Effect of Van Hiele group guided-discovery instructional approach on student engagement in learning plane geometry
##plugins.themes.bootstrap3.article.sidebar##
##plugins.themes.bootstrap3.article.main##
Abstract
Learning geometry involves using visual manipulatives, mathematical formulas, and verbal explanations to foster critical thinking, deductive reasoning, and problem-solving skills, thereby ensuring understanding of mathematical concepts. Despite this relevance, secondary school students' limited knowledge in plane geometry, especially in concepts such as polygons and circles, creates an epistemological barrier that hinders their engagement with more advanced geometric ideas. Thus, this study investigates the effectiveness of the Van Hiele Group Guided-Discovery Instructional Approach (VHGGDIA) on student engagement in learning plane geometry, employing a mixed-methods research approach with a Convergent Parallel design. It uses a quasi-experimental, non-equivalent control-group pre-posttest design. Two comparable secondary schools from a total of 11 schools were purposively selected and randomly assigned to the experimental and control groups. Honesty, independence, perseverance, attention, interaction, and collaboration — each of which demonstrates dedication, kindness, and teamwork — impact student engagement. The analysis incorporated data from interviews, observations, and a Likert scale questionnaire. Quantitative data analysis used descriptive statistics, independent and paired-samples tests, and ANCOVA, whereas qualitative data were assessed thematically. The study found that students using the VHGGDIA showed greater engagement in plane geometry than those taught via traditional methods. Further, the study concludes that VHGGDIA significantly enhances secondary school students' engagement in this subject.
##plugins.themes.bootstrap3.article.details##
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
The author is responsible for acquiring the permission(s) to reproduce any copyrighted figures, tables, data, or text that are being used in the submitted paper. Authors should note that text quotations of more than 250 words from a published or copyrighted work will require grant of permission from the original publisher to reprint. The written permission letter(s) must be submitted together with the manuscript.References
Abla, C., & Fraumeni, B. R. (2019). Student engagement: Evidence-based strategies to boost academic and social-emotional results. McREL International.
Achera, L. J., Belecina, R. R., & Garvida, M. D. (2015). The effect of group guided discovery approach on theperformance of students in geometry. International Journal of Multidisciplinary Research and Modern Education (IJMRME), 1(2), 331–342.
Adams, M., & Enu, J. (2023). Impact of activity-based instruction on grade 11 learners' achievement in plane geometry. African Journal of Educational Studies in Mathematics and Sciences, 19(1), 19–28.
Adler, J., & Sfard, A. (2016). Research for educational change: Transforming researchers' insights into improvement in mathematics teaching and learning. Routledge.
Akintade, C. A., Ogunrinade, S. O., & Awe, I. A. (2024). Effectiveness of geometrical instructional teaching strategy on junior secondary school students' achievement, gender and attitude in plane geometry in odeda local government, Ogun state, Nigeria. International Journal of Science and Research Archive, 11(2), 1306–1315. https://doi.org/10.30574/ijsra.2024.11.2.0485
Alex, J. K., & Mammen, K. J. (2016). Lessons learnt from employing Van Hiele theory based instruction in senior secondary school geometry classrooms. Eurasia Journal of Mathematics, Science and Technology Education, 12(8), 2223–2236. https://doi.org/10.12973/eurasia.2016.1228a
Alrajeh, T. S., & Shindel, B. W. (2020). Student engagment and math teachers support. Journal on Mathematics Education, 11(2), 167–180. https://doi.org/10.22342/jme.11.2.10282.167-180
Alwahaibi, I. S. H., Al-Hadabi, D. A. M., & Al-Kharousi, H. A. T. (2020). Cohen's criteria for interpreting practical significance indicators: A critical study. Cypriot Journal of Educational Sciences, 15(2), 246–258. https://doi.org/10.18844/cjes.v15i2.4624
Balım, A. G. (2009). The effects of discovery learning on students' success and inquiry learning skills. Eurasian Journal of Educational Research (EJER)(35), 1–20.
Bear, G. G., Harris, A., Saraiva de Macedo Lisboa, C., & Holst, B. (2019). Perceptions of engagement and school climate: Differences between once-retained and multiple-retained students in Brazil. International Journal of School & Educational Psychology, 7(1), 18–27. https://doi.org/10.1080/21683603.2017.1376725
Belay, S., Atnafu, M., Michael, K., & Ermias, M. A. (2016). Strategic policy for national science, technology and mathematics education. Japan International Cooperation Agency (JICA).
