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

Zandieh, Michelle; Adiredja, Aditya P.; Knapp, Jessica

doi:10.1007/s11858-019-01033-z

Cited by 12 publications

(5 citation statements)

References 24 publications

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“…Although Tall's model includes a cognitive viewpoint, in some cases, the metaphor theory by Lakoff and Núñez (2000) gives a deep insight on students' cognitive process of understanding mathematical concepts from a viewpoint of cognitive science. Students' use of metaphors in understanding linear algebra concepts was reported in some studies: e.g., (Plaxco & Wawro, 2015), (Zandieh, Adiredja, & Knapp, 2019). However, the metaphor theory by Lakoff and Núñez (2000) is more fundamental.…”

Section: B Metaphor Theory By Lakoff and Núñezmentioning

confidence: 99%

Relation between understandings of linear algebra concepts in the embodied world and in the symbolic world

Kawazoe

2023

epiDEMES

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For the use of embodied notions in teaching linear algebra, some studies indicate that it is helpful, whereas other studies indicate that it could be problematic or become an obstacle. Hence, additional research is needed. This study is focused on linear (in)dependence and basis, and investigates the relation between their understandings in the embodied and symbolic worlds. We also examine whether students' conceptions in the embodied world can be improved by the instruction emphasizing geometric images, as our previous studies identified some limitations of students' understanding in the embodied world. To address these issues, we designed four tasks aiming to assess students' conceptions of linear (in)dependence, basis, and dimension, and also designed linear algebra lessons emphasizing geometric images of these concepts. These tasks were conducted during the lessons and the data of 38 engineering students was collected. The analysis for the data showed that conceptions in the embodied world was positively associated with conceptions in the symbolic world; however, students' conceptions in the embodied world were not sufficiently improved by the geometric instruction implemented in this study.

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Section: B Metaphor Theory By Lakoff and Núñezmentioning

confidence: 99%

Relation between understandings of linear algebra concepts in the embodied world and in the symbolic world

Kawazoe

2023

epiDEMES

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“…The study that inspired the current paper asked students to explain the notion of a basis using everyday ideas and found that traveling is one of 22 different ideas that a group of women of color were able to generate [3]. It also uncovered nuances of the concept of basis, which has led to useful analytical codes for analyzing student understanding [19]. The study was designed to challenge deficit narratives about the intellectual capacity and contributions of women of color in mathematics by uncovering potential learning resources from this group of students.…”

Section: Basis Everyday Ideas and Women Of Color: Research Inspirationmentioning

confidence: 99%

“…The students used different everyday contexts to describe basis. Their examples include some of the ones reported in [3,4] and [19] (e.g., fashion/clothing, directions in a city, bricks, and recipe/ingredients), and some new ones (e.g., actions defining a typical morning for a person, basic human needs, colors for painting, and majors in a college). Their examples included details about linear independence, scalar multiples and linear combinations, subspaces, and change of basis.…”

Section: Students' Responsesmentioning

confidence: 99%

“…Those concepts can feel abstract and not tangible for students, but students' own intuitive examples can be helpful: it may be easier for students to grapple with the difference between a burrito, the space of all burritos, and representative ingredients one uses to make a burrito. The word "basis" and its nonmathematical uses in the language also provide an additional connection to students' intuition [19]. This need for a grounding imagery of an abstract content could also be seen in topics like the formal definition of a limit [1,8].…”

Section: Other Suitable Topicsmentioning

confidence: 99%

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Everyday Examples About Basis From Students: An Anti-Deficit Approach in the Classroom

Adiredja¹,

Bélanger-Rioux

Zandieh³

2019

PRIMUS

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In this paper we share a classroom implementation of a task about basis in linear algebra, which was originally developed for research about the topic. The task asks students to construct an everyday situation that captures the definition of basis, and then to critique it mathematically. Using this task, the original research study uncovered learning resources from a group of undergraduate women of color. A mathematician who was not involved in the original study was given the opportunity to work with a group of underrepresented minority students in a linear algebra course. She was inspired by the findings of the study and decided to implement the task independently in her course. She shares how she did it, how her students responded to the task, and how it helped her further develop her understanding of an anti-deficit perspective in teaching mathematics.

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“…Regarding the field of linear algebra education research, a comprehensive overview of the years 2008 to 2017 is provided by Stewart et al (2019a)-themes, results and perspectives from contemporary research are discussed detailing how "students reason about a variety of topic areas in linear algebra, as well as studies that provide evidence of promising directions for supporting students success through various teaching interventions and experiments in the classroom" (Stewart et al, 2019a, p. 1,017) in order to derive possible directions for future research. Moreover, several frameworks for student understanding of linear algebra concepts have been developed in recent years, for example by Zandieh et al (2019) in the context of bases of vector spaces, or • Larson and Zandieh (2013) regarding a conceptual framework concerned with the interpretation of matrix equations which was later expanded to include more general systems of linear equations (Zandieh and Andrews-Larson, 2019).…”

mentioning

confidence: 99%

Mathematics education research on algebra over the last two decades: quo vadis?

Veith,

Beste,

Kindervater

et al. 2023

Front. Educ.

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Algebra is a crucial component of mathematics education as it introduces learners to the mathematical world of modeling relationships and handling abstract quantities. The increasing volume of scholarly work in the field has been analyzed qualitatively in numerous systematic reviews—a quantitative breakdown of the field, however, remains a desideratum to date. With this study we contribute to closing this gap by reporting on the results of a bibliometric analysis. We retrieved data from Scopus and Web of Science databases and analyzed 1,825 articles published between 2003 and 2022. On the one hand, we provide insight into the current state of algebra education from primary up to tertiary education by describing the scientific production and its bibliographic topography. On the other hand, we analyzed the data to identify trends and future directions. The results of our study indicate, among other aspects, that APOS Theory and Realistic Mathematics Education are emerging themes in the field that have great potential to shape future research.

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

Cited by 12 publications

References 24 publications

Relation between understandings of linear algebra concepts in the embodied world and in the symbolic world

Relation between understandings of linear algebra concepts in the embodied world and in the symbolic world

Everyday Examples About Basis From Students: An Anti-Deficit Approach in the Classroom

Mathematics education research on algebra over the last two decades: quo vadis?

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