and control groups. The experimental group was taught through the inductive approach, while the control group received conventional instruction. Data were collected through achievement tests and interviews, and analysed using descriptive statistics, t-tests, and thematic analysis.


Findings – Students demonstrated significant conceptual, procedural, and factual difficulties in solving circle-theorem problems. However, the experimental group performed significantly better in the post-test than the control group. Interview findings also indicated that students perceived the inductive approach as more engaging, interactive, and effective in improving understanding. The study concluded that the inductive intervention positively influenced both achievement and attitudes toward learning the circle theorem.


Novelty – The study’s novelty lies in examining the effect of inductive teaching on students’ performance in solving circle-theorem problems within a pre-tertiary education context.


Significance – The study contributes to improving mathematics teaching strategies by emphasizing the potential of inductive teaching to enhance students’ achievement and attitudes toward complex concepts such as circle theorems, thereby supporting wider implementation and future research.

Article Details

How to Cite
Gona Akwasi Dimaweh , T., Bonyah, E., & Adu Obeng, B. (2026). The Impact of Inductive Teaching on Pre-Tertiary Students’ Academic Performance in Solving Circle Theorem Problems . International Journal of Mathematics and Mathematics Education, 4(1), 1–28. https://doi.org/10.56855/ijmme.v4i1.1782
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References

Abakah, F. (2019). Exploring Mathematics Learners’ Problem-Solving Skills in Circle Geometry in South African Schools:(A Case Study of a High School in the Northern Cape Province). University of South Africa (South Africa).

Abakah, F., & Brijlall, D. (2024). Finding an Effective Assessment Approach to Enhance the Teaching and Learning of Circle Geometry. Africa Education Review, 20(3), 93-116. https://doi.org/10.1080/18146627.2024.2402772

Abdullah, A. H., & Zakaria, E. (2011). An exploratory factor analysis of an attitude towards geometry survey in a Malaysian context. International Journal of Academic Research, 3(6), 190–193.Serin

Abdullah, A. H., Misrom, N. S., Kohar, U. H. A., Hamzah, M. H., Ashari, Z. M., Ali, D. F., ... & Abd Rahman, S. N. S. (2020). The effects of an inductive reasoning learning strategy assisted by the GeoGebra software on students’ motivation for the functional graph II topic. IEEE access, 8, 143848–143861. https://doi.org/10.1109/ACCESS.2020.3014202

Acharya, B. R. (2017). Factors affecting difficulties in learning mathematics by mathematics learners. International Journal of Elementary Education, 6(2), 8-15. https://doi.org/10.11648/j.ijeedu.20170602.11

Acharya, U. P. (2016). Effectiveness of inductive method in teaching geometry at secondary level (Doctoral dissertation, Department of Mathematics Education Central Department of Education).

Adolphus, T. (2011). Problems of teaching and learning of geometry in secondary schools in Rivers State, Nigeria. International Journal of Emerging Sciences, 1(2), 143-152.

Aidoo-Bervell, F. (2021). Assessing senior high school students’ thinking levels in solving problems on circle theorems-the case of Mfantsiman Girls’ Senior High School (Doctoral dissertation, University of Education, Winneba).

Akanmu, M. A., Fajemidagba, M. O., & Sunday, Y. (2014). Effects of Peer Square and Cooperative Learning Modes on Senior Secondary School Students’ Performance in Mathematics.

Akendita, P. A., Boateng, F. O., Arthur, Y. D., Banson, G. M., Abil, M., & Ahenkorah, M. (2025). The mediating role of teacher effective communication on the relationship between students’ mathematics interest and their mathematics performance. International Journal of Mathematics and Mathematics Education, 3(1), 1-17. https://doi.org/10.56855/ijmme.v3i1.1214

Akendita, P. A., Obeng, B. A., Abil, M., & Ahenkorah, M. (2024). Investigating the effect of socio-constructivist mathematics teaching on students’ mathematics achievement: The mediating role of mathematics self-efficacy. Educational Point, 1(2), e110. https://doi.org/10.71176/edup/15662

Akın, Y., & Cancan, M. (2007). Matematik Öğretiminde Problem Çözümüne Yönelik Öğrenci Görüşleri Analizi. Kazım Karabekir Eğitim Fakültesi Dergisi, 16, 374-390.

