Development of students' understanding of cosets, normality, and quotient groups

Asiala, Mark; Dubinsky, Ed; Mathews, David; Morics, Steven; Oktaç, Asuman

doi:10.1016/s0732-3123(97)90029-8

Cited by 56 publications

(19 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A similar error occurred when students commonly confuse normality with commutativity (Asiala et al, 1997). This type of reduction is consistent with Selden and Selden (1987) and Hart (1994) Lowering abstraction has also been illustrated when students reason using…”

Section: The First Level Is Abstraction Level As the Quality Of The Rsupporting

confidence: 79%

“…Dubinsky et al presented example students who never wrote out all of the elements of cosets and worked entirely with their representatives. Dubinsky and his colleagues also provided this type of genetic breakdown for binary operation (Brown, DeVries, Dubinsky, & Thomas, 1997), normality (Asiala, Dubinsky, Matthews, Morics, & Oktac, 1997), coset multiplication (Asiala et al, 1997), permutations (Asiala, Kleiman, Brown, & Matthews, 1998), and symmetries (Asiala et al, 1998). The researchers worked to validate the framework through analyzing student work on exams and interviewing students.…”

Section: Dubinsky Et Al Summarizementioning

confidence: 99%

“…Then a program (is_group) would input the set and operation into the four previous programs for each axiom to determine if they set and operation form a group (Leron & Dubinsky, 1995 (Asiala et al, 1997).…”

Section: Instruction Of Abstract Algebra: Innovationsmentioning

confidence: 99%

“…The first step towards the creation of the GCI was designing the open-ended survey. These questions reflected known areas of difficulty from the literature (such as a lack of an object view of cosets (Asiala et al, 1997) or misapplication of Lagrange (Hazzan & Leron, 1996)) while remaining representative of the domain.…”

Section: The Creation Of the Assessmentmentioning

confidence: 99%

See 3 more Smart Citations

The Design and Validation of a Group Theory Concept Inventory

Melhuish¹

2000

View full text Add to dashboard Cite

Within undergraduate mathematics education, there are few validated instruments designed for large-scale usage. The Group Concept Inventory (GCI) was created as an instrument to evaluate student conceptions related to introductory group theory topics. The inventory was created in three phases: domain analysis, question creation, and field-testing. The domain analysis phase included using an expert protocol to arrive at the topics to be assessed, analyzing curriculum, and reviewing literature. From this analysis, items were created, evaluated, and field-tested. First, 383 students answered open-ended versions of the question set. The questions were converted to multiple-choice format from these responses and disseminated to an additional 476 students over two rounds.Through follow-up interviews intended for validation, and test analysis processes, the questions were refined to best target conceptions and strengthen validity measures. The GCI consists of seventeen questions, each targeting a different concept in introductory group theory. The results from this study are broken into three papers. The first paper reports on the methodology for creating the GCI with the goal of providing a model for building valid concept inventories. The second paper provides replication results and critiques of previous studies by leveraging three GCI questions (on cyclic groups, subgroups, and isomorphism) that have been adapted from prior studies. The final paper introduces the GCI for use by instructors and mathematics departments with emphasis on how it can be leveraged to investigate their students' understanding of group theory concepts.Through careful creation and extensive field-testing, the GCI has been shown to ii be a meaningful instrument with powerful ability to explore student understanding around group theory concepts at the large-scale.iii Dedication To my parents for teaching me to have a strong work ethic, to live life with kindness, and to pursue a career that truly fulfills you.iv Acknowledgements

show abstract

Section: The First Level Is Abstraction Level As the Quality Of The Rsupporting

confidence: 79%

Section: Dubinsky Et Al Summarizementioning

confidence: 99%

Section: Instruction Of Abstract Algebra: Innovationsmentioning

confidence: 99%

Section: The Creation Of the Assessmentmentioning

confidence: 99%

See 2 more Smart Citations

The Design and Validation of a Group Theory Concept Inventory

Melhuish¹

2000

View full text Add to dashboard Cite

show abstract

“…Some sources of the trouble have been studied in [3] and [2]. For students who might not have difficulty with the content of the definition, we ensured trouble of another kind by asking the students to consider a situation in which coset multiplication was not well-defined.…”

Section: Methodsmentioning

confidence: 99%