Comparison between concept-based and procedure-based in circle theorems
DOI:
https://doi.org/10.58524/jasme.v5i1.468Keywords:
Circle theorems, Comparison, Concept-based, Procedure-based, Mixed methods design.Abstract
Background: The debate between concept-based instruction and procedure-based approaches to improving students’ performance, understanding, and skill development in Circle Theorems cannot be over-emphasized. The researchers employed the non-equivalent quasi-experimental design to investigate the effectiveness and appropriateness of the two methods, using circle theorems.
Aim: This study aims to compare the effectiveness of concept-based and procedure-based instructional approaches in the teaching of Circle Theorems among senior high school students.
Method: A quasi-experimental design was adopted involving 70 students selected from two purposively sampled schools. One school was assigned as the experimental group (concept-based instruction) and the other as the control group (procedure-based instruction). Geometry achievement tests were administered as pre-tests and post-tests. Data were analyzed using paired sample t-tests, independent sample t-tests, and effect size calculations with a significance level set at 5%.
Result: The findings showed statistically significant differences between the experimental and control groups. Students taught using concept-based instruction performed significantly better than those taught through procedure-based instruction. High effect sizes further supported the superiority of the concept-based approach.
Conclusion: Concept-based instruction enhances students’ understanding and performance in Circle Theorems. It is recommended that mathematics educators adopt teaching methods that promote conceptual understanding and active knowledge construction over algorithmic procedures.
References
Abreh, M. K., Owusu, K. A., &Amedahe, F. K. (2018). Trends in performance of WASSCE candidates in the science and mathematics in Ghana: Perceived contributing factors and the way forward. Journal of Education, 198(1), 113-123. https://doi.org/10.1177/0022057418800950
Abubakar, A., Hilman, H., &Kaliappen, N. (2018). New tools for measuring global academic performance. Sage Open, 8(3). https://doi.org/10.1177/2158244018790787
Ali, C. A. (2023). Exploration of the ability of preservice mathematics teachers using Kolb -experiential learning theory & learning styles. Indonesia Journal of Science and Mathematics Education, 6 (1), 1-16. https://doi.org/10.24042/ijsme.v6i1.10440
Ali, C. A. (2022). The didactical phenomenology in learning the circle equation. International Electronic Journal of Mathematics Education, 17(4), 1-11. https://doi.org/10.29333/iejme/12472
Asilo-Ebisa, G. F. L. , & Lomibao, L. S. (2024). Procedural knowledge-to-conceptual knowledge or conceptual knowledge-to-procedural knowledge: Which order of knowledge is better for conceptual understanding and procedural fluency?. Journal of Innovations in Teaching and Learning, 4(1), 1-6.
Bashiru, A., & Nyarko, J. (2019). Van Hiele geometric thinking levels of junior high school students of Atebubu Municipality in Ghana. African Journal of Educational Studies in Mathematics and Sciences, 15(1), 39-50. https://doi.org/10.4314/ajesms.v15i1.4
Biney, S. K. & Ali, C. A. (2023). Errors and misconceptions in solving linear inequalities in one variable. Journal of Advanced Sciences and Mathematics Education, 3(1), 15-30. https://doi.org/10.58524/jasme.v3i1.195
Borji, V., Radmehr, F., & Font, V. (2021). The impact of procedural and conceptual teaching on students' mathematical performance over time. International Journal of Mathematical Education in Science and Technology, 52(3), 404-426. https://doi.org/10.1080/0020739X.2019.1688404
Boson-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. https://doi.org/10.9734/ARJOM/2017/32330
Erebakyere, J., & Agye, D. D. (2022). Teaching and learning circle theorems with Dynamic Autograph technology: Should we employ the social interaction or the self-exploration strategy?. African Journal of Educational Studies in Mathematics and Sciences, 18 (1), 49-67. https://doi.org/10.4314/ajesms.v18i1.5
Engelbrecht, J., Bergsten, C., & Kågesten, O. (2017). Conceptual and procedural approaches to mathematics in the engineering curriculum: views of qualified engineers. European Journal of Engineering Education, 42(5), 570-586. https://doi.org/10.1080/03043797.2017.1343278
Ezer, F., & Aksüt, S. (2021). Opinions of graduate students of social studies education about qualitative research method. International Education Studies, 14(3), 15-32. https://doi.org/10.5539/ies.v14n3p15
Fletcher, J. (2018). Performance in mathematics and science in basic schools in Ghana. Academic Discourse: An International Journal, 10(1), 1-18.