Alio, B. C., & Harbor-Peter, V. F. (2000). The Effect of Policies Problem-Solving Technique on Secondary School Students, Advertisement in Mathematics. Abacus: JMAN, 25(1), 26-38.

Ameen, K. S., Salawu, S. A., & Bidemi, H. (2022). Identification of Mathematical Errors Committed by Senior School Students in Calculus. JURNAL PENDIDIKAN MATEMATIKA UNIVERSITAS LAMPUNG, 10(2), 106-120.

Ansong, E. K., Wiafe, D. A., & Amankwah, R. (2021). Application of GeoGebra to improve academic performance of students in geometry. International Journal of Computer Applications, 183(29), 26-32.

Atta, M. A., Ayaz, M., Nawaz, Q., & Khan, D. I. (2015). Comparative study of inductive & deductive methods of teaching mathematics at elementary. Gomal University Journal of Research, 31(1), 1019–8180.

Atta, S. A., & Bonyah, E. (2023). Designing a flipped classroom instruction to improve plane geometry learning among pre-service teachers in Ghana. Contemporary Mathematics and Science Education, 4(1), ep23004. https://doi.org/10.30935/conmaths/12674

Badu-Domfeh, A. K. (2020). Incorporating GeoGebra software in the teaching of circle theorem and its effect on the performance of students (Doctoral dissertation, University of Cape Coast). http://hdl.handle.net/123456789/4630

Bandura, A. (1997). Self-efficacy: The exercise of control. New York: Freeman

Bansilal, S., & Ubah, I. (2019). The use of semiotic representations in reasoning about similar triangles in Euclidean geometry. Pythagoras, 40(1), 1-10.

Barnes, A. (2021). Enjoyment in learning mathematics: Its role as a potential barrier to children’s perseverance in mathematical reasoning. Educational Studies in Mathematics, 106(1), 45-63.

Barut, M. E. O., & Retnawati, H. (2020, August). Geometry learning in vocational high school: Investigating the students’ difficulties and levels of thinking. In Journal of Physics: Conference Series (Vol. 1613, No. 1, p. 012058). IOP Publishing. https://doi.org/10.1088/1742-6596/1613/1/012058

Bernard, P., & Dudek-Różycki, K. (2019). Influence of training in inquiry-based methods on in-service science teachers’ reasoning skills. Chemistry Teacher International, 1(2), 20180023.

Biggs, J. (1996). Enhancing teaching through constructive alignment. Higher education, 32(3), 347-364.

Biggs, J. (2003). Aligning teaching for constructing learning. Higher Education Academy, 1(4), 1-4.

Boaler, J. (2015). Mathematical mindsets: Unleashing students' potential through creative math, inspiring messages and innovative teaching. John Wiley & Sons.

Bonyah, E., & Larbi, E. (2021). Assessing Van Hiele's Geometric Thinking Levels among Elementary Pre-Service Mathematics Teachers. African Educational Research Journal, 9(4), 844-851. https://doi.org/10.30918/AERJ.94.21.119

Bosson-Amedenu, S. (2017). Remedial students’ perception of difficult concepts in senior high school core mathematics curriculum in Ghana. Asian research journal of mathematics, 3(3), 1-13.

Bosson-Amedenu, S. (2018). Effect of use of WAEC syllabus on the mathematical achievement of WASSCE candidates in Ghana. Asian Research Journal of Arts & Social Sciences, 6(4), 1-8.

Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative research in psychology, 3(2), 77-101.

