Department of Mathematics Education

Prof F Machaba

College of Education
School of Teacher Education
Department: Mathematics Education
Professor
Tel: 012 429 8582
E-mail: emachamf@unisa.ac.za

Expertise

  • Learners misconceptions
  • Teaching and learning of Mathematical Literacy alongside Maths
  • Usage of everyday context in the teaching and learning of Maths

Qualifications

  • Doctoral degree in Mathematics Education - Tshwane University of Technology (TUT), 2014 
  • Master’s degree in Education from Tshwane University of Technology, 2003
  • B. Tech  in Educational Management, Tshwane University of Technology, 1999
  • B. Tech in Natural Science (Mathematics & Physics) also from TUT, 2000
  • BSc (Hons) (Mathematics Education) from Wits University, 2005

NRF Rating

C2

Currently teaching

  • PDM4803: Postgraduate Diploma in Mathematics
  • PDM4804: Postgraduate Diploma in Mathematics

Fields of academic interests

Research interest:

  • The integration of mathematics and everyday context
  • Relationship between Mathematics and Mathematical Literacy
  • Misconceptions in Mathematics

Field of Specialisation

Mathematics Education

Books

BOOK CHAPTERS:

  • Machaba, F., & Bedada, T. (2022).  Mathematics Educators’ Readiness for Online Education in the Fourth Industrial Revolution: A Case of Two Selected Universities in Ethiopia. In Education in Africa: The Fourth Industrial Revolution. (Pp 57 -76) Springer, Cham https://doi.org/10.1007/978-3-031-13927-7
  • Hlamulo Wiseman Mbhiza, Motshidisi Masilo, Zingiswa Jojo, and France Machaba (2022).   Emerging Realities from COVID-19 and the Fourth Industrial Revolution: Mathematics Education Lecturers’ Collaborative Autoethnographic Experiences In Education in Africa: The Fourth Industrial Revolution. (Pp 159 -179) Springer, Cham https://doi.org/10.1007/978-3-031-13927-7
  • Mbane, P. M., & Machaba, F. (2021). Roles of School Management Teams in Curriculum Delivery and Assessment in Primary Schools. In Investigating the Roles of School Management Teams in Curriculum Delivery (pp. 33-51). IGI Global. DOI: 10.4018/978-1-7998-7168-2.ch003
  • Machaba, F., & Dhlamini, J. (2021). Ethnomathematics as a Fundamental Teaching Approach. In Mathematics Teaching and Professional Learning in sub-Sahara Africa (pp. 59-76). Springer, Cham. https://doi.org/10.1007/978-3-030-82723-6_5#DOI

