Unveiling problem-solving strategies of pre-service mathematics teachers: A visual and discursive exploration

Mzwandile Wiseman Zulu; Vimolan Mudaly

doi:10.29333/ejmste/13344

Full Text (PDF)

Mzwandile Wiseman Zulu ¹ ^* , Vimolan Mudaly ¹

More Detail

¹ Department of Mathematics and Computer Science Education, School of Education, University of KwaZulu-Natal, Pinetown, SOUTH AFRICA^* Corresponding Author

Abstract

This study explores how pre-service mathematics teachers (PMTs) in South Africa use visualization and self-discourse to solve mathematical problems. Visualization is known to enhance mathematics learning, while effective communication skills are critical for teaching and learning mathematics, especially in contexts, where the language of instruction may not be the first language of students or teachers. By understanding the visualization techniques and discursive properties employed by PMTs, insights can be gained into how to improve mathematics learning and teaching. The study is informed by the commognitive framework and uses qualitative data from a purposive sample of 10 PMTs who participated in a performance test and semi-structured interviews. The study found that PMTs rely on mental visualization for simpler mathematical problems but use both symbolic and iconic visual mediators for more complicated problems. The use of language to engage in self-discursive activity during problem-solving was found to be key for successful visualization.

Keywords

visualization
mathematical discourse
commognition
problem-solving

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 19, Issue 7, July 2023, Article No: em2299

