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

Michelle Zandieh, Aditya Adiredja, Jessica Knapp

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

Original languageEnglish (US)
JournalZDM - Mathematics Education
DOIs
StatePublished - Jan 1 2019

Fingerprint

student
Pairing
Vector space
Flexibility
Resources
German language
interview
English language
deficit
flexibility
Group
Language
Color
Framework
resources

Keywords

  • Basis
  • Conceptual metaphor
  • Everyday examples
  • Linear algebra
  • Student thinking

ASJC Scopus subject areas

  • Education
  • Mathematics(all)

Cite this

Exploring everyday examples to explain basis : insights into student understanding from students in Germany. / Zandieh, Michelle; Adiredja, Aditya; Knapp, Jessica.

In: ZDM - Mathematics Education, 01.01.2019.

Research output: Contribution to journalArticle

@article{5ab005dc7f0a4c20bedbbe36084bbc76,
title = "Exploring everyday examples to explain basis: insights into student understanding from students in Germany",
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 = "Basis, Conceptual metaphor, Everyday examples, Linear algebra, Student thinking",
author = "Michelle Zandieh and Aditya Adiredja and Jessica Knapp",
year = "2019",
month = "1",
day = "1",
doi = "10.1007/s11858-019-01033-z",
language = "English (US)",
journal = "ZDM - International Journal on Mathematics Education",
issn = "1863-9690",
publisher = "Springer Verlag",

}

TY - JOUR

T1 - Exploring everyday examples to explain basis

T2 - insights into student understanding from students in Germany

AU - Zandieh, Michelle

AU - Adiredja, Aditya

AU - Knapp, Jessica

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Basis

KW - Conceptual metaphor

KW - Everyday examples

KW - Linear algebra

KW - Student thinking

UR - http://www.scopus.com/inward/record.url?scp=85061228727&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85061228727&partnerID=8YFLogxK

U2 - 10.1007/s11858-019-01033-z

DO - 10.1007/s11858-019-01033-z

M3 - Article

JO - ZDM - International Journal on Mathematics Education

JF - ZDM - International Journal on Mathematics Education

SN - 1863-9690

ER -