Journal articles

  • Machaba, F., & Mangwiro, C. (2024). Teacher Follow-up on Learners’ Initial Response to Teacher Questions. African Journal of Research in Mathematics, Science and Technology Education, 1-14. https://doi.org/10.1080/18117295.2023.2297127
  • Belay, A. M., Machaba, F., & Makgakga, T. P. (2024). Introducing a Supportive Framework to Address Students’ Misconceptions and Difficulties in the Learning Mathematical Proof Techniques: A Case of Debark University in Ethiopia. Research in Social Sciences and Technology, 9(1), 63-84. https://doi.org/10.46303/ressat.2024.4
  • Jameson, G., Machaba, M. F., & Matabane, M. E. (2023). An Exploration of Grade 12 Learners’ Misconceptions on Solving Calculus Problem: A Case of Limits. Research in Social Sciences and Technology, 8(4), 94-124. https://doi.org/10.46303/ressat.2023.34
  • Age, T. J., & Machaba, M. F. (2023). Effect of mathematical software on senior secondary school students’ achievement in geometry. EUREKA: Social and Humanities, (5), 82-93. https://doi.org/10.21303/2504-5571.2023.003151
  • Matabane, M. E., & Machaba, F. M. (2023). First Year University Students use of Words, Symbols and Images to Convey Mathematical Ideas: A Case of Definitions. Research in Social Sciences and Technology, 8(1), 92-105. https://doi.org/10.46303/ressat.2023.16
  • Mangwiro, C., & Machaba, F. (2022). Teacher Questioning Techniques to Elicit Learners’ Mathematical Thinking. The International Journal of Science, Mathematics and Technology Learning, 30 (1), 51-66. https://doi.org/10.18848/2327-7971/CGP/v30i01/51-66.
  • Bekene Bedada, T., & Machaba, M. F. (2022d). The development of the cycle model and its effect on mathematics learning using GeoGebra mathematical software. Education Inquiry, 1-24. https://doi.org/10.1080/20004508.2022.2137260
  • Bekene Bedada, T., & Machaba, M. F. (2022). The effect of GeoGebra on students’ abilities to study calculus. Education Research International, 2022. https://doi.org/10.1155/2022/4400024
  • Bedada, T. B., & Machaba, M. F. (2022). Investigation of student’s perception learning calculus with GeoGebra and cycle model. EURASIA Journal of Mathematics, Science and Technology Education, 18(10), em2164. https://doi.org/10.29333/ejmste/12443
  • Tola Bekene Bedada & France Machaba | (2022) The effect of GeoGebra on STEM students learning trigonometric functions, Cogent Education, 9:1, 2034240, https://doi.org/10.1080/2331186X.2022.2034240
  • Machaba, F., & Bedada, T. (2022). University lecturers’ preparedness to use technology in teacher training of mathematics during COVID-19: The case of Ethiopia. South African Journal of Higher Education, 36(1), 171-192. https://doi.org/10.20853/36-3-4560
  • Moyo, M., & Machaba, F. M. (2021). Grade 9 learners’ understanding of fraction concepts: Equality of fractions, numerator, and denominator. Pythagoras, 42(1), 13. https://doi.org/10.4102/pythagoras.v42i1.602
  • Moloto, M., & Machaba, F. (2021). Grade 6 teachers’ s mathematical Knowledge for teaching: The concept of fractions. Journal for the Education of Gifted Young Scientists, 9(4), 283-297. https://doi.org/10.17478/jegys.1000495
  • Sipholi, K., & Machaba, F. M. (2021). Co-operative learning as a tool in the teaching and learning of linear programming: A case of national curriculum vocational (NC (V)) level 3 multilingual students. South African Journal of Higher Education, 35(2), 246-264.  https://dx.doi.org/10.20853/35-2-4007
  • Modzuka, C., Long, C., & Machaba, F. (2019). Rasch Analysis of South Africa’s Grade 6 Annual National Assessment. African Journal of Research in Mathematics, Science and Technology Education, 23(1), 86-99.
  • Malatjie, F., & Machaba, F. (2019). Exploring Mathematics Learners’ Conceptual Understanding of Coordinates and Transformation Geometry through Concept Mapping. EURASIA Journal of Mathematics, Science and Technology Education, 15, 12.
  • Machaba, F., & Du Plooy, M. (2019). Mathematics and Mathematical Literacy on the Career Podium–Sharing Gold?. African Journal of Research in Mathematics, Science and Technology Education, 1-13
  • Machaba, F. M. (2018). Pedagogical Demands in Mathematics and Mathematical Literacy: A Case of Mathematics and Mathematical Literacy Teachers and Facilitators. Eurasia Journal of Mathematics, Science and Technology Education, 14(1), 95-108. ISSN(1305-8215)*
  • Machaba F. & Mwakapenda, W. (2017). Implications on differences and similarities of mathematics and mathematical literacy. International Journal of Educational Sciences (IJES) ISSN: 0975-1122
  • Machaba, F. (2016). The concepts of area and perimeter: Insights and misconceptions of Grade 10 Learners. Pythagoras, 37(1), 1-11  a304. http://dx.doi. org/10.4102/Pythagoras. v37i1.304 – ISSN : 2223-7895*
  • Machaba F& Mwakapenda W 2016c. Learners’ approaches to solving a mathematical task: does specialisation matter? Africa Education Review: 13 3-4, 172-190: 172–190. ISSN: 1814-6627 *