https://doi.org/10.29333/ejmste/13344

Publication date: 01 Jul 2023

Online publication date: 05 Jun 2023

Article Views: 1364

Article Downloads: 920

Open Access References How to cite this article

References

Abate, A., Atnafu, M., & Michael, K. (2022). Visualization and problem-based learning approaches and students’ attitude toward learning mathematics. Pedagogical Research, 7(2), em0119. https://doi.org/10.29333/pr/11725
Albay, E. M. (2019). Analyzing the effects of the problem-solving approach to the performance and attitude of first year university students. Social Sciences & Humanities Open, 1(1), 1-7. https://doi.org/10.1016/j.ssaho.2019.100006
Alkan, H., & Bukova Güze, E. (2005). Development of mathematical thinking in the student teachers. Gazi Education Faculty Journal, 25(3), 221-236.
Arcavi, A. (2003). The role of visual representation in the learning of mathematics. Educational Studies in Mathematics, 52(3), 215-241. https://doi.org/10.1023/A:1024312321077
Bermejo, V., Ester, P., & Morales, I. (2021). How the language of instruction influences mathematical thinking development in the first years of bilingual schoolers. Frontiers Psychology, 12, 1-11. https://doi.org/10.3389/fpsyg.2021.533141
Byrne, D. (2022). A worked example of Braun and Clarke’s approach to reflexive thematic analysis. Qual Quant, 56, 1391-1412. https://doi.org/10.1007/s11135-021-01182-y
Celik, H., & Ozdemir, F. (2020). Mathematical thinking as a predictor of critical thinking dispositions of pre-service mathematics teachers. International Journal of Progressive Education, 16(4), 81-98. https://doi.org/10.29329/ijpe.2020.268.6
Chitera, N., Kasoka, D., & Thomo, E. (2016). There is more to the teaching and learning of mathematics than the use of local languages: Mathematics teacher practices. Journal of Education and Learning, 10(4), 308-319. https://doi.org/10.11591/edulearn.v10i4.4959
de Koning, B. B., Boonen, A. J., Jongerling, J., van Wesel, F., & van der Schoot, M. (2022). Model method drawing acts as a doubleedged sword for solving inconsistent word problems. Educational Studies in Mathematics, 111(1), 29-45. https://doi.org/10.1007/s10649-022-10150-8
Diezmann, C. M. (2000). Making sense with diagrams: Students’ difficulties with feature-similar problems. In J. Bana, & A. Chapman (Eds.), Proceedings of the 23^rd Annual Conference of Mathematics Education Research Group of Australasia (pp. 228-234). MERGA.
Esmonde, I. (2009). Explanations in mathematics classrooms: A discourse analysis. Canadian Journal of Science, Mathematics and Technology Education, 9(2), 86-99. https://doi.org/10.1080/14926150902942072
Espinosa, F. (1997). Researching a problem of convergence with Mathematica: History and visualisation of a mathematical idea. International Journal of Mathematical Education in Science and Technology, 28(5), 697-706. https://doi.org/10.1080/0020739970280506
Gavilán-Izquierdo, J. M., & Gallego-Sánchez, I. (2021). How an upper secondary school teacher provides resources for the transition to university: A case study. International Electronic Journal of Mathematics Education, 16(2), 1-14. https://doi.org/10.29333/iejme/10892
Hawes, Z., & Ansari, D. (2020). What explains the relationship between spatial and mathematical skills? A review of evidence from brain and behavior. Psychonomic Bulletin & Review, 27, 465-482. https://doi.org/10.3758/s13423-019-01694-7
Ho, W. H., Hong, L. S., Tay, E. G., Leong, Y. H., & Ming, T. K. (2019). Passing a proof message: Student-teacher communication through a commognitive lens. In G. Hine, S. Blackley, & A. Cooke (Eds.), Mathematics education research: Impacting practice (Proceedings of the 42nd annual conference of the Mathematics Education Research Group of Australasia) (pp. 700-706). MERGA.
Hundeland, P. S., Carlsen, M., & Erfjord, I. (2020). Qualities of mathematical discourses in kindergartens. ZDM Mathematics Education, 52, 691-702. https://doi.org/10.1007/s11858-020-01146-w
Jourdain, L., & Sharma, S. (2016). Language challenges in mathematics education: A literature review. Waikato Journal of Education, 21(2), 43-56. https://doi.org/10.15663/wje.v21i2.269
Kahiya, A., & Brijlall, D. (2021). What are the strategies for teaching and learning mathematics that can be used effectively in a multilingual classroom? Technology Reports of Kansai University, 63(05), 7583-7595. https://hdl.handle.net/10321/3815
Kartal, O., Morrissey, S., & Popovic, G. (2020). Analysis of elementary pre-service teachers’ identification of mathematical problem-solving tasks and anticipated student solutions. The Mathematics Educator, 29(1), 85-111.
Lee, M. Y., & Lee, J. (2019). Pre-service teachers’ perceptions of the use of representations and suggestions for students’ incorrect use. EURASIA Journal of Mathematics, Science and Technology Education, 15(9), em1745. https://doi.org/10.29333/ejmste/103055
Lukenchuk, A. (2013). Paradigms of research for the 21st century. Peter Lang.
Maguire, M., & Delahunt, B. (2017). Doing a thematic analysis: A practical, step-by-step guide for learning and teaching scholars. All Ireland Journal of Teaching and Learning in Higher Education, 8(3), 3351-33514. http://ojs.aishe.org/index.php/aishe-j/article/view/3354
Mahlaba, S. C., & Mudaly, V. (2022). Exploring the relationship between commognition and the Van Hiele theory for studying problem-solving discourse in Euclidean geometry education. Pythagoras - Journal of the Association for Mathematics Education of South Africa, 43(1), 1-11. https://doi.org/10.4102/pythagoras.v43i1.659
Moleko, M. M. (2021). Teachers’ perspectives on addressing linguistic factors affecting visualization of mathematics word problems. EURASIA Journal of Mathematics, Science and Technology Education, 17(11), em2029. https://doi.org/10.29333/ejmste/11248
Monson, D., Krupa, E., Lesseig, K., & Casey, S. (2020). Developing secondary prospective teachers’ ability to respond to student work. Journal of Mathematics Teacher Education, 23, 209-232. https://doi.org/10.1007/s10857-018-9420-8
Mudaly, V. (2021). Constructing mental diagrams during problem-solving in mathematics. Pythagoras-Journal of the Association for Mathematics Education of South Africa, 42(1), 1-8. https://doi.org/10.4102/pythagoras.v42i1.633
