Investigating Students' Understanding of Square Numbers and Square Roots

The ideas related to square numbers and square roots, despite the apparent simplicity, appear problematic to high school students. I inquired into students' understanding of square numbers and square roots, focusing on obstacles that students face in considering these concepts and solution approaches that they prefer. The study followed a modified analytic induction methodology. A written questionnaire was administered to 51 pre-calculus 11 students and followed up with clinical interviews with 9 students. The study revealed significant obstacles in three categories: confusion of definitions, distribution of square numbers within the natural numbers and opaque representation of square numbers. Confusion of definitions included confusion both within and between the concepts of square numbers and square roots. Students used five different solution approaches; brute force, guess and check, rule application, pattern spotting and attention to structure. Students switched between solution approaches often, but showed personal preference toward particular solution approaches.