# Exploring everyday examples to explain basis: insights into student understanding from students in Germany

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## Abstract

There is relatively little research specifically about student understanding of basis. Our ongoing work addresses student understanding of basis from an anti-deficit perspective, which focuses on the resources that students have to make sense of basis using everyday ideas. Using data from a group of women of color in the United States, we previously developed an analytical framework to describe student understanding about basis, including codes related to characteristics of basis vectors and roles of basis vectors in the vector space. In this paper, we utilize the methods of the previous study to further enrich our findings about student understanding of basis. By analyzing interview data from students in Germany, we found that this group of students most often used ideas that we describe by the roles generating, structuring, and traveling, and the characteristics different and essential. Some of the themes that emerged from the data illustrate common pairings of these ideas, students’ flexibility in interpreting multiple roles within one everyday example, and the ways that the roles and characteristics motivate students to create additional examples. We also discuss two ways that differences between the German and English languages were pointed out by students in the interviews.

## Keywords

Linear algebra Basis Everyday examples Student thinking Conceptual metaphor## Notes

### Acknowledgements

This material is based upon work supported by the National Science Foundation under grant numbers DUE-1246083 and 1712524. 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 NSF.

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