Paper presentations

Peer reviewed conference papers

  • Moloto, M., Machaba, F., & Matabane, M (2023). Working with grade 6 learners ‘thinking in comparing fractions: the case of a behaviorist and constructivist teacher. In Duncan Mhakure & Connie Skelton (Eds). Proceedings of the 28th Annual National Congress of the Association for Mathematics Education of South Africa (AMESA), Mathematics for Hope: building connections in mathematics teaching and learning 26 – 30 June 2023 ISBN: 978-0-6397-8397-0
  • Moyo, M., Machaba, F., & Matabane, M. (2023) Grade 9 learners ‘misconceptions when comparing and ordering fractions.In Duncan Mhakure & Connie Skelton (Eds). Proceedings of the 28th Annual National Congress of the Association for Mathematics Education of South Africa (AMESA), Mathematics for Hope: building connections in mathematics teaching and learning 26 – 30 June 2023 ISBN: 978-0-6397-8397-0
  • Mokotedi L., Machaba, (2022). The Use of Mathematics in the Real World with Specific Reference to Numbers: A Case of Grade 8 Learners. In: Mosiane. T; L. Mokotedi; D Laubscher and Sfiso Mahlaba (Eds) Proceedings of the 27th Annual National Congress of the Association for Mathematics Education of South Africa, Digging Deeper: Teaching Mathematics for understanding in and beyond classroom, University of South Africa, 27 June – 01 July 202 ISBN: 978-0-6397-0883-6
  • Moyo M and Machaba (2022). Grade 9 Learners Understanding of The Concepts of Addition and Subtraction of Fractions: In Mosiane. T; L. Mokotedi; D Laubscher and Sfiso Mahlaba (Eds) Proceedings of the 27th Annual National Congress of the Association for Mathematics Education of South Africa, Digging Deeper: Teaching Mathematics for understanding in and beyond classroom, University of South Africa, 27 June – 01 July 202 ISBN: 978-0-6397-0883-6
  • Banjo B., Machaba (2022). Teachers’ Knowledge of Instructional Strategies When Teaching Quadratic Functions in Grade 10: In Mosiane. T; L. Mokotedi; D Laubscher and Sfiso Mahlaba (Eds) Proceedings of the 27th Annual National Congress of the Association for Mathematics Education of South Africa, Digging Deeper: Teaching Mathematics for understanding in and beyond classroom, University of South Africa, 27 June – 01 July 202 ISBN: 978-0-6397-0883-6
  • Sibanda, E., & Machaba, M. F. (2022). Grade 8 learners ‘misconceptions in surface area and volume relationships: In K R Langenhoven & C H Stevenson-Milln (Eds). Proceedings of the 30th Annual Conference of the Southern African Association for Research in Mathematics, Science and Technology Education. Western Cape: SAARMSTE. ISBN: 978-0-6398352-4-2
  • Banjo B., Machaba (2021). Teachers' knowledge of learners' thinking in the teaching of quadratic functions.  In : Z Jojo & M Du Plooy (Eds) Proceedings of the 26th Annual National Congress of the Association for Mathematics Education of South Africa, Developing Equitable Mathematical Teaching and Learning Practices that Empower Teachers and Learners in the 4IR Era, University of South Africa, 14th– 16th July 2021.  ISBN: 978-0-620-94779-4
  • Mokotedi L., Machaba, (2021). EXPLORING GRADE 8 LEARNERS’ CONCEPTIONS OF NUMBER IN CONTEXT: A DISCUSSION ON MATHEMATICAL DISCOURSES. In: Z Jojo & M Du Plooy (Eds) Proceedings of the 26th Annual National Congress of the Association for Mathematics Education of South Africa, Developing Equitable Mathematical Teaching and Learning Practices that Empower Teachers and Learners in the 4IR Era, University of South Africa, 14th– 16th July 2021.  ISBN: 978-0-620-94779-4
  • Malatjie and Machaba (2019) Corporative learning as a tool to develop conceptual and procedural knowledge in solving algebraic equations: a case study of grade 11 mathematics learners. In: J Kriek, A Ferreira K Padayachee, S Putten,  D Mogashana and W Raucher (Eds).  ISTE Conference on Mathematics, Science and Technology. Education: Towards effective Teaching and meaningful learning Mathematics, Science and Technology Education, Mopani Camp in Kruger National Park, University of South Africa. (pp. 149–160). 21 – 25 October 2019 ISBN 978-1-77615-062-5
