Fundamental influences related to language-based difficulties in financial mathematics

  • A. Bayaga Nelson Mandela University, Port Elizabeth, South Africa
  • X. Khalo University of Fort Hare, East London
  • G. Moyo University of Zululand, Richards Bay
Keywords: errors, financial mathematics, language difficulty


Motivated in part by a sustained amount of research in South Africa and principally guided by techniques of problem-solving suggested by Polya as well as error analysis by Newman, the current research examines fundamental influencers (underlying factors) relating errors due to language difficulties in financial mathematics concerning the language of instruction. The current research was accomplished using a case study design. The sample size was 105 out of a population of 186, with assumption of confidence and precision levels at 95 per cent and 0.5 respectively. The aim of the study was addressed by using both sets of structured-interview and document analysis for collecting data. Analysis of data was conducted by both content analysis as well as correlation analysis, wherein, the analysis revealed that errors committed by learners in financial mathematics were due to language difficulties. In contrast, misinterpretation of the mathematical semantics was not as a result of not indicating answers as expected, not following instructions, and not understanding instructions.

Author Biographies

A. Bayaga, Nelson Mandela University, Port Elizabeth, South Africa

Department of Mathematics, Science & Technology Education (MSTE) and

Department of Senior Secondary Education




X. Khalo, University of Fort Hare, East London
G. Moyo, University of Zululand, Richards Bay

Department of Social science



Almog, N. and B. Ilany. 2012. “Absolute value inequalities: High school students’ solutions and misconceptions.” Educational Studies in Mathematics 81(3): 347‒364.

Ay, Y. 2017. “A review of research on the misconceptions in mathematics education.” Education Research Highlights in Mathematics, Science and Technology: 1‒12.

Aygor, N. and H. Ozdag. 2012. “Misconceptions in linear algebra: The case of undergraduate students.” Procedia ‒ Social and Behavioral Sciences 46, 2989–2994.

Ayres, P. 2000. “Mental effort and errors in bracket expansion tasks.” In Mathematics education beyond 2000, ed. J. Bana and A. Chapman, 80‒86.

Baldwin, E. E. and J. T. Yun. 2012. “Mathematics curricula and formative assessments: Toward an error-based approach to formative data use in mathematics.” Santa Barbara, CA: University of California Educational Evaluation Center.

Brodie, K. 2005. Using cognitive situative perspective to understand teacher interaction with learner error. Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education 2: 177‒184.

Brodie, K. 2014. “Learning about learner errors in professional learning communities.” Educational Studies in Mathematics 85: 221–239.

Brodie, K. and Y. Shalem. 2011. Accountability conversations: Mathematics teachers’ learning through challenge and solidarity. Journal of Mathematics Teacher Education 14(6): 419–439.

Columba, L. 2012. “Sorting Mathematical Representations: Words, Symbols, and Graphs.” Learning & Teaching 12: 3‒8.

DBE see Department of Basic Education.

Demby, A. 1997. “Algebraic procedures used by 13-to-15-year-olds.” Educational Studies in Mathematics 33: 45‒70.

Department of Basic Education. 2011. Curriculum and Assessment Policy Statement Grades 10 – 12 Mathematics. (Accessed 23 January 2019).

Department of Basic Education. 2014. National Senior Certificate Examination National Diagnostic Report, 12. (Accessed 10 January 2019).

Dobbins, A., J. C. Gagnon, and T. Ulrich. 2014. “Teaching geometry to students with math difficulties using graduated and peer-mediated instruction in a response-to-intervention model.” Preventing School Failure 58(1): 17–25.

Duran, M. 2013. “Opinions of primary 7th-grade students about visual mathematics literacy.” Mehmet Akif Ersoy University Journal of Educational Sciences Institute 2(2): 38‒51.

Durkin, K. and B. Rittle-Johnson. 2015. “Diagnosing misconceptions: Revealing changing decimal fraction knowledge.” Learning and Instruction 37(2015): 21‒29.

Gardee, A. and K. Brodie. 2015. “A teacher’s engagement with learner errors in her Grade 9 mathematics classroom.” Pythagoras 36(2), Art. 293, 9 pages. 10.4102/pythagoras.v36i2.293.

Hadjidemetriou, C. and J. S. Williams. 2002. “Children’s graphical conceptions.” Research in Mathematics Education 4: 69‒87.

Hansen, A. 2011. Children’s errors in mathematics: Understanding common misconceptions in primary school. 2nd Edition. Exeter: Learning Matters Ltd.

Healy, L. and C. Hoyles. 2000. “A study of proof conceptions in algebra.” Journal for Research in Mathematics Education 31(4): 396‒428.

Ho, S. Y. and T. Lowrie. 2014. The model method: Students’ performance and its effectiveness. The Journal of Mathematical Behavior 35: 87‒100.