Brijlall, D., & Abakah, F. (2022). High school learners’ challenges in solving circle geometry problems. PONTE International Journal of Sciences and Research; Vol. 78, Issue 12 (1). https://doi.org/10.21506/j.ponte.2022.12.9

Bruno, A. (2013). Using diagrams that will enhance conceptual understanding and skills development in circle theorems among SHS 2 students of Mankessim senior high school (Doctoral dissertation, University of Education, Winneba).

Chan, F. T., Li, N., Chung, S. H., & Saadat, M. (2017). Management of sustainable manufacturing systems-a review on mathematical problems. International Journal of Production Research, 55(4), 1210-1225.

Chan, M. C. E., & Clarke, D. (2017). Structured affordances in the use of open-ended tasks to facilitate collaborative problem solving. ZDM, 49(6), 951-963.

Chuang, S. (2021). The applications of constructivist learning theory and social learning theory on adult continuous development. Performance Improvement, 60(3), 6-14.

Clements, D. H., & Sarama, J. (2011). Early childhood teacher education: The case of geometry. Journal of mathematics teacher education, 14(2), 133-148.

CRDD (2010). Teaching syllabus for senior high school mathematics. Accra: Curriculum Research and Development Division. Ghana Education Service

Dewey, J. (1986). Experience and education. In The educational forum (Vol. 50, No. 3, pp. 241-252). Taylor & Francis Group.

Elliott, A. C., & Woodward, W. A. (2007). Statistical analysis quick reference guidebook: With SPSS examples. Sage.

Fabiyi, T. R. (2017). Geometry concepts in mathematics perceived difficult to learn by senior secondary school students in Ekiti State, Nigeria. IOSRT Journal of Research and Method in Education, 7(1), 83-90.

Fani, T., & Ghaemi, F. (2011). Implications of Vygotsky's zone of proximal development (ZPD) in teacher education: ZPTD and self-scaffolding. Procedia-Social and Behavioral Sciences, 29, 1549-1554.

Field, A. (2009). Discovering statistics using SPSS: Book plus code for E version of text (Vol. 896). London, UK: SAGE Publications Limited.

Field, A. (2013). Discovering statistics using IBM SPSS statistics (4th ed.). SAGE.

Ghana Statistical Service, 2020. Multiple Indicator Cluster Survey (MICS2017/18), Survey Findings Report. GSS, Accra, Ghana.

Ghasemi, A., & Zahediasl, S. (2012). Normality tests for statistical analysis: a guide for non-statisticians. International journal of endocrinology and metabolism, 10(2), 486.

Gholam, A. P. (2019). Inquiry-based learning: Student teachers’ challenges and perceptions. Journal of Inquiry and Action in Education, 10(2), 6.

Hailikari, T., Virtanen, V., Vesalainen, M., & Postareff, L. (2022). Student perspectives on how different elements of constructive alignment support active learning. Active Learning in Higher Education, 23(3), 217-231. https://doi.org/10.1177/1469787421989

Herbst, P., Gonzalez, G., & Macke, M. (2005). How Can Geometry Students Understand What It Means to. Mathematics Educator, 15(2), 17-24.

Hidalgo, F. S. J. (2017). Tips on how to teach effectively (A Description of 60 teaching methods). Paranaque City https://www.sunstar.com.ph/article/1500934/Davao/Opinion/Hidalgo-1stNational-ICT-Summit-of-DepEd

Hiebert, J. (2007). The effects of classroom mathematics teaching. Second handbook of research on mathematics teaching and learning: A project of the national council of teachers of mathematics, 1, 371.

Hiele, P. M. V. (1986). Structure and insight: A theory of mathematics education. (No Title).

Imoko, B. I., & Isa, S. A. (2015). Impact of computer Genues on pupils achievement in mathematics in primary achievement in mathematics in primary school Lafia Local Government Area: A tool for technological development. In Proceedings of September 2015 Annual National Conference of mathematical Association of Nigeria (pp. 63-71).