  • Lisema, N & Machaba F (2019). An Exploration of Teaching Srategies of Core and Extended curricula in teaching the concept of solids: A Case of three selected schools at Mafeteng District in Lesotho. In B. Goba & J. Naidoo (Ed). Proceedings of the 25th Annual National Congress of the Association for Mathematics Education of South Africa, Reclaiming our African pride through mathematics teaching, Mpumalanga, (pp. 286- 300). Tshwane University of Technology,  01 July – 05 July  2019. ISBN: 978-0-620-71520-1Machaba, F.M. (2017). The integration of mathematics and everyday knowledge: Grade 10 mathematics and mathematical literacy learners’ solution strategies. In R. Seah, M.  Horne & C. Orellana (Eds),   Proceeding of the 54th conference of the Mathematical Association of Victoria (MAV) (pp.  103 - 108), La Trobe University, Bundoora, Australia: ISBN 978-1-876949-61-7
  • Machaba, F. (2016). A teacher and her Grade 10 Learners’ understanding about the teaching and learning of Mathematical Literacy. In B. Goba & J. Naidoo (Ed). Proceedings of the 22th Annual National Congress of the Association for Mathematics Education of South Africa, Reclaiming our African pride through mathematics teaching, Mpumalanga, (pp. 286- 300). Tshwane University of Technology, 27 June – 01 July 2016. ISBN: 978-0-620-71520-1*.
  • Machaba F 2016a.  Subject specialists’ views on the praxis of Mathematics and Mathematical Literacy in the Secondary Schools: In: S McKinney, P Gray, MA Makgopa, SK Sharma, S Pahi, D Jackson-Sillah, S Vallipuram, R Kuamr (Eds.).  Papers presented at the 2016 LSME International Conferences on Responsible Research in Education and Management and its Impact: London school of Management Education, pp. 235–262.  ISBN 978-0-9931224-2-2
  • Machaba, F; & Makgakga S.(2016). Grade 9 learner’s understanding of  the concept of equal sign. In: J Kriek, B Bantwini, C Ochonogor, J Dhlamini,  L Gooses. (Eds).  ISTE Conference on Mathematics, Science and Technology. Education: Towards effective Teaching and meaningful learning Mathematics, Science and Technology Education, Mopani Camp in Kruger National Park, University of South Africa. (pp. 149–160). 23 – 28 October 2017 ISBN 978-1-86888-907-5*
  • Machaba, F & Mphuthi, G (2016). Grade 9 learners’ conceptions of algebraic expression: A Case study of one of the schools in Mt Ayliff District. In: J Kriek, B Bantwini, C Ochonogor, J Dhlamini,L Gooses. (Eds).  ISTE Conference on Mathematics, Science and Technology. Education: Towards effective Teaching and meaningful learning Mathematics, Science and Technology Education, Mopani Camp in Kruger National Park, University of South Africa. (pp. 149–160). 23 – 28 October 2017 ISBN 978-1-86888-907-5*
  • Mphuthi, G, &  Machaba,F (2016). Grade 9 learners’ conceptions of algebraic expression: A Case study of one of the schools in Mt Ayliff District. In: J Kriek, B Bantwini, C Ochonogor, J Dhlamini,L Gooses. (Eds).  ISTE Conference on Mathematics, Science and Technology. Education: Towardeffective Teaching and meaningful learning Mathematics, Science and Technology Education, Mopani Camp in Kruger National Park, University of South Africa. (pp. 149–160). 23 – 28 October 2017 ISBN 978-1-86888-907-5*
  • Machaba, F., & Mwakapenda.W (2015). Teachers’ views on mathematics and mathematical literacy tasks. In M. Satsope, B. Chigonga & K. Masha (Eds). Proceeding of the 21th AMESA Annual conference, Limpopo, (pp. 334- 337). University of Limpopo, 29 June – 3 July 2015.: ISBN: 978-0-620-66616-9.*
  • Machaba, F., & Mwakapenda.W (2015). Teachers’ views on mathematics and mathematical literacy tasks. In M. Satsope, B. Chigonga & K. Masha (Eds). Proceeding of the 21th AMESA Annual conference, Limpopo, (pp. 334- 337). University of Limpopo, 29 June – 3 July 2015.: ISBN: 978-0-620-66616-9.*
  • Machaba, F. (2007). Learning mathematics through intergration with context that draw on learners Everyday experiences both in M and ML: a pilot study. In M. Setati, N. Chitera & A. Essien(Eds). Proceedings of the 13th Annual National Congress of the Association for Mathematics Education of South Africa, (pp. 207 – 220). White River Mpumalanga, 2 – 6 July 2007: ISBN: 978 – 0 – 62038906-8