Ingram, J., F. Baldry, and A. Pitt. 2013. “The influence of how teachers interactionally manage mathematical mistakes on the mathematics that students experience.” In Proceedings of the 8th Congress of the European Society of Research in Mathematics Education, ed. B. Ubuz, Ç. Haser, and M. Mariotti, 1487–1495. Ankara: European Society of Research in Mathematics Education.

Israel, G. D. 2009. Determining the sample size. Program Evaluation and Organisational Development. IFAS, University of Florida. PEOD-6.

Keçeli, V. and N. Turanlı. 2013. “Misconceptions and common errors in complex numbers.” Hacettepe University Journal of Education 28(1): 223‒234.

Koklu, O. and A. Topcu. 2012. “Effect of Cabri-assisted instruction on secondary school students’ misconceptions about graphs of quadratic functions.” International Journal of Mathematical Education in Science and Technology 43(8): 999–1011.

Kula, S. and E. Bukova Güzel. 2014. “Misconceptions are emerging in mathematics student teachers’ limit instruction and their reflections.” Quality & Quantity 48: 3355‒3372.

Leinhardt, G., O. Zaslavsky, and M. K. Stein. 1990. “Functions, graphs, and graphing: Tasks, learning, and teaching.” Review of Educational Research 60(1).

Lamport, L. 2012. “How to write a 21st-century proof.” Journal of Fixed Point Theory and Applications 11: 43‒63.

Luneta, K. and P. J. Makonye. 2010. “Learners’ errors and misconceptions in lementary analysis: A case study of a Grade 12 class in South Africa.” Acta Didactica Napocenia 3(3): 36‒45.

Lin, B., Y. Ko, and Y. Kuo. 2014. “Changes in pre-service teachers’ algebraic misconceptions by using computer-assisted instruction.” International Journal of Technology in Mathematics Education 21(3): 89‒101.

Lin, Y. C., D. C. Yang, and M. N. Li. 2015. “Diagnosing students’ misconceptions in number sense via a web-based two-tier test.” Eurasia Journal of Mathematics, Science & Technology Education 12(1): 41‒55.

Mercer, N. and C. Sams. 2006. “Teaching children how to use language to solve maths problems.” Language and Education 20(6): 507‒528.

Murray, H. 2012. “Problems with word problems in mathematics.” Learning and Teaching Mathematics 13: 55‒58.

Ojose, B. 2015. “Students’ misconceptions in mathematics: Analysis of remedies and what research says.” Ohio Journal of School Mathematics 72: 30‒34.

Peng, A. 2009. Teacher knowledge of students’ mathematical errors. Sweden: Umea Mathematics Education Research Centre, Umea University.

Pfeiffer, K. 2010. “The role of proof validation in students’ mathematical learning.” MSOR Connections 10(2): 17‒21.

Polya, G. 1957. How to solve it. 2nd Edition. Anchor Books, Garden City, New York.

Sakpakornkan, N. and T. Harries. 2003. “Pupils’ processes of thinking: Learning to solve algebraic problems in England and Thailand.” In Proceeding of the British society for research into learning mathematics 23: 91‒97, ed. J. Williams.

Seng, L. K. 2012. “An error analysis of form 2 (grade 7) students in simplifying algebraic expressions: A descriptive study.” Electronic Journal of Research in Educational Psychology 8(1): 139‒162.

Sheinuk, L. C. 2010. “Intermediate phase mathematics teachers reasoning about learners’ mathematical thinking.” Unpublished Master of Education thesis, Wits School of Education, Johannesburg, South Africa.

Schütz, R. 2002. Vygotsky and language acquisition. vygot.html (Accessed 31 March 2019).

Skemp, R. R. 2006. “Relational understanding and instrumental understanding.” Mathematics Teaching 12(2): 88‒95.

Türkdoğan, A., M. Güler, B. Ö. Bülbül, and Ş. Danişman. 2015. “Studies about misconceptions in mathematics education in Turkey: A thematic review.” Mersin University Journal of the Faculty of Education 11(2): 215‒236.

Uys, M., J. van der Walt, R. van den Berg, and S. Botha. 2007. “English medium of instruction: A situation analysis.” South African Journal of Education 27(1): 69‒82.

Van Jaarsveld, P. 2016. “Making a case for specific language as an aspect of rigour in initial teacher education mathematics programmes.” Perspectives in Education 34(1): 150‒166.

Watson, A. 2010. “Developing and deepening mathematical knowledge in teaching: Being and knowing.”

White, A. L. 2010. “Numeracy, literacy and Newman’s Error Analysis.” Journal of Science and Mathematics Education in Southeast Asia 33(2): 129‒148.

Yang, D. C. and Y. C. Lin. 2015. “Assessing 10- to 11-year-old children’s performance and misconceptions in number sense using a four-tier diagnostic test.” Educational Research 57(4): 368‒388.

How to Cite
Bayaga, A., X. Khalo, and G. Moyo. 2021. “Fundamental Influences Related to Language-Based Difficulties in Financial Mathematics”. South African Journal of Higher Education 35 (3), 29-44.
General Articles