Bizimana, E. (2025). Student engagement in learning: Exploring the role of perceived student cohesiveness, equity, teacher support, and teacher autonomy support under the framework of self-determination theory. International Journal of Changes in Education, 3(1), 49–60. https://doi.org/10.47852/bonviewIJCE52024500
Brezavšček, A., Jerebic, J., Rus, G., & Žnidaršič, A. (2020). Factors influencing mathematics achievement of university students of social sciences. Mathematics, 8(12), 2134. https://doi.org/10.3390/math8122134
Bruner, J. S. (1961). The act of discovery. Harvard educational review.
Çelik, H. C. (2018). The effects of activity based learning on sixth grade students’ achievement and attitudes towards mathematics activities. Eurasia Journal of Mathematics, Science and Technology Education, 14(5), 1963–1977. https://doi.org/10.29333/ejmste/85807
Cesnaviciene, J., Buksnyte-Marmiene, L., & Brandisauskiene, A. (2022). The importance of teacher support and equity in student engagement and achievement in low SES school contexts. The New Educational Review, 69(3), 157–169. https://doi.org/10.15804/tner.2022.69.3.12
Chianson, M. M., Kurumeh, M. S., & Obida, J. A. (2011). Effect of cooperative learning strategy on students' retention in circle geometry in secondary schools in Benue State, Nigeria. American Journal of Scientific and Industrial Research, 2(1), 33–36. https://doi.org/10.5251/ajsir.2011.2.1.33.36
Connolly, S. (2010). The impact of Van Hiele-based geometry instruction on student understanding. Mathematical and Computing Sciences Masters.
Creswell, J. W., & Creswell, J. D. (2018). Mixed methods procedures. Research Defign: Qualitative, Quantitative, and Mixed Methods Approaches, 31(3), 75–77.
Dorra, B. T. (2021). Exploring the challenges of teaching similarity of triangles, the case of Areka town primary schools, Ethiopia. University of South Africa. https://ir.unisa.ac.za/handle/10500/28479
Emanet, E. A., & Kezer, F. (2021). The effects of student-centered teaching methods used in mathematics courses on mathematics achievement, attitude, and anxiety: A meta-analysis study. Participatory Educational Research, 8(2), 240–259. https://doi.org/10.17275/per.21.38.8.2
Fabiyi, T. R. (2017). Geometry concepts in mathematics perceived difficult to learn by senior secondary school students in Ekiti State, Nigeria. IOSR Journal of Research & Method in Education (IOSR-JRME), 7(1), 83–90. https://doi.org/10.9790/7388-0701018390
Festus, A. B. (2013). Activity-based learning strategies in the mathematics classrooms. Journal of Education and Practice, 4(13), 8–14.
Fredricks, J. A., Blumenfeld, P. C., & Paris, A. H. (2004). School engagement: Potential of the concept, state of the evidence. Review of Educational Research, 74(1), 59–109. https://doi.org/10.3102/00346543074001059
Fredricks, J. A., Wang, M.-T., Linn, J. S., Hofkens, T. L., Sung, H., Parr, A., & Allerton, J. (2016). Using qualitative methods to develop a survey measure of math and science engagement. Learning and Instruction, 43, 5–15. https://doi.org/10.1016/j.learninstruc.2016.01.009
Garner, B. (2015). Impact of student-centered learning in mathematics. Doctoral dissertation, Wittenberg University.
Goodwin, B., & Hubbell, E. R. (2013). The 12 touchstones of good teaching: A checklist for staying focused every day. ASCD.
Gravetter, F. J., & Wallnau, L. B. (2017). Statistics for the behavioral sciences. Cengage Learning.
Hidayati, N. A., Fahmi, S., & Farida, K. (2019). The comparative of mathematics learning using guided discovery method and expository method to mathematics learning outcomes. Journal of Physics: Conference Series, 1321(3), 032103. https://doi.org/10.1088/1742-6596/1321/3/032103
Jablonski, S., & Ludwig, M. (2023). Teaching and learning of geometry—A literature review on current developments in theory and practice. Education Sciences, 13(7), 682. https://doi.org/10.3390/educsci13070682
Jansen, A. (2020). Engagement with mathematics. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 273–276). Springer International Publishing. https://doi.org/10.1007/978-3-030-15789-0_100040
Juman, Z. A. M. S., Mathavan, M., Ambegedara, A. S., & Udagedara, I. G. K. (2022). Difficulties in learning geometry component in mathematics and active-based learning methods to overcome the difficulties. Shanlax International Journal of Education, 10(2), 41–58.
