Mathematics discourse in instruction during functions lessons in grade 10 rural classrooms

Authors

DOI:

https://doi.org/10.38140/ijrcs-2024.vol6.05

Keywords:

Functions lessons, mathematics discourse, mathematics instruction, rural teaching

Abstract

Despite the global significance of functions in mathematics education, there has been limited research on how South African rural teachers address specific mathematical concepts related to functions. This qualitative multiple case study, conducted within a post-structural paradigm, delved into the discourses of Grade 10 teachers during functions lessons in rural classrooms. The study focused on the teaching of mathematical concepts related to functions and involved five mathematics teachers from rural school sites in Acornhoek, Mpumalanga Province, South Africa. These teachers were selected based on their experience in teaching mathematics. The research employed semi-structured interviews, unstructured classroom observations, and Video-Stimulated Recall Interviews with all five teachers. By narrowing the focus to one teacher's lesson, this paper analyses the presentation of functions concepts using the Mathematical Discourse in Instruction (MDI) framework. The study revealed that clear teaching materials and learner-engaging instructional methods enable meaningful engagement and concept internalisation. Through the visible use of the components of the MDI framework, the teacher successfully engaged learners, clarified misconceptions, and encouraged learners' participation, ultimately enhancing the coherence and understanding of mathematical concepts related to functions in the Grade 10 classroom.

Author Biography

Matobako Sempe, University of South Africa, South Africa

Department of Mathematics Education, University of South Africa, Pretoria, South Africa.

References

Adler, J., & Ronda, E. (2015). A framework for describing mathematics discourse in instruction and interpreting differences in teaching. African Journal of Research in Mathematics, Science and Technology Education, 19(3), 237-254. https://journals.co.za/doi/abs/10.1080/10288457.2015.1089677

Adler, J., & Venkat, H. (2014). Teachers’ mathematical discourse in instruction: Focus on examples and explanations. In H. Rollnick, H. Venkat, J. Loughran & M. Askew (Eds.), Exploring content knowledge for teaching science and mathematics (pp. 132–146). London: Routledge.

Ayish, N. and Deveci, T. (2019). Student Perceptions of Responsibility for Their Own Learning and for Supporting Peers' Learning in a Project-Based Learning Environment. International Journal of Teaching and Learning in Higher Education, 31(2), 224-237. https://eric.ed.gov/?id=EJ1224347

Creswell, J. W. (2013). Educational research: Planning, conducting, and evaluating. W. Ross MacDonald School Resource Services Library.

Denbel, D. G. (2015). Functions in the Secondary School Mathematics Curriculum. Journal of Education and Practice, 6(1), 77–81. https://eric.ed.gov/?id=EJ1083845

Department of Basic Education (DBE). (2011). Curriculum and Assessment Policy Statement (CAPS): Senior and FET Phase Mathematics, Grades 10-12. Department for Basic Education.

Dlamini, S. and Essien, A.A. (2023). practices teachers use to mediate the sepedi mathematics register in multilingual foundation phase classrooms. Bbook of proceedings–long papers, p.59.

Hatch, J. A. (2002). Doing qualitative research in education settings. Suny Press.

Malahlela, M. V. (2017). Using errors and misconceptions as a resource to teach functions to grade 11 learners [Doctoral dissertation, University of the Witwatersrand]. University of the Witwatersrand. https://core.ac.uk/download/pdf/188776309.pdf

Mbhiza, H.W. (2021). Grade 10 mathematics teachers’ discourses and approaches during algebraic functions lessons in Acornhoek, rural Mpumalanga Province, South Africa [Doctoral dissertation, University of the Witwatersrand]. University of the Witwatersrand. https://wiredspace.wits.ac.za/bitstreams/72a99e7f-1a4a-4c89-86f5-febe8d08e978/download

Mellor, K., Clark, R., & Essien, A.A. (2018). Affordances for learning linear functions: A comparative study of two textbooks from South Africa and Germany. Pythagoras, 39(1), 1-12. https://doi.org/10.4102/pythagoras.v39i1.378

Moalosi, S. S. (2014). Enhancing teacher knowledge through an object-focused model of professional development [Doctoral dissertation, University of the Witwatersrand]. University of the Witwatersrand.

Moeti, M. P. (2015). Investigation into competent teachers’ choice and use of examples in teaching algebraic functions in Grade 11 in South African context: a case of two teachers [Doctoral dissertation, University of the Witwatersrand]. University of the Witwatersrand. http://hdl.handle.net/10539/19302

Mugwagwa, T. M. (2017). The influence of using computers to remedy learner errors and misconceptions in functions at grade 11 [Doctoral dissertation, University of the Witwatersrand]. University of the Witwatersrand. https://hdl.handle.net/10539/25026

Ogbonnaya, U. I., & Mushipe, M. (2020). The efficacy of GeoGebra-assisted instruction on students’ drawing and interpretations of linear functions. International Journal of Learning, Teaching and Educational Research, 19(9), 1–14. https://doi.org/10.26803/ijlter.19.9.1

Pournara, C., Sanders, Y., Adler, J., & Hodgen, J. (2016). Learners' errors in secondary algebra: Insights from tracking a cohort from Grade 9 to Grade 11 on a diagnostic algebra test. Pythagoras, 37(1), 1-10. http://dx.doi.org/10.4102/pythagoras.v37i1.334

Ronda, E., & Adler, J. (2017). Mining mathematics in textbook lessons. International Journal of Science and Mathematics Education, 15, 1097-1114. https://doi.org/10.1007/s10763-016-9738-6

Sarwadi, H. R. H., & Shahrill, M. (2014). Understanding students’ mathematical errors and misconceptions: The case of year 11 repeating students. Mathematics Education Trends and Research, 2014 1-10. https://doi.org/10.5899/2014/metr-00051

Scott, P., Mortimer, E., & Ametller, J., (2011). Pedagogical link?making: a fundamental aspect of teaching and learning scientific conceptual knowledge. Studies in Science Education, 47(1), 3-36. https://doi.org/10.1080/03057267.2011.549619

Sehole, L., Sekao, D., & Mokotjo, L. (2023). Mathematics conceptual errors in the learning of a linear function-a case of a Technical and Vocational Education and Training college in South Africa. The Independent Journal of Teaching and Learning, 18(1), 81-97. https://hdl.handle.net/10520/ejc-jitl1-v18-n1-a6

Setati, M., Adler, J., Reed, Y., & Bapoo, A. (2002). Incomplete journeys: Code-switching and other language practices in mathematics, science and English language classrooms in South Africa. Language and education, 16(2), 128. https://doi.org/10.1080/09500780208666824

Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematising. Cambridge University Press.

Ubah, I. J. A., & Bansilal, S. (2018). Pre-service mathematics teachers’ knowledge of mathematics for teaching: quadratic functions. Problems of Education in the 21st Century, 76(6), 847.

Venkat, H., Adler, J., Rollnick, M., Setati, M., & Vhurumuku, E. (2009). Mathematics and science education research, policy and practice in South Africa: What are the relationships? African Journal of Research in Mathematics, Science and Technology Education, 13(sup1), 5-27. https://doi.org/10.1080/10288457.2009.10740659

Vygotsky, L. S., & Cole, M. (1978). Mind in society: Development of higher psychological processes. Harvard University Press.

Published

2024-04-02

How to Cite

Mbhiza, H. W., & Sempe, M. (2024). Mathematics discourse in instruction during functions lessons in grade 10 rural classrooms. Interdisciplinary Journal of Rural and Community Studies, 6, 1-20. https://doi.org/10.38140/ijrcs-2024.vol6.05