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.

DOI: https://doi.org/10.1007/s10763-019-10009-0

Abstract

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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