Ješková, Z., Lukác, S., Hancová, M., Šnajder, L., Guniš, J., Balogová, B., & Kireš, M. (2016). Efficacy of Inquiry-Based Learning in Mathematics, Physics and Informatics in Relation to the Development of Students’ Inquiry Skills. Journal of Baltic Science Education, 15(5), 559-574.

Kashefi, H., Ismail, Z., Yusof, Y. M., & Mirzaei, F. A. R. I. B. A. (2013). Generic skills in engineering mathematics through blended learning: A mathematical thinking approach. International Journal of Engineering Education, 29(5), 1222-1237.

Khurshid, F., & Ansari, U. (2012). Effects of innovative teaching strategies on students’ performance. Global Journal of Human Social Science Linguistics & Education, 12(10), 47-54.

Kim, H. Y. (2013). Statistical notes for clinical researchers: assessing normal distribution (2) using skewness and kurtosis. Restorative dentistry & endodontics, 38(1), 52.

Kirschner, P., Sweller, J., & Clark, R. E. (2006). Why unguided learning does not work: An analysis of the failure of discovery learning, problem-based learning, experiential learning and inquiry-based learning. Educational psychologist, 41(2), 75-86.

Koch, T. (2006). Establishing rigour in qualitative research: The decision trail. Journal of Advanced Nursing, 53, 91–100.

Koskinen, R., & Pitkäniemi, H. (2022). Meaningful learning in mathematics: A research synthesis of teaching approaches. International Electronic Journal of Mathematics Education, 17(2), em0679.

Kwadwo, A. E., & Asomani, W. D. (2021). Investigating colleges of Education students’ difficulty in understanding circle geometry. ADRRI Journal of Physical and Natural Sciences, 4(3 (4) October-December), 1-27.a

Laborde, C. (2005). The hidden role of diagrams in students’ construction of meaning in geometry. In Meaning in mathematics education (pp. 159-179). New York, NY: Springer US.

Lappan, G. (2000). A vision of learning to teach for the 21st century. School science and mathematics, 100(6), 319-326.

Lim, S. K. (1992). Applying the Van Hiele theory to the teaching of secondary school geometry. Institute of Education Teaching and Learning 13(1), 32-40

Lin, F. L., & Yang, K. L. (2007). The reading comprehension of geometric proofs: The contribution of knowledge and reasoning. International Journal of Science and Mathematics Education, 5(4), 729-754.

Lincoln, Y.S. and Guba, E.G., 1985. Naturalistic inquiry. Newbury Park, California: Sage.

Mensah, Y. A., Atteh, E., Boadi, A., & Assan-Donkoh, I. (2022). Exploring the impact of Problem-based Learning Approach on Students’ performance in solving Mathematical problems under circles (geometry). J Educ Soc Behav Sci, 35(9), 35-47. https://doi.org.10.9734/JESBS/2022/v35i930455

Mensah-Wonkyi, T., & Adu, E. (2016). Effect of the inquiry-based teaching approach on students’ understanding of circle theorems in plane geometry. African Journal of Educational Studies in Mathematics and Sciences, 12, 61-74.

Mesa, V., Gómez, P., & Cheah, U. H. (2012). Influence of international studies of student achievement on mathematics teaching and learning. In Third international handbook of mathematics education (pp. 861-900). New York, NY: Springer New York.

Mulligan, J. (2015). Looking within and beyond the geometry curriculum: connecting spatial reasoning to mathematics learning. Zdm, 47(3), 511-517.

Mullis, I. V. S., Martin, M. O., Foy, P., & Hooper, M. (2016). TIMSS 2015 International Results in Mathematics. International Association for the Evaluation of Educational Achievement, TIMSS2015.https://doi.org/timss2015.org/download-center/

Mullis, I. V., Martin, M. O., Foy, P., & Drucker, K. T. (2012). PIRLS 2011 international results in reading. International Association for the Evaluation of Educational Achievement. Herengracht 487, Amsterdam, 1017 BT, The Netherlands.

