Generalization strategies and representations used by final-year elementary school students

Abstract

Recent research has highlighted the role of functional relationships in introducing elementary school students to algebraic thinking. This functional approach is here considered to study essential components of algebraic thinking such as generalization and its representation, as well as the strategies used by students and their connection with generalization. This paper jointly describes the strategies and representations of generalization used by a group of 33 sixth-year elementary school students, with no former algebraic training, in two generalization tasks involving a functional relationship. The strategies applied by the students differed depending on whether they were working on specific or general cases. To answer questions on near specific cases they resorted to counting or additive operational strategies. As higher values or indeterminate quantities were considered, the strategies diversified. The correspondence strategy was the most used and the common approach when students generalized. Students were able to generalize verbally as well as symbolically and varied their strategies flexibly when changing from specific to general cases, showing a clear preference for a functional approach in the latter.

KEYWORDS:

• Algebraic thinking
• early algebra
• generalization
• strategies
• functional relationships
• representations

Acknowledgments

This study was developed within the Spanish projects of Research and Development with reference codes EDU2016-75771-P and PID2020-113601GB-I00, financed by the Spanish Ministry of Economy and Competitiveness. This work is part of the doctoral studies of the first author supported by Universidad de Costa Rica.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 For reasons of confidentiality each student was assigned a number preceded by the letter S.

Additional information

Funding

This study was supported by Spanish national R + D + I projects EDU2016-75771-P and PID2020-113601GB-I00, financed by the State Research Agency (SRA) from Spain; and Universidad de Costa Rica (UCR) [Supports the doctoral studies of the first author].