# Mathematical Skills and Learning by Invention in Small Groups

## Abstract

The purpose of the present research was to investigate how the effectiveness of learning-by-invention activities may be influenced by the composition of the small groups that engage in them in terms of the mathematical skills of their members. Undergraduates engaged in an “inventing standard deviation” activity. Groups that included both high- and low-skill members generated a broader range of solution attempts and more high-quality solution attempts during the activity. Both the range and quality of solution attempts that were generated related to better uptake of the standard deviation formula from a later lesson. These results suggest that the composition of the small groups that work together may have an impact on the effectiveness of learning-by-invention activities.

## Keywords

Collaborative learning Collaborative problem solving Learning by invention Group composition Mathematical skill## Notes

### Acknowledgments

This research and collaboration was supported by a Studienstiftung des Deutschen Volkes [German National Academic Foundation] Fellowship to Michael Wiedmann and by a Humboldt Research Fellowship to Jennifer Wiley. The data reported here were collected as part of a thesis project submitted by Michael Wiedmann in partial fulfillment of the requirements for the Diploma in Psychology at the University of Freiburg. The authors thank Kelly Currier, Pat Cushen, Olga Goldenberg, Thomas Griffin, Robert Hickson, Allison Jaeger, and Andy Jarosz for their assistance with coding, data collection, and discussions on this project.

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