Generalization Strategies in Finding the nth Term Rule for Simple Quadratic Sequences

Biza, Irene; Hewitt, Dave; Watson, Anne and Mason, John (2020). Generalization Strategies in Finding the nth Term Rule for Simple Quadratic Sequences. International Journal of Science and Mathematics Education, 18(6) pp. 1105–1126.



In this study, we identify ways in which a sample of 18 graduates with mathematics-related first degrees found the nth term for quadratic sequences from the first values of a sequence of data, presented on a computer screen in various formats: tabular, scattered data pairs and sequential. Participants’ approaches to identifying the nth term were recorded with eye-tracking technology. Our aims are to identify their strategies and to explore whether and how format influences these strategies. Qualitative analysis of eye-tracking data offers several strategies: Sequence of Differences, Building a Relationship, Known Formula, Linear Recursive and Initial Conjecture. Sequence of Differences was the most common strategy, but Building a Relationship was more likely to lead to the right formula. Building from Square and Factor Search were the most successful methods of Building a Relationship. Findings about the influence of format on the range of strategies were inconclusive but analysis indicated sporadic evidence of possible influences.

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