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Learners’ errors in secondary algebra: insights from tracking a cohort from Grade 9 to Grade 11 on a diagnostic algebra test

Pournara, Craig; Hodgen, Jeremy; Sanders, Yvonne; Adler, Jill


Craig Pournara

Jeremy Hodgen

Yvonne Sanders

Jill Adler


It is well known that learner performance in mathematics in South Africa is poor. However, less is known about what learners actually do and the extent to which this changes as they move through secondary school mathematics. In this study a cohort of 250 learners was tracked from Grade 9 to Grade 11 to investigate changes in their performance on a diagnostic algebra test drawn from the well-known Concepts in Secondary Maths and Science (CSMS) tests. Although the CSMS tests were initially developed for Year 8 and Year 9 learners in the UK, a Rasch analysis on the Grade 11 results showed that the test performed adequately for older learners in SA. Error analysis revealed that learners make a wide variety of errors even on simple algebra items. Typical errors include conjoining, difficulties with negatives and brackets and a tendency to evaluate expressions rather than leaving them in the required open form. There is substantial evidence of curriculum impact in learners’ responses such as the inappropriate application of the addition law of exponents and the distributive law. Although such errors dissipate in the higher grades, this happens later than expected. While many learner responses do not appear to be sensible initially, interview data reveals that there is frequently an underlying logic related to mathematics that has been previously learned.


Pournara, C., Hodgen, J., Sanders, Y., & Adler, J. (2016). Learners’ errors in secondary algebra: insights from tracking a cohort from Grade 9 to Grade 11 on a diagnostic algebra test. Pythagoras, 37(1),

Journal Article Type Article
Acceptance Date Sep 2, 2016
Publication Date Oct 31, 2016
Deposit Date Nov 11, 2016
Publicly Available Date Nov 11, 2016
Journal Pythagoras
Print ISSN 1012-2346
Electronic ISSN 1012-2346
Publisher AOSIS
Peer Reviewed Peer Reviewed
Volume 37
Issue 1
Public URL
Publisher URL


Pournara et al Tracking algebra errors Pythagoras 2016.pdf (1.9 Mb)

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