Kaiser, H. F. (1974). An index of factorial simplicity. Psychometrika, 39(1), 31–36. https://doi.org/10.1007/BF02291575
Kim, H.-Y. (2013). Statistical notes for clinical researchers: Understanding standard deviations and standard errors. Restorative dentistry & endodontics, 38(4), 263–265. https://doi.org/10.5395/rde.2013.38.4.263
Kocagul, M. (2024). Learning activity matters: Tips for student engagement. Participatory Educational Research, 11(1), 1–15. https://doi.org/10.17275/per.24.1.11.1
Latif, A., Bano, H., & Muhammad, N. (2025). Student engagement in classrooms: A study of cognitive and behavioral engagement across different subject areas. Journal of Applied Linguistics and TESOL (JALT), 8(3), 70–77. https://doi.org/10.63878/jalt907
Lei, H., Cui, Y., & Zhou, W. (2018). Relationships between student engagement and academic achievement: A meta-analysis. Social Behavior and Personality: an international journal, 46(3), 517–528. https://doi.org/10.2224/sbp.7054
Maamin, M., Maat, S. M., & Iksan, Z. H. (2021). The influence of student engagement on mathematical achievement among secondary school students. Mathematics, 10(1), 41. https://doi.org/10.3390/math10010041
Machisi, E., & Feza, N. N. (2021). Van Hiele theory-based instruction and grade 11 students' geometric proof competencies. Contemporary Mathematics and Science Education, 2(1), ep21007. https://doi.org/10.30935/conmaths/9682
McLeod, S. A. (2019). What does effect size tell you. Simply psychology, 10, 1–3.
Mentari, W. N., & Syarifuddin, H. (2020). Improving student engagement by mathematics learning based on contextual teaching and learning. Journal of Physics: Conference Series, 1554(1), 012003. https://doi.org/10.1088/1742-6596/1554/1/012003
Ministry of Education. (2010). Mathematics grade ten-student textbook. The Federal Democratic Republic of Ethiopia.
Ministry of Education. (2021). Education sector development programmed VI (ESDP VI) (2013 2017 E.C. 2020/21 – 2024/25 G.C.). The Federal Democratic Republic of Ethiopia.
Moenikia, M., & Zahed-Babelan, A. (2010). A study of simple and multiple relations between mathematics attitude, academic motivation and intelligence quotient with mathematics achievement. Procedia - Social and Behavioral Sciences, 2(2), 1537–1542. https://doi.org/10.1016/j.sbspro.2010.03.231
NCTM. (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics.
Ndebil, M. B., & Ali, C. A. (2024). Cooperative learning as a strategy of improving mathematics performance and attitudes. International Journal of Educational Innovation and Research, 3(1), 62–74. https://doi.org/10.31949/ijeir.v3i1.7163
Nyman, M. (2020). What do students' feel about mathematics?: Compulsory school students' emotions and motivation towards mathematics. Doctoral dissertation, Stockholms universitets förlag.
Ramdhani, M. R., Usodo, B., & Subanti, S. (2017). Discovery learning with scientific approach on geometry. Journal of Physics: Conference Series, 895(1), 012033. https://doi.org/10.1088/1742-6596/895/1/012033
Remillard, H. A. (2015). The effect of cooperative learning on middle school math students. Heritage University.
Samuels, P. (2017). Advice on exploratory factor analysis. Birmingham City University.