Peer reviewed in international conference papers

  • Moyo M & Machaba MF (2022) Grade 9 learners understanding of the concepts of Multiplication and Division of fractions. Rethinking Teaching and Learning in the New Normal Proceedings of the 9th South Africa International Conference on Education: 26 – 28 October 2022 
  • Matabane M., Machaba MF., & Mwakapenda W (2022) Transition from Secondary School to University Mathematics: A Case of First-Year Students’ Experiences of Mathematical Writing: Rethinking Teaching and Learning in the New Normal Proceedings of the 9th South Africa International Conference on Education: 26 – 28 October 2022 
  • Machaba F (2016).  Subject specialists’ views on the praxis of Mathematics and Mathematical Literacy in the Secondary Schools: In: S McKinney, P Gray, MA Makgopa, SK Sharma, S Pahi, D Jackson-Sillah, S Vallipuram, R Kuamr (Eds.) Papers presented at the 2016 LSME International Conferences on Responsible Research in Education and Management and its Impact: London school of Management Education, pp. 235–262.  ISBN 978-0-9931224-2-2*
  • Machaba, F., & Mwakapenda W (2014).  Grade 11 learners’ responses to Tasks in Mathematics and Mathematical Literacy. In P. Webb, M. Grace, & L. Webb (Eds). Proceeding of the 22nd Annual Conference   of SAARMSTE, (pp. 65 – 77). Nelson Mandela Metropolitan University, Port Elizabeth, 13 – 16 January 2014. (ISBN: 978-0-9869800-8-4)*.
  • Machaba, F., & Mwakapenda, W. (2016). Facilitator’s views on the implementation of Mathematics and Mathematical Literacy. In W. Mwakapenda, T. Sedumedi & M. Makgato (Eds). Proceedings of the 24th annual conference of the Southern African Association for Research in Mathematics, Science and Technology (pp.190). Tshwane University of Technology, Arts Campus, Pretoria, South Africa, 12 January – 15 January 2016.  978-0-9922269-2-3.
  • Machaba, F., & Mwakapenda (2013).  A Textual analysis of Grade 11 learners’ responses to Tasks in Mathematics and Mathematical Literacy. In D. Nampota & M. Kazima (Eds). Proceedings of the 20th Annual conference of the SAARMSTE, (pp. 147-156). Lilongwe Malawi, 16-19 January (ISBN: 978-0-9869800-4-6)*.
  • Machaba, F., & Mwakapenda W (2012). Context in Mathematics Education: Methodologies, Parallels and Intra-Perspective. In T. Mamiala & F. Kwayise (Eds). Proceedings of the 19th Annual conference of the SAARMSTE, (pp. 65 – 77). North West University, Mafikeng, 18-21 January (ISBN: 978-0-9869800-0-8)*.
  • Machaba , F. ( 2005). Insights and Misconceptions of Grade 10 Learners in a south African school (Soshanguve). In C. Kasanda, L. Muhammed, S. Akpo & E. Ngololo (Eds). Proceedings of the 13th Annual conference of the SAARMSTE, (pp. 435 – 439). Namibia, 9-12 January. ISBN:081-127 3704
  • Modzuka, C.; Machaba, F., Long. C., & Howie, S. (2016). A jump from results to inferences about schooling: Analysis of Grade 6 Mathematics. In W. Mwakapenda, T. Sedumedi & M. Makgato(Eds). Proceedings of the 24th annual conference of the Southern African Association for Research in Mathematics, Science and Technology (pp. 83-84). Tshwane University of Technology, Arts Campus, Pretoria, South Africa. 978-0-9922269-2-3.
  • Machaba, F., Phiri, L., Ndlovu, W., & Mwakapenda, W.  (2016). Literacy, reading and experiences in Mathematics: A discussion on mathematical discourses. In W. Mwakapenda, T. Sedumedi & M. Makgato (Eds). Proceedings of the 24th annual conference of the Southern African Association for Research in Mathematics, Science and Technology (pp. 83-84). Tshwane University of Technology, Arts Campus, Pretoria, South Africa. 978-0-9922269-2-3.
  • Machaba, F. (2007). Learning mathematics through intergration with context that draw on learners Every day experiences both in M and ML: a pilot study. In M. Setati, N. Chitera & A. Essien(Eds). Proceedings of the 13th Annual National Congress of the Association for Mathematics Education of South Africa, (pp. 207 – 220). White River Mpumalanga, 2 – 6 July 2007: ISBN: 978 – 0 – 62038906-8

