n Learning and Teaching Mathematics - "Completing the square" - a conceptual approach

Volume 2013, Issue 14
  • ISSN : 1990-6811


The method of completing the square is a useful algebraic technique. Within the South African school context, "completing the square" is most often used for three specific purposes: (i) solving quadratic equations, (ii) writing parabola equations in turning point format, and (iii) writing circle equations in centre-radius format. In my experience, learners who have good algebraic skills master the technique of completing the square fairly quickly. Learners who are less algebraically confident take a little longer to acquire the skill but are nonetheless able to master the technique with sufficient practice. However, for most learners the method of completing the square is little more than an arcane process of algebraic manipulation accomplished somewhat mechanically through the use of a guiding algorithm or mantra such as . As such, most learners leave school without really understanding the conceptual basis of the technique. This is sad because the conceptual heart of the process is not only simple but beautifully elegant. A more conceptual approach to introducing learners to the technique of completing the square is likely not only to demystify the method for many learners, but is also likely to free learners from their reliance on rote algebraic manipulation. This article explores strategies for teaching the method of completing the square using a more conceptual approach.

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