Santos, M. S. M. D., Sobretodo, M. L., & Hortillosa, A. D. (2022). The Van Hiele model in teaching geometry. World Journal of Vocational Education and Training, 4(1), 10–22. https://doi.org/10.18488/119.v4i1.3087
Shernoff, D. J., Kelly, S., Tonks, S. M., Anderson, B., Cavanagh, R. F., Sinha, S., & Abdi, B. (2016). Student engagement as a function of environmental complexity in high school classrooms. Learning and Instruction, 43, 52–60. https://doi.org/10.1016/j.learninstruc.2015.12.003
Shernoff, D. J., Ruzek, E. A., & Sinha, S. (2017). The influence of the high school classroom environment on learning as mediated by student engagement. School psychology international, 38(2), 201–218. https://doi.org/10.1177/0143034316666413
Shih, S.-S. (2021). Factors related to Taiwanese adolescents’ academic engagement and achievement goal orientations. The Journal of Educational Research, 114(1), 1–12. https://doi.org/10.1080/00220671.2020.1861584
Shimizu, Y. (2025). Learning engagement as moderator between self-efficacy, math anxiety, use of diagrams, and complex plane problem-solving. Eurasia Journal of Mathematics, Science and Technology Education, 21(2), em2586. https://doi.org/10.29333/ejmste/15956
Shrestha, N. (2021). Factor analysis as a tool for survey analysis. American Journal of Applied Mathematics and Statistics, 9(1), 4–11. https://doi.org/10.12691/ajams-9-1-2
Singh, N. A., & Kumar, N. (2022). Geometry and its uses in day to day life. International Research Journal of Modernization in Engineering Technology and Science, 4(5), 2703–2709.
Siregar, N. C., Rosli, R., & Maat, S. M. (2020). The effects of a discovery learning module on geometry for improving students' mathematical reasoning skills, communication and self-confidence. International Journal of Learning, Teaching and Educational Research, 19(3), 214–228. https://doi.org/10.26803/ijlter.19.3.12
Skilling, K., Bobis, J., Martin, A. J., Anderson, J., & Way, J. (2016). What secondary teachers think and do about student engagement in mathematics. Mathematics Education Research Journal, 28(4), 545–566. https://doi.org/10.1007/s13394-016-0179-x
Subagis, J. (2021). Discovery learning rise student's activeness and understanding compound figure area. Journal of Physics: Conference Series, 1957(1), 012014. https://doi.org/10.1088/1742-6596/1957/1/012014
Subban, P. K., & Round, P. (2015). Differentiated instruction at work. Reinforcing the art of classroom observation through the creation of a checklist for beginning and pre-service teachers. Australian Journal of Teacher Education, 40(5), 117–131. https://doi.org/10.14221/ajte.2015v40n5.7
Suratno, J., Tonra, W. S., & Ardiana, A. (2019). The effect of guided discovery learning on students’ mathematical communication skill. In The 2nd International Conference on Science, Mathematics, Environment, and Education, (Vol. 2194, pp. 020119). https://doi.org/10.1063/1.5139851
Tanujaya, B., Prahmana, R. C. I., & Mumu, J. (2017). Mathematics instruction, problems, challenges and opportunities: A case study in Manokwari regency, Indonesia. World Transactions on Engineering and Technology Education, 15(3), 287–291.
Trowler, V. (2010). Student engagement literature review. The Higher Education Academy.
Ugwoke, E. O., Olulowo, T. G., & Adedayo, I. O. (2020). Using guided discovery to improve students’ retention and academic attitudes to financial accounting concepts. Education Research International, 6690082. https://doi.org/10.1155/2020/6690082
van Hiele, P. M. (1986). Structure and insight: A theory of mathematics education. Academic Press.
Vojkuvkova, I. (2012). The van Hiele model of geometric thinking. In WDS’12 Proceedings of Contributed Papers, Prague (pp. 72–75).
Wang, M.-T., Fredricks, J. A., Ye, F., Hofkens, T. L., & Linn, J. S. (2016). The math and science engagement scales: Scale development, validation, and psychometric properties. Learning and Instruction, 43, 16–26. https://doi.org/10.1016/j.learninstruc.2016.01.008
Wang, Y., & Tambi, F. B. (2024). Correlation between students perceived parental expectations and students academic engagement: The intermediary effect of academic self-efficacy. Journal of Pedagogical Research, 8(3), 16–33. https://doi.org/10.33902/jpr.202427683
White, H., & Sabarwal, S. (2014). Quasi-experimental design and methods. Methodological Briefs: Impact Evaluation 8, 8, 1–16.
Zakaria, Z. (2010). The effects of cooperative learning on students' mathematics achievement and attitude towards mathematics. Journal of Social Sciences, 6(2), 272–275. https://doi.org/10.3844/jssp.2010.272.275
Zhang, D. (2017). Effects of visual working memory training and direct instruction on geometry problem solving in students with geometry difficulties. Learning Disabilities: A Contemporary Journal, 15(1), 117–138.