Mudaly, V., & Rampersad, R. (2010). The role of visualization in students’ conceptual understanding of graphical functional relationships. African Journal of Research in Mathematics, Science and Technology Education, 14(1), 36-48. https://doi.org/10.1080/10288457.2010.10740671
Mudaly, V., & Reddy, L. (2016). The role of visualization in the proving process of Euclidean geometry problems. International Scientific Research Journal, 72(8), 178-204. https://doi.org/10.21506/j.ponte.2016.8.13
Osman, S., Yang, C. N., Abu, M. S., Ismail, N., Jambari, H., & Kumar, J. A. (2018). Enhancing students’ mathematical problem-solving skills through bar model visualization technique. International Electronic Journal of Mathematics Education, 13(3), 273-279. https://doi.org/10.12973/iejme/3919
Ozsoy, G. (2018). Pre-service teachers’ use of visual representations. International Electronic Journal of Elementary Education, 11(1), 49-54. https://doi.org/10.26822/iejee.2018143960
Pantziara, M., Gagatsis, A., & Elia, I. (2009). Using diagrams as tools for the solution of non-routine mathematical problems. Educational Studies in Mathematics, 72, 39-60. https://doi.org/10.1007/s10649-009-9181-5
Rathour, L., Obradovic, D., Tiwari, S. K., Mishra, L. N., & Narayan, V. (2022). Visualization method in mathematics classes. Computational Algorithms and Numerical Dimensions, 1(4), 141-146. https://doi.org/10.22105/cand.2022.159701
Rellensmann, J., Schukajlow, S., & Leopold, C. (2017). Make a drawing. Effects of strategic knowledge, drawing accuracy, and type of drawing on students' mathematical modelling performance. Educational Studies in Mathematics, 95(1), 53-78. https://link.springer.com/article/10.1007/s10649-016-9736-1
Rif'at, M. (2018). The exploring of visual imagery: In their relation to the students' mathematical identity. Higher Education Research, 3(5), 75-91. http://dx.doi.org/10.11648/j.her.20180305.11
Ripardo, R. B. (2017). Teaching mathematics from the perspective of Mathematics as a discourse. Ciência & Educação (Bauru), 23(4), 899-915. https://doi.org/10.1590/1516-731320170040014
Robertson, S., & Graven, M. (2020a). A mathematics teacher’s response to a dilemma: ‘I’m supposed to teach them in English, but they do not understand’. South African Journal of Childhood Education, 10(1), 1-11. https://doi.org/10.4102/sajce.v10i1.800
Robertson, S., & Graven, M. (2020b). Language as an including or excluding factor in mathematics teaching and learning. Mathematics Education Research Journal, 32, 77-101. https://doi.org/10.1007/s13394-019-00302-0
Samo, D., & Kartasasmita, D. B. (2017). Developing contextual mathematical thinking learning model to enhance higher-order thinking ability for middle school students. International Education Studies, 10(12), 17-29. https://doi.org/10.5539/ies.v10n12p17
Samosa, R. C., Dominguez, J. M., Budaño, S. D., Ronquillo, C. J., & Yumul, R. E. (2021). Visualize, represent and solve problem technique as teaching strategy to improve the learner’s problem-solving skill in mathematics 2. International Journal of Academic Multidisciplinary Research, 5(12), 75-78. https://doi.org/10.13140/RG.2.2.28700.62083
Stacey, K. (2007). What is mathematical thinking and why is it important? 39-48. http://www.criced.tsukuba.ac.jp/math/apec/apec2007/paper_pdf/Kaye%20Stacey.pdf
Stake, R. E. (2006). Multiple case study analysis. Guilford Press.
Sfard, A. (2007). When the rules of discourse change, but nobody tells you: Making sense of mathematics learning from a commognitive standpoint. The Journal of the Learning Sciences, 16(4), 565-613. https://doi.org/10.1080/10508400701525253
Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge University Press. https://doi.org/10.1017/CBO9780511499944
Sfard, A. (2015). Learning, commognition and mathematics. In D. Scott, & E. Hargreaves (Eds.), The SAGE handbook of learning (pp. 129-138). SAGE. https://doi.org/10.4135/9781473915213.n12
Shatri, K., & Buza, K. (2017). The use of visualization in teaching and learning process for developing critical thinking of students. European Journal of Social Sciences Education and Research, 4(1), 71-74. https://doi.org/10.26417/ejser.v9i1.p71-74
Supardi, L., Zayyadi, M., Lanya, H., Hasanah, S. I., & Hidayati, S. N. (2021). Commognitive analysis of students’ errors in solving high order thinking skills problems. Turkish Journal of Computer and Mathematics Education, 12(6), 950-961. https://doi.org/10.17762/turcomat.v12i6.2373
Tasdan, B. T., & Kabar, M. G. (2022). Pre-service mathematics teachers’ responding to student thinking in their teaching experiences. Journal of Pedagogical Research, 6(1), 87-109. https://doi.org/10.33902/JPR.2022175553
Tiwari, S., Obradovic, D., Rathour, L., Mishra, L. N., & Mishra, V. N. (2021). Visualization In Mathematics Teaching. Journal of Advances in Mathematics, 21, 431-439. https://doi.org/10.24297/jam.v20i.9136
Toscano, R., Gavilán-Izquierdo, J. M., & Sánchez, V. (2019). A study of pre-service primary teachers’ discourse when solving didactic-mathematical tasks. EURASIA Journal of Mathematics, Science and Technology Education, 15(11), em1762. https://doi.org/10.29333/ejmste/108631
Vale, I., & Barbosa, A. (2018). Mathematical problems: the advantages of visual strategies. Journal of the European Teacher Education Network, 13, 23-33.
Van Zoest, L., Stockero, S. L., Leatham, K. R., Leatham, B. E., Atanga, N. A., & Ochieng, M. A. (2017). Attributes of instances of student mathematical thinking that are worth building on in whole-class discussion. Mathematical Thinking and Learning, 19(1), 33-54. https://doi.org/10.1080/10986065.2017.1259786
Yildiz, C. (2016). Comparing the mathematical thinking experiences of students at faculty of education and faculty of arts and sciences. The Turkish Online Journal of Educational Technology, (Special Issue), 480-488.
Yilmaz, R., & Argun, Z. (2018). Role of visualization in mathematical abstraction: The case of congruence concept. International Journal of Education in Mathematics, Science and Technology, 6(1), 41-57. https://doi.org/10.18404/ijemst.328337

