Enhancing South African Mathematics Teachers’ Big Ideas Knowledge and Self-Directed Learning: A blended Learning Professional Development Intervention
Keywords:
self-directed learning; mathematics big ideas; mathematics-teacher professional development; blended-learning interventionAbstract
The South African school mathematics curricula does not emphasize the big ideas, these are only briefly mentioned and there is no elaboration on the benefits of teaching according to the big ideas. Additionally, professional development for school teachers in South Africa does not focus on teaching according to the big ideas in mathematics. Hence, the principal intention of this research was to ascertain how to enhance mathematics teachers’ self-directed learning, by developing knowledge of big ideas in mathematics. Within a blended learning professional development programme, the study conceptualizes teachers’ engagement with the big ideas in mathematics, utilizing self-directed learning as the guiding framework. This basic qualitative empirical study purposively selected all the Senior Phase and Further Education and Training mathematics teachers at a school (n = 5). Data was generated from an initial and concluding focus-group interview and activity submissions from a blended learning professional development programme. The study’s findings suggested it was effective in developing the participants’ self-directed learning characteristics, collaboration, lifelong learning and increased motivation. Simultaneously, the acquisition of big ideas knowledge resulted in improved curriculum continuity, initiated teachers to relook at the way that they teach mathematics to promote a more coherent and integrated learning experience, highlighted the real-world relevance and encouraged them to self-direct their learning in the future. Consequently, this study has the potential to close the identified gap in literature and to form the basis for designing and creating in-service professional development programmes and possibly even pre-service training programmes for mathematics teachers in the future.
https://doi.org/10.26803/ijlter.25.2.25
References
Abdullah, M.H. (2001, December). Self-directed learning. ERIC Digest, 169. https://eric.ed.gov/?id=ED459458
Admiraal, W., Kruiter, J., Lockhorst, D., Schenke, W., Sligte, H., Smit, B., Tigelaar, D., & de Wit, W. (2016). Affordances of teacher professional learning in secondary schools. Studies in Continuing Education, 3(38), 281-298. https://doi.org/10.1080/0158037X.2015.1114469
Askew, M. (2013). Big Ideas in primary mathematics: Issues and directions. Perspectives in Education, 31(3), 5-18. https://doi.org/10.38140/pie.v31i3.1814
Bayar, A. (2014). The components of effective professional development activities in terms of teachers' perspective. International Online Journal of Educational Sciences, 6(2), 319-327. http://dx.doi.org/10.15345/iojes.2014.02.006
Bishara, S. (2021). The cultivation of self-directed learning in teaching mathematics. World Journal on Educational Technology: Current Issues, 13(1), 82-95. https://doi.org/10.18844/wjet.v13i1.5401
Bosch, C. (2017). Promoting self-directed learning through the implementation of cooperative learning in a higher education blended learning environment. [Doctoral dissertation, North West University]. Faculty of Education: North-West University. http://hdl.handle.net/10394/26102
Bosch, C., Mentz, E., & Goede, R. (2019). Self-directed learning: A conceptual overview. In E. Mentz, J. de Beer, & R. Bailey (Eds.), Self-directed learning for the 21st century: Implications for higher education (pp. 1-36). AOSIS. https://doi.org/10.4102/aosis.2019.BK134.01?authuser=0
Brandt, W. C. (2020). Measuring student success skills: A review of the literature on self-
direction. National Center for the Improvement of Educational Assessment. https://files.eric.ed.gov/fulltext/ED607782.pdf
Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3, 77-101. http://dx.doi.org/10.1191/1478088706qp063oa
Busetto, L., Wick, W., & Gumbinger, C. (2020). How to use and assess qualitative research methods. Neurological Research and Practice, 2(14), 1-10. https://doi.org/10.1186/s42466-020-00059-z
Charles, R.I. (2005). Big ideas and understandings as the foundation for elementary and
middle school mathematics. Journal of Mathematics Education, 7(3), 9-24. https://jaymctighe.com/wp-content/uploads/2011/04/MATH-Big-Ideas_NCSM_Spr05v73p9-24.pdf
Cheng, S-F. Kuo, C-L., Lin, K-C., & Lee-Hsieh, J. (2010). Development and preliminary testing of a self-rating instrument to measure self-directed learning ability of nursing students. International Journal of Nursing Studies, 47, 1152-8. https://doi.org/10.1016/j.ijnurstu.2010.02.002
Ciuk, S., & Latusek, D. (2018). Ethics in qualitative research. In M. Ciesielska, & D. Jemielniak (Eds.), Qualitative Methodologies in Organization Studies (pp.195-213). Palgrave Macmillan. https://doi.org/10.1007/978-3-319-65217-7_11
Creswell, J. W. (2009). Research design: Qualitative, quantitative, and mixed methods
approaches (3rd ed.). SAGE Publications.
