First Advisor

Eva Thanheiser

Date of Publication

Spring 6-2-2015

Document Type


Degree Name

Doctor of Philosophy (Ph.D.) in Mathematics Education


Mathematics and Statistics




Student teachers -- Training of, Mathematics -- Study and teaching (Elementary) -- Methodology, Numeration -- Study and teaching (Elementary) -- Methodology



Physical Description

1 online resource (viii, 218 pages)


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 the design theory of Realistic Mathematics Education. I found that alternate numeration systems can be leveraged to create opportunities for PSTs to (a) engage in guided reinvention of an algorithm, (b) improve understanding of base ten by comparing it to other numeration systems, and (c) reflect on their learning experience and the learning experiences of children.


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