National Council of Teachers of Mathematics (2003). Principles and Standards for School Mathematics. Reston VA: NCTM

Newcombe, N. S., Booth, J. L., & Gunderson, E. A. (2019). Spatial skills, reasoning, and mathematics. The Cambridge handbook of cognition and education, 100-123.

Novita, R., Putra, M., Rosayanti, E., & Fitriati, F. (2018, September). Design learning in mathematics education: Engaging early childhood students in geometrical activities to enhance geometry and spatial reasoning. In Journal of Physics: Conference Series (Vol. 1088, No. 1, p. 012016). IOP Publishing.

Ntow, F. D., & Hissan, Y. (2021). The impact of concept-based instruction on senior high school students’ achievement in circle theorems. African Journal of Educational Studies in Mathematics and Sciences, 17(1), 113-132.

O’connor, T. G., Rutter, M., & English and Romanian Adoptees Study Team. (2000). Attachment disorder behavior following early severe deprivation: Extension and longitudinal follow-up. Journal of the American Academy of Child & Adolescent Psychiatry, 39(6), 703-712.

Obeng, B. A., Banson, G. M., Owusu, E., & Owusu, R. (2024). Analysis of senior high school students’ errors in solving trigonometry. Cogent Education, 11(1), 2385119. https://doi.org/10.1080/2331186X.2024.2385119

Oladosu, L. O. (2014). Secondary school students’ meaning and learning of circle geometry.

Oppong-Gyebi, D. H. (2004). Geometric and spatial thinking in early childhood education. Engaging young children in mathematics: Standards for early childhood mathematics education, 267-297.

Oppong-Gyebi, E., Bonyah, E., & Clark, L. J. (2023). Constructive instructional teaching and learning approaches and their mathematical classroom teaching practices: A junior high school perspective. Contemporary Mathematics and Science Education, 4(1), ep23002. https://doi.org/10.30935/conmaths/12541

Owusu, R., Bonyah, E., & Arthur, Y. D. (2023). The effect of GeoGebra on university students’ understanding of polar coordinates. Cogent Education, 10(1), 2177050. https://doi.org/10.1080/2331186X.2023.2177050

Özerem, A. (2012). Misconceptions in geometry and suggested solutions for seventh grade students. Procedia-Social and Behavioral Sciences, 55, 720-729.

Pallant, J. (2020). SPSS survival manual: A step by step guide to data analysis using IBM SPSS. Routledge.

Park, Y. S., Konge, L., & Artino Jr, A. R. (2020). The positivism paradigm of research. Academic medicine, 95(5), 690-694.

Piaget, J. (1952). Jean Piaget.BiggsBiggs

Piaget, J. (1983). Piaget’s theory. Handbook of Child Psychology. 4th edition. Vol. 1. New York: Wiley.

Piaget, J., & Cook, M. (1952). The origins of intelligence in children (Vol. 8, No. 5, pp. 18-1952). New York: International universities press.

Pierce, R., & Stacey, K. (2011). Using dynamic geometry to bring the real world into the classroom. In Model-centered learning (pp. 41-55). Brill.

Prahmana, R. C. I., & D’Ambrosio, U. (2020). Learning Geometry and Values from Patterns: Ethnomathematics on the Batik Patterns of Yogyakarta, Indonesia. Journal on Mathematics Education, 11(3), 439-456.

Prince, M. J., & Felder, R. M. (2006). Inductive teaching and learning methods: Definitions, comparisons, and research bases. Journal of engineering education, 95(2), 123-138.

Rahmah, M. A. (2017). Inductive-deductive approach to improve mathematical problem solving for Junior High School. Journal of Physics: Conference Series, 8(12). Retrieved from https://doi.org/10.1088/1742-6596/755/1/011001

Ramadhani, R. (2018). The enhancement of mathematical problem solving ability and self-confidence of students through problem based learning. Jurnal Riset Pendidikan Matematika, 5(1), 127-134.

