A Critical Analysis of Errors Made by Rural and Urban Students in ‘O’ Level Mathematics Paper 1 (4008/1) in Shurugwi and Gweru Districts, Zimbabwe

Authors

  • Silvanos Chirume Zimbabwe Open University

DOI:

https://doi.org/10.24203/ajeel.v5i2.4652

Keywords:

mathematical error, “O” Level students, rural students, urban students, types of errors, error analysis, error rectification

Abstract

This study critically investigated and analysed mathematical errors made by forty rural and urban Zimbabwe Ordinary Level students who wrote a test adopted from the ZIMSEC 2012 past examination paper (4008/1). Twenty students at a rural school in Shurugwi District and twenty students of similar characteristics (except for location or district) at an urban school in Gweru District were randomly sampled. Questions 1 and 7 (arithmetic and algebraic manipulations), 2 and 21 (psychomotor skills- measurement, shading, locus and geometric constructions) and 8 and 15 (word problems) were purposively sampled and students’ written and marked scripts were subjected to a critical analysis of errors. The errors were classified into eight categories proposed by Dufresne (2012) and these were error in knowledge, error in skill, error in concept, error in making connections, error in strategy effectiveness, error in convention, error in process and error in format. Mixed methods (QUAL-quan, content and interpretivist) analyses of errors made by the rural students and those made by the urban students were made. The study offers possible strategies that teachers in rural and urban areas can use to rectify students’ mathematical errors in the classroom situation and contributes to the body of knowledge on mathematical error analysis.    

Author Biography

Silvanos Chirume, Zimbabwe Open University

Lecturer and Programme Coordinator for BSc Mathematics and Statistics, Zimbabwe Open University

References

• Ball, D. L., Thames, M., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education 59(5), pp. 389-407. http://dx.doi.org/10.1177/0022487108324554

• Bingolbali, E., Akkoç, H., Ozmantar, M.F. & Demir, S. (2011). Pre-Service and In-Service Teachers‟ Views of the Sources of Students‟ Mathematical Difficulties. International Electronic Journal of Mathematics Education – IΣJMΣ 6, (1), pp. 40-59.

• Chirume, S. (2012). Reducing Mathematics Anxiety and Building Positive Attitudes: A Challenge For Teachers and Students. The Dyke, 6(1), pp.15-33.

• Chirume, S. & Chikasha, A.S. (2014). A Critical Analysis of the Factors Affecting Achievement in Secondary School Mathematics in Zimbabwe: A Case Study of Gweru District. Merit Research Journal of Education and Review, 2(9), pp. 194-202.

• Cohen, L.G. & Spenciner, L.J. (2007). Assessment of Children and Youth with Special Needs. Merrill, pp. 262-263.

• Dufresne, R. (2012). Math 151 Error Analysis. Retrieved on 29/10/15 from http://people.qatar.tamu.edu/raelene.dufresne/education/math150/Math_150/Resources_files/erroranalysis.pdf

• Elbrink, M. (2008). Analyzing and Addressing Common Mathematical Errors in Secondary Education. [Extended Thesis Abstracts]. B.S. Undergraduate Mathematics Exchange, 5(1), pp. 1-4

• Ernest, P. (2004). The Philosophy of Mathematics Education. Routledge Falmer, Taylor and Francis e-Library, ISBN 0-203-49701-5 [Master e-book]

• Error Pattern Analysis, (n.d). Retrieved on from http://specialconnections.ku.edu/~specconn/page/instruction/math/pdf/patternanalysis.pdf

• Gardee, A., & Brodie, K. (2015). A teacher’s engagement with learner errors in her Grade 9 mathematics classroom. Pythagoras, 36(2), pp. 1-9. Retrieved on 8/04/16 from http://dx.doi.org/10.4102/pythagoras.v36i2.293

• Hirashima, T., & Horiguchi, T. (2016). Creation of Cognitive Conflict by Error-Visualization: Error-Based Simulation and Its Practical Use in Science Learning. Springer International Publishing Switzerland, J.M. Spector et al. (eds.), Learning, Design, and Technology, DOI 10.1007/978-3-319-17727-4_9-1

• Kessel, C. (ed.) (2009). Teaching Teachers Mathematics: Research, Ideas, Projects, Evaluation. Mathematical Sciences Research Institute, Berkeley, California

• Koehler , M.J., Mishra, P., Kereluik, K., Shin, T.S., & Graham, C.R. (2014). The Technological Pedagogical Content Knowledge Framework. In J.M. Spector, J.M. et al. (eds.), Handbook of Research on Educational Communications and Technology, Springer Science+Business Media New York, 101 DOI 10.1007/978-1-4614-3185-5_9.

• Lester Jr, F.K. (2005). On the theoretical, conceptual, and philosophical foundations for research in mathematics education. ZDM 37(6), pp. 457-467.

• Livingston, K.D. (2015). Correcting errors in the L2 classroom: students' and teachers' perceptions. Revista Electrónica del Lenguaje, (2), pp. 1-36.

• Lourens, R., Molefe, N. & Brodie, K. (2011). Workshop: Error Analysis of Mathematics Test Items. Retrieved on 29/10/15 from http://directorymathsed.net/download/Lourens.pdf

• Luneta, K. (2015). Understanding students’ misconceptions: An analysis of final Grade 12 examination questions in geometry. Pythagoras, 36(1), Art. #261, 11 pages. Retrieved on 21/6/16 from http://dx.doi.org/10.4102/pythagoras.v36i1.261

• Nyikahadzoyi, M.R. (2013). Teachers’ knowledge of the concept of a function: A theoretical framework. International Journal of Science and Mathematics Education 13 (Suppl 2): pp. 261-283.

• Ross, A. & Onwuegbuzie, A.J. (2012). Prevalence of Mixed Methods Research in Mathematics Education. The Mathematics Educator, 22(1), pp. 84–113.

• Shalem, Y., Sapire, I., & Sorto, M.A. (2014). Teachers’ explanations of learners’ errors in standardised mathematics assessments. Pythagoras, 35(1), pp. 1-11.

• Zemelman, S., Daniels, H., & Hyde, A. (2005). Best practice: New standards for teaching and learning in America’s school (3rd Edition). Portsmouth, NH: Heinemann.

• ZIMSEC (2012a). Zimbabwe General Certificate of Education (ZGCE) ‘O’ Level Syllabus Mathematics 4008/4028. Retrieved on 21/04/15 from http://www.zimsec.co.zw/O_SYLLABUS/O-MATHEMATICS.pdf.

• ZIMSEC (2012b). Zimbabwe School Examinations Council: General Certificate of Education Ordinary Level Mathematics 4008/1 Paper 1 [Questions 1, 2, 7, 8, 15, and 21] ZIMSEC, Harare.

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Published

2017-04-22

How to Cite

Chirume, S. (2017). A Critical Analysis of Errors Made by Rural and Urban Students in ‘O’ Level Mathematics Paper 1 (4008/1) in Shurugwi and Gweru Districts, Zimbabwe. Asian Journal of Education and E-Learning, 5(2). https://doi.org/10.24203/ajeel.v5i2.4652

Issue

Vol. 5 No. 2 (2017): April 2017

Section

Articles

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