Dall, N. (2022, December 15). Complex equation of maths education in South Africa. The UNESCO Courier.https://courier.unesco.org/en/articles/complex-equation-maths-education-south-africa
DeJonckheere, M., & Vaughn, L.M. (2019). Semistructured interviewing in primary care
research: A balance of relationship and rigour. Family Medical Community Health, 7, Article e000057. http://dx.doi.org/10.1136/fmch2018-000057
Department of Basic Education (South Africa). (2011). Curriculum and assessment policy statement, Grades 10-12, Mathematics. Government Printing Works.
Department of Basic Education (South Africa). (2018). Mathematics teaching and learning framework for South Africa. Teaching mathematics for understanding. Government Printing Works.
Dhaliwal, M.K. (2015). Teachers becoming lifelong learners. The Business & Management Review, 5(4), 259-264.https://cberuk.com/cdn/conference_proceedings/2015iciee_india46.pdf
Fadillah, A., Nopitasari, D., & Pradja, B. (2020). Blended learning model during the COVID-19 pandemic: Analysis of student’s' mathematical disposition. JTAM (Jurnal Teori dan Aplikasi Matematika), 4(2), 173-181. https://doi.org/10.31764/jtam.v4i2.2582
Fleming, J., & Zegwaard, K.E. (2018). Methodologies, methods and ethical considerations for conducting research in work-integrated learning. International Journal of Work-Integrated Learning - Special Issue, 19(3), 205-213. https://files.eric.ed.gov/fulltext/EJ1196755.pdf
Francom, G.M. (2010). Teach me how to learn: Principles for fostering students’ self-directed learning skills. International Journal of Self-Directed Learning, 7(1), 29-44. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.469.3531&rep=rep1&type=pdf#page=34
Friese, S. (2022). ATLAS.ti 22 User Manual. ATLAS.ti Scientific Software Deveolpment
GmbH. https://doc.atlasti.com/ManualWin.v22/ATLAS.ti_ManualWin.v22.pdf
Garrison, D.R. (1997). Self-directed learning: Toward a comprehensive model. Adult Education Quarterly, 48(1), 18-33. https://doi.org/10.1177/074171369704800103
Gencel, I. E., & Saracaloglu, A. S. (2018). The effect of layered curriculum on reflective thinking and on self-directed learning readiness of prospective teachers. International Journal of Progressive Education, 14(1), 8-20. https://doi.org/10.29329/ijpe.2018.129.2
Gibbs, A. (1997). Focus groups. Social Research Update, 19(8), 1-8. https://openlab.citytech.cuny.edu/hermacdonaldsbs2000fall2015b/files/201106/Focus-Groups_Anita-Gibbs.pdf
Guest, G., Namey. E., & Chen, M. (2020). A simple method to assess and report thematic saturation in qualitative research. PLOS One, 15(5), Article e0232076. https://doi.org/10.1371/journal.pone.0232076
Hood, S. (2022). The impact of blended professional development on teacher efficacy and practice (Doctoral dissertation, St. John’s University, New York). Retrieved from https://scholar.stjohns.edu/cgi/viewcontent.cgi?article=1423&context=theses_dissertations
Independent Examinations Board. (2022). 27. Mathematics 2022 (Updated Jan 2021).pdf. https://www.ieb.co.za/documents/3795047f-1d2d-4a2b-8a44-4e2c17f5e4a5
Jnanathapaswi, S. (2021). Thematic analysis and coding: an overview of the qualitative paradigm. An Introduction to Social Science Research. http://dx.doi.org/10.6084/m9.figshare.17159249
Johnson, D.W., & Johnson, R.T. (2019). The impact of cooperative learning on self- directed learning. In E. Mentz, J. De Beer, & R. Bailey (Eds.), Self-Directed Learning for the 21st Century: Implications for Higher Education (pp. 37–66). AOSIS.
https://doi.org/10.4102/aosis.2019.BK134.02
Kahlke, R.M. (2014). Generic qualitative approaches: Pitfalls and benefits of methodology mixology. International Journal if Qualitative Methods, 13, 37-52. https://doi.org/10.1177/160940691401300119
Kivunja, C., & Kuyini, A.B. (2017). Understanding and applying research paradigms in educational contexts. International Journal of Higher Education, 6(5), 26- 41.https://doi.org/10.5430/ijhe.v6n5p26
Knowles, M. S. (1975). Self-directed learning: A guide for learners and teachers. The Adult Education Company.