Razali, N. M., & Wah, Y. B. (2011). Power comparisons of shapiro-wilk, kolmogorov-smirnov, lilliefors and anderson-darling tests. Journal of statistical modeling and analytics, 2(1), 21-33.

Rodd, M. (2010). Geometrical visualisation--epistemic and emotional. For the learning of Mathematics, 30(3), 29-35.

Ryan, R. M., & Deci, E. L. (2000). Intrinsic and extrinsic motivations: Classic definitions and new directions. Contemporary educational psychology, 25(1), 54-67.

Salman, M. F. (2017). Language and Problem Solving: The Mathematics Education Link. Library and Publications Committee, University of Ilorin.

Segbefia, C. R. (2020). Effect of Inductive Teaching Method on Senior High School Students’ Achievement in Circle Theorems (Doctoral dissertation, University of Cape Coast).

Serin, H. (2018). Perspectives on the teaching of geometry: teaching and learning methods. Journal of Education and Training, 5(1), 131-137. https://doi.org/10.5296/jet.v5i1.xxxx

Siller, H. S., & Ahmad, S. (2024). Analyzing the impact of collaborative learning approach on grade six students’ mathematics achievement and attitude towards mathematics. EURASIA Journal of Mathematics, Science and Technology Education, 20(2), em2395.

Simamora, R. E., & Saragih, S. (2019). Improving Students’ Mathematical Problem Solving Ability and Self-Efficacy through Guided Discovery Learning in Local Culture Context. International Electronic Journal of Mathematics Education, 14(1), 61-72.

Sjøberg, S. (2010). Constructivism and learning. International Encyclopedia of Education, May, 485–490. https://doi.org/10.1016/B978-0-08-044894-7.00467-X

Suglo, E. K., Bornaa, C. S., Iddrisu, A. B., Atepor, S., Adams, F. X., & Owuba, L. A. (2023). Teacher's Pedagogical Content Knowledge and Students' Academic Performance in Circle Theorem. Online Submission, 2(3), 29-41.

Swindal, D. N. (2000). Learning geometry and a new language. Teaching Children Mathematics, 7(4), 246-250.

Tay, M. K., & Wonkyi, T. M. (2018). Effect of using Geogebra on senior high school students’ performance in circle theorems. African Journal of Educational Studies in Mathematics and Sciences, 14, 1-18.

Vygotsky, L. S. (1978). In Cole M. (Ed.), Mind in society: The development of higher psychological process. Cambridge: Harvard University Press.

WAEC, & GOG. (2019). West African senior school certificate examination 2013 - 2018 past questions and chief examiners’ reports for core subjects. Accra, Ghana: WAEC & KBSL

WAEC. (2011). The chief examiners’ reports for the west African senior school certificate examination for school candidates, 2011. Accra https://doi.org/www.waecgh.org

WAEC. (2017). The chief examiners’ reports for the west African senior school certificate examination for school candidates, 2017. Accra https://doi.org/www.waecgh.org

WAEC. (2018). The chief examiners’ reports for the west African senior school certificate examination for school candidates, 2018. Accra. https://doi.org/www.waecgh.org

WAEC. (2020). The chief examiners’ reports for the west African senior school certificate examination for school candidates, 2020. Accra https://doi.org/www.waecgh.org

West African Examinations Council (2012). Chief Examiners’ Report on West African Senior School Certificate Examination May/June 2012

West African Examinations Council (2016). Chief Examiners’ Report on West African Senior School Certificate Examination May/June 2016

Williams, M. K. (2017). John Dewey in the 21st century. Journal of Inquiry and Action in Education, 9(1), 7.

Yang, K. L., & Lin, F. L. (2008). A model of reading comprehension of geometry proof. Educational Studies in Mathematics, 67(1), 59-76.

Ye, J. C. (2022). Geometry of Deep Learning. Springer Singapore.