# Students’ development of structure sense for the distributive law

## Abstract

After being introduced to the distributive law in meaningful contexts, students need to extend its scope of application to unfamiliar expressions. In this article, a process model for the development of structure sense is developed. Building on this model, this article reports on a design research project in which exercise tasks support students in developing their structure sense for the distributive law by means of structural mappings and guiding examples. A design experiment was conducted in six groups, each consisting of two eighth graders. Two contrasting cases are qualitatively analyzed and compared in terms of the development of the students’ structure sense for the distributive law. Theoretically, this article provides a development model for structure sense. Empirically, six characteristics of these development processes are reconstructed. Under certain conditions that are discussed in the end, the exercise tasks can help students to develop their structure sense for the distributive law.

### Keywords

Algebra Design research Distributive law Structure sense## Notes

### Acknowledgements

I would like to thank Susanne Prediger and the anonymous reviewers for their valuable and constructive feedback on previous versions of this paper.

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