In-Service Teachers’ Perceptions and Interpretations of Students’ Errors in Mathematics


  • Million Chauraya Midlands State University,
  • Samuel Mashingaidze Midlands State University,


This paper reports on findings of a research study that investigated in-service secondary school teachers’ perceptions and interpretations of students’ errors in mathematics. The study used a survey research design in which a questionnaire with two sections was used to collect data. The first section sought to find out the teachers’ perceptions of the nature of errors. In the second part the teachers were asked to explain five common errors in algebra. A sample of forty-two mathematics teachers randomly drawn from one university in Zimbabwe constituted the respondents for the study. The findings showed that teachers perceived errors as not solely due to the student, but also as due to other factors arising from teaching and the nature of the subject. The teachers also regarded errors as useful for further inquiry in mathematics, as a normal part of learning, and as a result of previous knowledge not well understood by learners. In their explanations of given errors in algebra the teachers gave mainly procedural explanations, some of which lacked clarity or were incorrect. The study recommends the need for pre-service and in-service teacher professional development programmes to incorporate error analyses so as to develop teachers’ understanding of the nature and role of errors in the teaching and learning of mathematics.

Author Biographies

Million Chauraya, Midlands State University,

Department of Applied Education, Lecturer

Samuel Mashingaidze, Midlands State University,

Department of Applied Education, Lecturer


Booth, L. R. (1984). Algebra: Children's strategies and errors. A report on strategies and errors in a secondary mathematics project. London: NFER-NELSON Publications Co. Ltd.
Booth, L. R. (1988). Children's Difficulties in Beginning Algebra. In A. F. Coxford (Ed.), The Ideas of Algebra, K-12 (pp. 20-32). Reston VA: NCTM.
Booth, L. R., Barbieri, C., Eyer, F., & Pare-Blagoev, E. J. (2014). Persistent and Pernicious Errors in Algebraic Problem Solving. Journal of Problem Solving, 7(1), 10-23.
Booth, L. R., & Koedinger, K. R. (2008). Key misconceptions in algebraic problem solving. In B. C. Love, K. McRae & V. M. Sloutsky (Eds.), Proceedings of the Annual Conference of the Cognitive Science Society (pp. 571-576). Austin, TX: Cognitive Science Society.
Borasi, R. (1987). Exploring Mathematics through the Analysis of Errors. For the Learning of Mathematics, 7(3), 2-8.
Borasi, R. (1994). Capitalising on Errors as "Springboards for Inquiry": A Teaching Experiment. Journal for Research in Mathematics Education, 25(2), 166-208.
Brodie, K. (2014). Learning about learner errors in professional learning communities. Educational Studies in Mathematics, 85(2), 221-239.
Brown, G., & Quinn, R. J. (2006). Algebra Students' Difficulty with Fractions: An Error Analysis. Australian Mathematics Teacher, 62(4), 28-40.
Erlwanger, S. (1973). Benny's Conception of Rules and Answers in IPI Mathematics Journal of Children's Mathematical Behavior, 1(2), 87-107.
Gagatsis, A., & Christou, C. (1997). Errors in mathematics: A multidimensional approach. Scientia Paedagogica Experimentalis, 34(1), 403-434.
Gagatsis, A., & Kyriakides, L. (2000). Teachers' Attitudes Towards their Students' Mathematical Errors. Educational Research and Evaluation, 6(1), 24-58.
Hall, R. D. G. (2002). An Analysis of Errors Made in the Solution of Simple Linear Equations. Philosophy of Mathematics Education Journal, 15(1), 1-67.
Legutko, M. (2008). An Analysis of Students' Mathematical Errors in the Teaching-Research Process. In B. Czarnocha (Ed.), Handbook of Mathematics Teaching Research: Teaching Experiment - A Tool for Teacher-Researchers (pp. 141-152). Poland: University of Rzeszow: Rzeszow.
Lourens, F., & Molefe, N. (2011). Error Analysis of Mathematics Test Items. Paper presented at the 11th International Conference of the Mathematics Education into the 21st Century Project, Grahamstown, Rhodes University.
McNamara, J., & Shaughnessy, M. M. (2011). Student errors: What can they tell us about what students do understand?
Nesher, P. (1987). Towards an Instructional Theory: the Role of Students' Misconceptions For the Learning of Mathematics 7. Montreal, Canada: FLM Publishing Association.
Olivier, A. (1996). Handling pupils' misconceptions. Pythagoras, 21(10-19).
Peng, A., & Luo, Z. (2009). A framework for examining mathematics teacher knowledge as used in error analysis. For the Learning of Mathematics, 29(3), 22-25.
Radatz, H. (1979). Error Analysis in Mathematics Education. Journal for Research in Mathematics Education, 10(3), 163-172.
Shalem, Y., & Sapire, I. (2012). Teacher learning about learners' errors. Paper presented at the Teacher Education Conference, University of Pretoria, Pretoria.
Shalem, Y., Sapire, I., & Sorto, M. A. (2014). Teachers' explanations of learners' errors in standardised mathematics assessments. PYTHAGORAS, 35(1), 1-11.
Sheinuk, L. C. (2010). Intermediate phase mathematics teachers' reasoning about learners' mathematical thinking. (Master of Education), University of the Witwatersrand, Johannesburg.
Smith, J. P., Disessa, A. A., & Roschelle, J. (1993). Misconceptions Reconceived: A Constructivist Analysis of Knowledge in Transition. THE JOURNAL OF THE LEARNING SCIENCES, 3(2), 115-163.
Usiskin, Z. (1995). Why is Algebra Important to Learn? American Educator, 1(1), 30-37.
Usiskin, Z. (1999). Conceptions of School Algebra and Uses of Variables. In B. Moses (Ed.), Algebraic Thinking, Grades K-12: Readings from NCTM's School-Based Journals and Other Publications (pp. 7-13). Reston, Va: National Council of Mathematics.
Vaismoradi, M., Turunen, H., & Bondas, T. (2013). Content analysis and thematic analysis: Implications for conducting a qualitative descriptive study. Nursing and Health Sciences, 15(1), 398-405.
White, A. L. (2005). Active Mathematics in Classrooms: Finding out why children make mistakes - and then doing something to help them. Square One, 15(4), 15-19.