How to cite this article

APA

Zulu, M. W., & Mudaly, V. (2023). Unveiling problem-solving strategies of pre-service mathematics teachers: A visual and discursive exploration. Eurasia Journal of Mathematics, Science and Technology Education, 19(7), em2299. https://doi.org/10.29333/ejmste/13344

Vancouver

Zulu MW, Mudaly V. Unveiling problem-solving strategies of pre-service mathematics teachers: A visual and discursive exploration. EURASIA J Math Sci Tech Ed. 2023;19(7):em2299. https://doi.org/10.29333/ejmste/13344

AMA

Zulu MW, Mudaly V. Unveiling problem-solving strategies of pre-service mathematics teachers: A visual and discursive exploration. EURASIA J Math Sci Tech Ed. 2023;19(7), em2299. https://doi.org/10.29333/ejmste/13344

Chicago

Zulu, Mzwandile Wiseman, and Vimolan Mudaly. "Unveiling problem-solving strategies of pre-service mathematics teachers: A visual and discursive exploration". Eurasia Journal of Mathematics, Science and Technology Education 2023 19 no. 7 (2023): em2299. https://doi.org/10.29333/ejmste/13344

Harvard

Zulu, M. W., and Mudaly, V. (2023). Unveiling problem-solving strategies of pre-service mathematics teachers: A visual and discursive exploration. Eurasia Journal of Mathematics, Science and Technology Education, 19(7), em2299. https://doi.org/10.29333/ejmste/13344

MLA

Zulu, Mzwandile Wiseman et al. "Unveiling problem-solving strategies of pre-service mathematics teachers: A visual and discursive exploration". Eurasia Journal of Mathematics, Science and Technology Education, vol. 19, no. 7, 2023, em2299. https://doi.org/10.29333/ejmste/13344