Lee, H., & Mori, C. (2021). Reflective practices and self-directed learning competencies in
second language university classes. Asia Pacific Journal of Education, 41(1), 130-151. https://doi.org/10.1080/02188791.2020.1772196
Loeng, S. (2020). Self-Directed Learning: A Core Concept in Adult Education. Education
Research International, 1, Article 3816132. https://doi.org/10.1155/2020/3816132
Luneta, K. (2024). Revisiting the shortage of effective Mathematics teachers in Southern Africa. African Journal of Teacher Education and Development, 3(1), a86. https://doi.org/10.4102/ajoted.v3i1.86
Mack, L. (2010). The philosophical underpinnings of educational research. Polyglossia, 19. http://en.apu.ac.jp/rcaps/uploads/fckeditor/publications/polyglossia/Polyglossia_V19 _Lindsay.pdf
Mahlaba, S.C. (2020). The state of South African mathematics education: situating the hidden promise of multiple-solution tasks. EURASIA Journal of Mathematics, Science and Technology Education, 16(12), Article em1921. https://doi.org/10.29333/ejmste/9279
Mapungubwe Institute for Strategic Reflection. (2022). Recommendations on the pedagogy of mathematics in South Africa. https://www.mistra.org.za/wp-content/uploads/2022/04/Recommendations-on-the-pedagogy-of-mathematics-in-South-Africa-FINAL.pdf
McMullin, C. (2023). Transcription and qualitative methods: implications for third sector research. Voluntas, International Society for Third-Sector Research, 34, 140–153.https://doi.org/10.1007/s11266-021-00400-3
Merriam, S.B., & Tisdell, E.J. 2016. Qualitative research: a guide to design and Implementation (4th ed.). Jossey-Bass.
Mitchell, I., Keast, S., Panizzon, D., & Mitchell, J. (2016). Using big ideas to enhance teaching and student learning. Teachers and Teaching: Theory and Practice, 23(5), 1-15. https://doi.org/10.1080/13540602.2016.1218328
Mulaudzi, L. V., & Mosia, M. (2025). Exploring continuing professional teacher development for mathematics teachers in South Africa: Needs, providers, and implications for skills planning. International Journal of Learning, Teaching and Educational Research, 24(11), 161–184. https://ijlter.net/index.php/ijlter/article/view/2579
Nieuwenhuis, J. 2019a. Qualitative research designs and data-gathering techniques. In
K. Maree (Ed.), First steps in research (3rd ed.) (pp. 80-117). Van Schaik Publishers.
Nieuwenhuis, J. 2019b. Analysing qualitative data. In K. Maree (Ed.), First steps in research (3rd ed.) (pp.118-155). Van Schaik Publishers.
Nowell, L. S., Norris, J. M., White, D. E., & Moules, N. J. (2017). Thematic analysis: striving to meet the trustworthiness criteria. International Journal of Qualitative Methods, 16(1). https://doi.org/10.1177/1609406917733847
Nurnberger-Haag, J., Courtney, S.A., & Plaster, K.B. (2024). Big ideas of mathematics: A construct in need of a teacher-, student-, and family-friendly framework. Electronic Journal for Research in Science and Mathematics Education, 28(1), 1-31. https://ejrsme.icrsme.com/article/view/23428
Olivier, W. (2016). Reflection on the status of structured in-service training programme for in-service secondary school mathematics teachers in South Africa. (Advisory Committee on Mathematics report). http://www.samf.ac.za/Content/Files/Documents/In_service_Training_Secondary_School_Mathematics.pdf
Oswald, D.F. (2003). Instructional-design theory for fostering self-directed learning
[Doctoral dissertation, Indiana University]. https://www.learntechlib.org/p/126750/
Robinson, J.D., & Persky, A.M. (2020). Developing self-directed learners. American
Journal of Pharmaceutical Education, 84(3), 292-296.
https://doi.org/10.5688/ajpe847512
Rosli, R. & Aliwee, M. F. (2021). Professional development of mathematics teacher: a systematic literature review. Contemporary Educational Research Journal, 11(2):81-92. https://doi.org/10.18844/cerj.v11i2.5415
Sebatana, M.J., & Dudu, W.T. (2021). Exploring collaboration as a 21st-century skill to
enhance self-directed learning while teaching particulate nature of matter through
problem-based learning. In E. Mentz, D. Laubscher, & J. Olivier (Eds.), Self-
Directed Learning: An imperative for education in a complex society (pp. 193–210 ).
