# Growth in children’s understanding of generalizing and representing mathematical structure and relationships

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## Abstract

We share here results from a quasi-experimental study that examines growth in students’ algebraic thinking practices of generalizing and representing generalizations, particularly with variable notation, as a result of an early algebra instructional sequence implemented across grades 3–5. Analyses showed that, while there were no significant differences between experimental and control students on a grade 3 pre-assessment measuring students’ capacity for generalizing and representing generalizations, experimental students significantly outperformed control students on post-assessments at each of grades 3–5. Moreover, experimental students were able to more flexibly interpret variable in different roles and were better able to use variable notation in meaningful ways to represent arithmetic properties, expressions and equations, and functional relationships. This study provides important evidence that young children can learn to think algebraically in powerful ways and suggests that the earlier introduction of algebraic concepts and practices is beneficial to students.

## Keywords

Algebraic thinking Early algebra Instructional intervention Quantitative methods Elementary grades## Notes

### Acknowledgments

The research reported here was supported in part by the National Science Foundation under Awards No. 1219605 and 1219606. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

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