Mapping Design Principles to Instructional Realities in Early Grade Mathematics in South Africa: A Framework for Designing and Evaluating Learning and Teaching Support Materials

References

• Anghileri, J. (2006). Teaching number sense (2nd ed.). Continuum.
   Google Scholar
• Askew, M. (2012). Transforming primary mathematics. Routledge.
   Google Scholar
• Barton, Bill. (2012). Preface to ‘Ethnomathematics and philosophy’. In H. Forgasz & F.D. Rivera (Eds.), Towards equity in mathematics education: Gender, culture and diversity. Springer.
   Google Scholar
• Bell, P., Hoadley, C. M., & Linn, M. C. (2004). Design-based research in education. Internet environments for science education, 2004, 73–85.
   Google Scholar
• Clarkson, P.C. (2009). Mathematics teaching in Australian multilingual classrooms: Developing an approach to the use of classroom languages. In R. Barwell (Ed.), Multilingualism in mathematics classrooms: Global perspectives (pp. 145–160). Multilingual Matters.
   Google Scholar
• Clements, D.H., & Sarama, J. (2021). Learning and teaching early math: The learning trajectories approach. Routledge.
   Google Scholar
• diSessa, A.A., & Cobb, P. (2004). Ontological innovation and the role of theory in design experiments. The Journal of the Learning Sciences, 13(1): 77–103.
   Web of Science ®Google Scholar
• Erath, K., Ingram, J., Moschkovich, J., & Predlger, S. (2021). Designing and enacting instruction that enhances language for mathematics learning: A review of the state of development and research. Mathematics Education, 53, 245–262.
   Google Scholar
• Hoadley, U. (2016). A review of the research literature on teaching and learning in the foundation phase in South Africa. Research on Socioeconomic Policy Working Paper 05/16.
   Google Scholar
• Marton, F. (2014). Necessary conditions of learning. Routledge.
   Google Scholar
• McKenney, S., & Reeves, T. (2012). Conducting educational design research. Routledge.
   Google Scholar
• Morrison, S., Venkat, H., & Askew, M. (2021) Journeys toward sociomathematical norms in the foundation phase. (SAJCE Special Issue.) South African Journal of Childhood Education, 11(1), 1–8.
   Web of Science ®Google Scholar
• Mostert, I.E. (2021). Number and comparison in early grade mathematics: Learning from isiXhosa and English canonical texts. Doctoral Dissertation. University of Johannesburg.
   Google Scholar
• Nag S., Chiat S., Torgerson C., & Snowling, M.J. (2014). Literacy, foundation learning and assessment in developing countries: Final report. Department for International Development, University of Oxford.
   Google Scholar
• Plomp, T. (2007). An introduction to educational design research. Institute for Curriculum Development
   Google Scholar
• Porteus, K. (2022). Improving rural early grade mathematics: Design principles and patterns of improvement. In Venkat & Roberts (Eds.), Early grade mathematics in South Africa. Oxford University Press.
   Google Scholar
• Porteus, K., & Mostert, I. (2022). Moving beyond counting in ones: A South African framework for number picture representations. Association for Mathematics Education of South Africa (AMESA). Proceedings, 27th Annual National Congress. North-West University, Potchefstroom.
   Google Scholar
• Porteus, K., Roberts, N., & Moloi, Q. (2021). Grade 3 maths backlogs under Covid: Exploring the form and function of Grade 3 maths backlogs in interventions in rural and urban South Africa. Research Report submitted to the Zenex Foundation.
   Google Scholar
• Ramadiro, B. (2018). The influence of Neville Alexander on the South African language debate. In T. Kamusella & F. Ndhlovu (Eds.), The social and political history of southern Africa’s languages (pp. xxi–xxxiv). Palgrave Macmillan.
   Google Scholar
• Ramadiro, B. (2022). Implementing multilingual teacher education: Reflections on the University of Fort Hare's bi/multilingual Bachelor of Education Degree Programme. Education as Change, 26, 1–21.
   Google Scholar
• Ramadiro, B., & Porteus, K. (2017). Foundation phase matters: Language and learning in South African Rural Schools. Magic Classroom Collective Press.
   Google Scholar
• Roberts, N. (2018). Students’ mathematics knowledge in a Bachelor of Education (foundation and intermediate phase) programme. In R. Govender, & K. Junqueira (Eds.), Proceedings of the 24th Annual National Congress of the Association for Mathematics Education of South Africa, 2018, 124–139.
   Google Scholar
• Roberts, N. (2019). The standard written algorithm for addition: Whether, when and how to teach it. Pythagorus, 40(1), 1–17.
   Web of Science ®Google Scholar
• Ryan, R., & Deci, E.L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development and well-being. American Psychologist, 55(1), 68–78.
   PubMed Web of Science ®Google Scholar
• Spaull, N., & Kotze, J. (2015). Starting behind and staying behind in South Africa: The case of insurmountable learning deficits in mathematics. International Journal of Educational Development, 41, 13–24.
   Web of Science ®Google Scholar
• Spaull, N. & Taylor, S. 2022. What works and what scale? Returning to a tradition of evidence-based system-wide programmes. In Spaull & Taylor (Eds). 2022. Interventions: Early Grade Reading and Mathematics Interventions in South Africa. (pp 300–316). Oxford University Press.
   Google Scholar
• Taylor, N. (2019). Inequalities in teacher knowledge in South Africa. In: Spaull, N. & Jansen, J. (Eds.), South African schooling: The enigma of inequality. Policy Implications of Research in Education, vol. 10. Springer. https://doi.org/10.1007/978-3-030-18811-5_14
   Google Scholar
• Venkat, H. (2013). Using temporal range to theorize early number teaching in South Africa. For the Learning of Mathematics, 33(2), 31–37.
   Google Scholar
• Venkat, H., & Graven, M. (2023). Incorporating attention to mental mathematics in pre-service teacher education: The Mental Mathematics Work-Integrated Learning Project. SAARMSTE Symposium.
   Google Scholar
• Watson, A., & Mason, J. (2006). Mathematics as a constructive activity. Routledge.
   Google Scholar
• Watson, A., & Mason, J. (2009). Seeing an exercise as a single mathematical object: Using variation to structure sense making. Mathematical Thinking and Learning, 8(2), 91–111.
   Google Scholar