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The Design And Validation Of A Group Theory Concept Inventory, Kathleen Mary Melhuish
The Design And Validation Of A Group Theory Concept Inventory, Kathleen Mary Melhuish
Dissertations and Theses
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 consensus 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 …
An Investigation Of The Role Of Alternate Numeration Systems In Preservice Teacher Mathematics Content Courses, Jodi I. Fasteen
An Investigation Of The Role Of Alternate Numeration Systems In Preservice Teacher Mathematics Content Courses, Jodi I. Fasteen
Dissertations and Theses
Alternate numeration systems are common in preservice teacher (PST) mathematics curricula, but there is limited research on how to leverage alternate systems to promote the development of mathematical knowledge for teaching. I analyzed the role of alternate numeration systems in three ways. I conducted a thematic analysis of current PST textbooks to consider the role of alternate numeration systems in written curricula. I conducted a teaching experiment to analyze PSTs' mathematical activity as they engaged with a base five task sequence to reinvent an algorithm for multiplication. And I introduced problematizing mathematical contexts as a design heuristic, situating this within …