North-West University Self-Directed Learning Series Volume 6. AOSIS.
https://doi.org/10.4102/aosis.2021.BK279.08
Sebotsa, T., De Beer, J., & Kriek, J. (2021). Self-directed learning: A sine qua non in in-
service teacher education. In E. Mentz, D. Laubscher, & J. Olivier (Eds.), Self-
Directed Learning: An imperative for education in a complex society (pp. 165–192).
North-West University Self-Directed Learning Series Volume 6. AOSIS.
https://doi.org/10.4102/aosis.2021.BK279.07
Siemon, D. (2022). Teaching with the big ideas in mathematics. DET (Department of
Education and Training). https://www.education.vic.gov.au/Documents/school/teachers/teachingresources/discipline/maths/teaching-with-the-big-ideas-in-mathematics.pdf
Sim, J., & Waterfield, J. (2019). Focus group methodology: some ethical challenges. Quality and Quanity, 53, 3003–3022. https://doi.org/10.1007/s11135-019-00914-5
Song, B. K. (2021). E-portfolio implementation: examining learners’ perception of usefulness, self-directed learning process and value of learning. Australasian Journal of Educational Technology, 37(1),68-81. https://doi.org/10.14742/ajet.6126
Sriarunrasme, J., Techataweewan, W., & Mebusaya, R.P. (2015). Blended learning supporting self-directed learning and communication skills of Srinakharinwirot University’s first year students. Journal Social and Behaviour Science, 197, 1564-1569. https://doi.org/10.1016/j.sbspro.2015.07.111
Staker, H., & Horn, M.B. (2012). Classifying K-12 Blended Learning. Innosight Institute. http://www.christenseninstitute.org/wpcontent/uploads/2013/04/Classifying-K-12blended-learning.pdf
Steen, L.A. (Ed.). (1990). On the shoulders of giants: new approaches to numeracy. National Research Council. The National Academies Press. https://doi.org/10.17226/1532
Taylor, P.C., & Medina, M.N.D. (2013). Educational research paradigms: From positivism to multiparadigmatic. Journal for Meaning Centered Education, 1. http://www.meaningcentered.org/journal/volume-01/educational-research-paradigms-from-positivism-tomultiparadigmatic/
Theron, H. (2025). Global trends in contributing factors to mathematics performance in
secondary schools: lessons for South Africa 2015–2024. International Journal of Learning, Teaching and Educational Research, 24(1), 278-297. https://doi.org/10.26803/ijlter.24.1.14
Thornton, K. (2010). Sharing reflections: enhancing learners’ experiences of self-directed learning. In A.M. Stoke (Ed.), Proceedings of the 35th Japan Association Language Teaching Annual International Conference (pp. 417 – 426). Japan Association forLanguage Teaching. https://jalt-publications.org/archive/proceedings/2009/E116.pdf
Tout, D., & Spithill, J. (2015). Big ideas in mathematics teaching. The Research Digest, 11. https://www.researchgate.net/publication/305181401_Big_Ideas_in_Mathematics_Teaching
Uz, R., & Uzun, A. (2018). The influence of blended learning environment on self-regulated and self-directed learning skills of learners. European Journal of Educational Research, 7(4), 877-886. https://doi.org/10.12973/eu-jer.7.4.877
Wang, X., Niu, J., Fang, B., Han, G., & He, J. (2025). Empowering teachers' professional development with LLMs: An empirical study of developing teachers' competency for instructional design in blended learning. Teaching and Teacher Education, 165,
https://doi.org/10.1016/j.tate.2025.105091.
Williams, M., & Moser, T. (2019). The art of coding and thematic exploration in qualitative research. International Management Review, 15(1),45-55. http://www.imrjournal.org/uploads/1/4/2/8/14286482/imr-v15n1art4.pdf
Wittmann, G., & Olivier, J. (2019). Professional development in fostering self-directed learning in german second additional language teachers. Per Linguam, 35(3),125-142. http://dx.doi.org/10.5785/35-3-870
Zambo, R., & Zambo, D. (2008). The impact of professional development in mathematics on teachers’ individual and collective efficacy: The stigma of underperforming. Teacher Education Quarterly, 35(1),159-168. http://www.jstor.org/stable/23479036
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Dorothy Laubscher, Lara-Ann Koch, Gordon Sekano
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
All articles published by IJLTER are licensed under a Creative Commons Attribution Non-Commercial No-Derivatives 4.0 International License (CCBY-NC-ND4.0).
