A Systematic Analysis of Errors in the Simplification of a Rational Expression

Ruhl, K.A., Belward, S.R., and Balatti, J. (2011) A Systematic Analysis of Errors in the Simplification of a Rational Expression. In: Proceedings of the Eighth Southern Hemisphere Conference on Teaching and Learning Undergraduate Mathematics and Statistics, pp. 314-321. From: Volcanic Delta 2011 the Eighth Southern Hemisphere Conference on Teaching and Learning Undergraduate Mathematics and Statistics, 27 November - 2 December 2011, Rotorua, New Zealand.

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Abstract

Exploring the errors that mathematics students frequently make is a means by which teachers can gain a better understanding of students’ difficulties. Reported here are the process by which the algebraic working of 95 undergraduate students who incorrectly simplified a rational expression was analysed and the results of the analysis. Initially, a deductive approach to analysing the errors was planned, categorising students’ mistakes using the error types identified, named and described in the literature. In reviewing the literature, however, it became clear that this would be no simple task. The large body of literature, while rich in examples of “typical errors” that could be expected in students’ working, had two limitations. Firstly, the error types lacked precise descriptions and were mainly described by example only. Secondly, insufficient details of the procedures used to categorise the errors prevented replication of the categorising process. Consequently, a mainly inductive approach, that categorised the errors by their location and inferred student operation was devised. This systematic approach resulted in generating descriptions of three error categories.

Item ID: 21097
Item Type: Conference Item (Refereed Research Paper - E1)
ISBN: 978-0-473-20019-0
Date Deposited: 19 Mar 2012 22:33
FoR Codes: 13 EDUCATION > 1301 Education Systems > 130103 Higher Education @ 20%
13 EDUCATION > 1303 Specialist Studies in Education > 130303 Education Assessment and Evaluation @ 40%
13 EDUCATION > 1302 Curriculum and Pedagogy > 130208 Mathematics and Numeracy Curriculum and Pedagogy @ 40%
SEO Codes: 93 EDUCATION AND TRAINING > 9301 Learner and Learning > 930101 Learner and Learning Achievement @ 50%
93 EDUCATION AND TRAINING > 9302 Teaching and Instruction > 930299 Teaching and Instruction not elsewhere classified @ 50%
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