Research report

  • Machaba, F. (2014).Teachers and Facilitators’ views on solving Mathematics and Mathematical Literacy tasks. Unpublished doctoral thesis, Tshwane University of Technology, Pretoria, South Africa.
  • Machaba, F. (2003). Challenges facing Grade 5 educators in the implementation of curriculum 2005 in Primary schools of the Soshanguve South Cluster. Unpublished Masters’ dissertation, Tshwane University of Technology, Pretoria, South Africa.
  • Machaba, F. (2005). Insights and misconceptions that grade 10 learners in one school in Soshanguve have with the concepts of area and perimeter. Unpublished Research project, Bsc (hons) University of Witwatersrand, Johannesburg, South Africa.

Professional positions, fellowships & awards

Scholarships and grant awards:

  • Best Honours research award in mathematics education from Wits University.

Membership of academic and professional associations:

  • A Member of Association  for Mathematics Education  in South Africa ( AMESA)
  • A Member of Southern African Association for  research in Mathematics, Science and Technology  (SAARMSTE)
  • Reviewer of AMESA, SAARMSTE conference papers

Positions held:

  • External moderator – Tshwane University of Technology
  • External examiner for Post Graduate students- Tshwane University of Technology
  • Independent subject specialist of Independent schools for UMALUSI.

Projects

Community engagement/ Research project:

  • Supervision of teaching practice for mathematics student teachers in the ODeL environment – Leader   
  • Mathematics Teaching and Learning Intervention Progranme (MTLIP) – Team member
  • Mathematics Instruction in Sub-Saharan African countries (MTPTD) – Team member
  • Developing Mathematics Teaching Proficient Teachers (DMTPT) – Team member
  • FIRSTMATHS project – co –coordinator
  • subject specialist of Independent schools for UMALUSI 
  • 500 schools project at UNISA

Other

  • Prof France Machaba is a Full Professor at the University of South Africa. He holds a Doctoral degree in Mathematics Education from Tshwane University of Technology (TUT) (2014), a Master’s degree in Education from Tshwane University of Technology (2003), a B. Tech (Educational Management, 1999) and B. Tech in Natural Science (Mathematics & Physics, 2000) also from TUT, and a BSc (Hons) (Mathematics Education) from Wits University (2005). Prof Machaba is a reviewer of articles in journals, including the Pythagoras Journal, the African Journal of Research in Mathematics, Science and Technology Education, the European Journal of Social Sciences, the Mathematics and Science International Journal and The International Journal of Science, Mathematics and Technology Learning and African Education review journal.  He is a registered member of the Southern African Association for Research in Mathematics, the Association for Mathematics Education of South Africa (AMESA), and the Institute for Science and Technology Education (ISTE). He is one of the guest editors of the Journal of Education studies of a special issue entitled, “Mathematics Education and Quest for mathematics educating in the 4IR and Covid-19”. He has received awards in mathematics education including the best Honours research award in mathematics education from Wits University. Prof Machaba has worked as a Senior Education Specialist in Mathematics (Senior Phase) at Gauteng North District, Department of Basic Education, a mathematics & science teacher at Primary and Secondary in Gauteng schools, including part-time lecturer (mathematics & natural science) at TUT. He is a founder of Association for Mathematics Education in South Africa (AMESA) branch for Gauteng North District.  He was a member of the data-informed practice improvement project (DIPIP)-an initiative research project by Wits University and Gauteng department of education aimed at improving teaching and learning in mathematics.  He is an External moderator and examiner of Tshwane University of Technology Bed degree and Bed (hons) in Mathematics and Mathematical Literacy. He is also an independent subject specialist of Independent schools for UMALUSI.