### Secondary school students’ errors and misconceptions in learning algebra

#### Abstract

The aim of the study is to develop an understanding of the kinds and sources errors and misconceptions that characterise students’ learning of school algebra. Systematic random sampling was used to draw sixty-five participants from a population of two hundred and twenty-three form three students. A cross sectional survey design was employed to collect data using written tests, a structured questionnaire and interviewing of the students from one high school in Zimbabwe. Content analysis technique was applied to textual data from three sources in order to determine the types of errors and misconceptions. The main findings are that both procedural and conceptual errors were prevalent that errors and misconceptions can be explained in terms of the students’ limited understanding of the nature of algebra; in particular their fragile grasp of the notion of a variable. Sources of misconceptions could be explained in terms of the abstract nature of algebra Mathematics educators should embrace errors and misconceptions in their teaching and should not regard them as obstacles to learning but rather engage with them for better understanding of algebraic concepts by students. Future studies can be carried on systematic errors as one of the ways of improving students’ understanding school mathematics.

#### Keywords

#### Full Text:

PDF#### References

A. Tecla, “ Students’ academic achievements and learning outcomes in mathematics among secondary schools in Nigeria.”, Educational Journal of Mathematics, Science and Technology Education, Volume 34 Number 2, pp. 12-22, 2007

J.A. Gillian, (1990). “Contemporary abstract algebra, (2nd Ed.).” D.C: Heath and Company, 1990.

B. S. Witzel, C.D. Mecrer and M.D. Miller, “Teaching algebra to students with learning difficulties: An investigation of an explicit instruction model.” Learning Disabilities Research and Practice, Volume 18 Number 2, pp. 121-131, 2003

C.E. Greenes and R Rubestein, R. (2008). Algebra and algebraic thinking in school mathematics, Seventieth Yearbook, NCTM, 2008.

D.M.S. Gatawa, “The politics of the school curriculum: An introduction.” Harare: College Press, 2008.

Z. Ndemo and D.K. Mtetwa, “Negotiating the transition from secondary to undergraduate mathematics: Reflections by some Zimbabwean students.” Middle Eastern and African Journal of Educational Research, Volume 14, pp. 67-78, 2015.

M.J. Prince and R.M. Felder, “Inductive teaching and learning methods: Definitions, comparisons, and research bases.” Journal of Engineering, Volume 3, pp. 123-138, 2006.

G. Polya, “How to solve It.”, Princeton: Princeton University Press, 2011.

D.K. Mtetwa, L. Mudehwe and S. Munyira, “Learning Mathematics for Personal Understanding and Productions: A Viewpoint.” Pythagoras, Volume 72, pp. 50-62, 2011.

M. Umameh, “Survey of students’ poor performance in mathematics.” Bristol: University of Bristol, 2011.

E. Gunawaden, “Secondary school students’ misconceptions in algebra”, Unpublished Doctoral Thesis, Ontario Institute for Studies in Education, University of Toronto, 2011.

Z. Usiskin, “Conceptions of school algebra and uses of variables.” in Coxford, Shulte, A. P. The ideas of algebra, K-12. NCTM Yearbook. Reston, VA: NCTM, 1988.

[13] M. Denscombe, “The Good Research Guide for Small Scale Projects.” New York: McGraw Hill, pp. 153-172, 2010.

J. H. McMillan and S. Schumacher, “Research in Education: Evidence-Based Inquiry. Seventh Edition.” New Jersey: Pearson Education, 2010.

C. Daymon and L. Holloway, I, “Qualitative Research Methods in Public Relations and Marketing Communications.” London &New York: Routledge, 2011.

A.H. Schoenfeld and A. Arcavi, “On the meaning of variable.” Mathematics Teacher, Volume 81 pp. 420-427, 1988

S. Wagner and C. Kieran, “Research Issues in the Learning and Teaching of Algebra.” Reston: NCTM and Lawrence Erlbaum, 1989.

L. Lee and D. Wheeler, “Algebraic Thinking in High School Students: Their Conceptions of Generalisation and Justification.” Montreal: Concordia University, 1987.

J. Leitzel, J. (1989). “Critical Considerations for the Future of Algebra Instruction.” in Wagner, Kieran (eds.), Research Issues in the Learning and Teaching of Algebra. Reston (VA): NCTM, 1989.

M.M. Socas, M. M. (1997). Difficulties, obstacles and errors in learning mathematics in secondaryeducation. In Rico, Mathematics education at the secondary level. ICE/Horsori, pp. 125-150, 1997.

R.M.Young and T. O’Shea, “Errors in children’s subtraction.” Cognitive Science, Volume 5, pp.153-177, 1981.

M.R. Nyikahadzoyi, “Prospective Zimbabwean “A” Level mathematics teachers’knowledge of the concept of a function.” Unpublished Doctoral Dissertation. University of the Western Cape, 2006.

M. Jones, “Demystifying Functions: The Historical and Pedagogical Difficulties of the Concept of Function.” Rose –Hulman Undergraduate Math Journal, Volume 7 Number 2, pp. 1-20, 2006.

L.J. Nyaumwe, “students' perceptions of factors and gender differences that influence their achievement in 'o’ level mathematics in mashonaland central region.”, Zimbabwe Bulletin of Teacher Education, Volume 13 Number, pp. 53-64, 2004.

K. Brodie, “Mathematical relationships in Mathematics Education: Participation by Laura Black; Heather Mendick; Yvette Solomon.”, Educational Studies in Mathematics, Volume, 76, Number 2, pp. 237-241.

J. Lochhead and J.P. Mestre, “From words to algebra: mending misconceptions.” in Coxford, Shulte, The ideas of algebra, K-12. Yearbook ed. NCYM, pp. 127-135, 1988.

K. Van Lehn and R.M. Jones, “What mediates the self-explanation effect? Knowledge gaps, schemas, or analogies?” in Polson (Ed.), Proceedings of 15th Annual Conference of Cognitive Science Society, pp. 1034-1039, 1993.

R. Lins and J. Kaput, “The early development of algebraic reasoning: the current state of the field.”, in Stacey, Chick, Kendal, Proceedings of the 12th study conference: The Future of the teaching and Learning of Algebra , ed. Dordecht; The Netherlands: Kluwer Academic Publishers, pp. 47-70, 2004.

D. Tall, D and M.J. Thomas, “Encouraging versatile thinking in algebra using aComputer.” Educational Studies in Mathematics, 22, 125-147, 2008.

K. Luneta and J. Makonye, “Learner errors and misconceptions elementary analysis: A case study of a grade 12 class in South Africa. Acta Didactics Napocensia, 3(3), 35-45, 2010.

A.C. Stephens, “Developing students’ understandings of variable.” Mathematics Teaching in the Middle School, Volume 2 pp. 96-100, 2005.

DOI: https://doi.org/10.11591/edulearn.v12i4.9556

### Refbacks

- There are currently no refbacks.

Copyright (c) 2018 Universitas Ahmad Dahlan

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

**Journal of Education and Learning (EduLearn)**

ISSN: 2089-9823, e-ISSN 2302-9277

Published by Intelektual Pustaka Media Utama (IPMU) *in collaboration with *the Institute of Advanced Engineering and Science (IAES) and Universitas Ahmad Dahlan (UAD).