### Abstract

**Background:**

Flexibility in transforming algebraic expressions is recognized as fundamental for a rich procedural knowledge. Here, flexibility in-depth is proposed as the ability to apply one strategy to a wide range of unfamiliar expressions.**Material and methods:**

In this study, design experiments with four groups of students were conducted to support students’ flexibility in-depth in regard to the application of the distributive law with the help of worked examples. The data from these experiments was analyzed qualitatively with the method of content analysis.**Results:**

Students’ flexibility in-depth translates into their abilities to reconstruct the distributive property within an expression via its perceived relevant structural features. The students’ use individual cornerstones for this reconstruction, for example worked examples or certain focal points in an expression like the multiplication sign.**Conclusions:**

Transforming expressions and especially applying formulas to algebraic expressions is thus an interpretative and reconstructive process.

### License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, 2016, Volume 12, Issue 10, 2719-2732

https://doi.org/10.12973/eurasia.2016.1307a

Publication date: 25 Jul 2016

Article Views: 1561

Article Downloads: 1064

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