What Group Theory Can Do for You: From Magmas to Abstract Thinking in School Mathematics

Veith, Joaquin M.; Bitzenbauer, Philipp

doi:10.3390/math10050703

Cited by 9 publications

(27 citation statements)

References 39 publications

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“…The Hildesheim Teaching Concept is a teaching concept focusing on introductory group theory elements aimed at secondary and undergraduate mathematics education. Details regarding the Hildesheim Teaching Concept are presented in our earlier contribution [8]. Hence, we only outline the main aspects here.…”

Section: The Hildesheim Teaching Conceptmentioning

confidence: 99%

“…Over the past 10 years, research into educational aspects of abstract algebra has gained increasingly more traction. With the works of Wasserman et al [1][2][3][4] and Melhuish [5][6][7], various studies have shown the benefits of learning abstract algebra and group theory in particular, as well as different pitfalls for students-an overview of the research results in this regard is presented in [8].…”

Section: Introduction 1literature Reviewmentioning

confidence: 99%

“…In addition, in our prior research contributions (cf. [8,11,13]) we derived desiderata regarding abstract algebra education from the literature (cf. [12,[17][18][19][20][21][22]).…”

Section: Introduction 1literature Reviewmentioning

confidence: 99%

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Exploring Learning Difficulties in Abstract Algebra: The Case of Group Theory

2022

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In an earlier contribution to Education Sciences we presented a new concept inventory to assess students’ conceptual understanding of introductory group theory—the CI2GT. This concept inventory is now leveraged in a pretest-post-test design with N=143 pre-service teachers to enrich this body of work with quantitative results. On the one hand, our findings indicate three recurring learning difficulties which will be discussed in detail. On the other hand, we provide a summative evaluation of the Hildesheim Teaching Concept and discuss students’ learning gain in different sub-domains of group theory. Together, the results allow for an empirical perspective on educational aspects of group theory and thus bridge the gap between qualitative and quantitative research in this field which constitutes a desideratum to date.

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Section: The Hildesheim Teaching Conceptmentioning

confidence: 99%

Section: Introduction 1literature Reviewmentioning

confidence: 99%

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Exploring Learning Difficulties in Abstract Algebra: The Case of Group Theory

2022

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“…In addition, the perceived difficulty was well below the center of the scale (µ=2.88), insinuating that the abstract concepts of algebra (cf. Veith & Bitzenbauer, 2022) were didactically conveyed in a comprehensible manner and did not evoke a sense of overload.…”

Section: Discussion Of Rq1mentioning

confidence: 99%

“…In recent years a body of research has emerged, entirely dedicated towards exploring educational aspects of abstract algebra (Wasserman, 2014(Wasserman, , 2016(Wasserman, , 2017(Wasserman, , 2018 and group theory in particular (Melhuish, 2015(Melhuish, , 2019Melhuish & Fagan, 2018;Pramasdyahsari, 2020;Veith & Bitzenbauer, 2022;Veith et al, 2022aVeith et al, , 2022bVeith et al, , 2022c. Even though group theory is mostly taught on university level mathematics, numerous connections to primary and secondary school mathematics have been uncovered (cf.…”

Section: Introductionmentioning

confidence: 99%

The role of affective learner characteristics for learning about abstract algebra: A multiple linear regression analysis

Veith

Girnat

Bitzenbauer

2022

EURASIA J Math Sci Tech Ed

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Recent research has boosted the inclusion of introductory group theory into secondary and undergraduate mathematics education due to manifold potentials, e.g., with regards to the promotion of students' abstract thinking. However, in addition to research on cognitive processes, learners' affective characteristics have largely remained unexplored in the context of teaching and learning group theory to date. In this paper, we contribute to closing this gap: We report on an empirical study investigating n=143 students' affective characteristics within a two-weeks course program-the Hildesheim teaching concept. In our study, this concept was used to introduce preservice primary teachers into group theory. A multiple linear regression analysis reveals that neither mathematics-specific ability self-concept nor subject interest are significant predictors of the achieved conceptual understanding of group theory after the intervention indicating that group theory is not reserved for only the mathematically interested students or students with a high mathematics-specific self-concept.

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How do pre-service teachers view Galois theory? A questionnaire study

Veith,

Girnat,

Winkler

et al. 2024

EURASIA J Math Sci Tech Ed

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algebra is an important part of mathematics teacher education as it provides the rigorous mathematical foundations for many mathematics topics covered in school classrooms. Throughout their academic career, many secondary mathematics teachers even enroll in more advanced algebra courses, which often culminate in Galois theory. However, very little is known about educational aspects of Galois theory and respective mathematics education research is scarce. We contribute to closing this gap by reporting on the results of an exploratory questionnaire study with a sample of n=39 pre-service mathematics teachers, inquiring about the raison d’être of incorporating Galois theory into teacher education: Is Galois theory viewed as useful for their later profession and which connections are drawn to the secondary mathematics classroom? On the one hand, the results of our study indicate that a vast majority of pre-service teachers do not perceive studying Galois theory as meaningful and struggle to exemplify connections between Galois theory and secondary school mathematics. On the other hand, a small share of the participants experienced Galois theory as an important part of mathematics that elegantly connects a variety of algebraic and geometric notions.

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What Group Theory Can Do for You: From Magmas to Abstract Thinking in School Mathematics

Cited by 9 publications

References 39 publications

Exploring Learning Difficulties in Abstract Algebra: The Case of Group Theory

Exploring Learning Difficulties in Abstract Algebra: The Case of Group Theory

The role of affective learner characteristics for learning about abstract algebra: A multiple linear regression analysis

How do pre-service teachers view Galois theory? A questionnaire study

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