Geary, D. C., vanMarle, K., Chu, F. W., Rouder, J., Hoard, M. K., & Nugent, L. (2018). Early conceptual understanding of cardinality predicts superior school-entry number-system knowledge. Psychological science, 29(2), 191-205. https://doi.org/10.1177/0956797617729817
Gopalan, M., Rosinger, K., & Ahn, J. B. (2020). Use of quasi-experimental research designs in education research: Growth, promise, and challenges. Review of Research in Education, 44(1), 218-243. https://doi.org/10.3102/0091732X20903302
Hakim, L. & Yasmadi, B. (2021). Conceptual and procedural knowledge in mathematics education. Design Engineering, 9, 1271-1280.
Hechter, J., Stols, G., & Combrinck, C. (2022). The reciprocal relationship between conceptual and procedural knowledge—a case study of two calculus problems. African Journal of Research in Mathematics, Science and Technology Education, 26(2), 111-124. https://doi.org/10.1080/18117295.2022.2101271
Howe, C., Hennessy, S., Mercer, N., Vrikki, M., & Wheatley, L. (2019). Teacher–student dialogue during classroom teaching: Does it really impact student outcomes? Journal of the Learning Sciences, 28(4-5), 462–512. https://doi.org/10.1080/10508406.2019.1573730
Hurrell, D. P. (2021). Conceptual knowledge OR Procedural knowledge OR conceptual knowledge AND Procedural knowledge: Why the conjunction is important for teachers. Australian Journal of Teacher Education, 46(2), 56-71. https://doi.org/10.14221/ajte.2021v46n2.4
Hussein & Yusuf. (2022). Conceptual knowledge and its importance in teaching mathematics. Middle Eastern Journal of Research in Education and Social Sciences. 3. 50-65. https://doi.org/10.47631/mejress.v3i1.445
Hussein, Y. F., & Csíkos, C. (2023). The effect of teaching conceptual knowledge on students’ achievement, anxiety about, and attitude toward mathematics. Eurasia Journal of Mathematics, Science and Technology Education, 19(2), https://doi.org/10.29333/ejmste/12938
Joung, E., & Kim, Y. R. (2022). Identifying preservice teachers’ concept-based and procedure-based error patterns in multiplying and dividing decimals. International Journal of Education in Mathematics, Science, and Technology (IJEMST), 10(3), 549-567. https://doi.org/10.46328/ijemst.2227
Khoule, A., Bonsu, N. O., & El Houari, H. (2017). Impact of conceptual and procedural knowledge on student’s mathematics anxiety. International Journal of Educational Studies in Mathematics, 4(1), 8-18.
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(1), 61-74–74.
Mullis, I. V. S., Martin, M. O., Foy, P., Kelly, D. L., & Fishbein, B. (2020). TIMSS 2019 international results in mathematics and science. Retrieved from Boston College, TIMSS & PIRLS International Study Center.
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. https://doi.org/10.4314/ajesms.v17i1.8
Rittle-Johnson, B., & Siegler, R. S. (2022). The relation between conceptual and procedural knowledge in learning mathematics: A review. In C. Donlan (Ed.), The development of mathematical skills (pp. 75–110). https://doi.org/10.4324/9781315784755-6
Setiawan, Y. E. S., & Sunardi. (2023). Classification of errors in determining trigonometry function values at standard positions. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 8(2). https://doi.org/10.23917/jramathedu.v8i2.1625
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.
Uğraş, M. (2019). Determination of the effects of problem-based STEM activities on certain variables and the views of the student. International Online Journal of Educational Sciences. 11: 1-22. https://doi.org/10.15345/iojes.2019.01.001
West African Examinations Council (2013-2022). Chief examiners’ report on west african senior school certificate examination May/Jun 2017, WAEC: Accra.
Yu, J., Landy, D., & Goldstone, R. L. (2018). Comparing and discussing multiple strategies: An approach to improving algebra instruction. Quarterly Journal of Experimental Psychology, 91(1), 1-19. https://doi.org/10.1080/00220973.2021.1903377
Downloads
Published
Issue
Section
License
Authors who publish with Journal of Advanced Sciences and Mathematics Education agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution-ShareAlike 4.0 International License (CC BY-SA 4.0) that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
Journal of Advanced Sciences and Mathematics Education is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
