Theses Doctoral

Diagrammatic Reasoning Skills of Pre-Service Mathematics Teachers

Karrass, Margaret

This study attempted to explore a possible relationship between diagrammatic reasoning and geometric knowledge of pre-service mathematics teachers. Diagrammatic reasoning skills, as a sequence of steps from visualization, to interpretation, to formalisms, are at the core of teachers"™ content knowledge for teaching. However, there is no course in the mathematics curriculum that systematically develops diagrammatic reasoning skills, except Geometry. In the course of this study, a group of volunteers in the last semester of their teacher preparation program were presented with "visual proofs" of certain theorems from high school mathematics curriculum and asked to prove/explain these theorems by reasoning from the diagrams. The results of the interviews were analyzed with respect to the participants"™ attained van Hiele levels. The study found that participants who attained higher van Hiele levels were more skilled at recognizing visual theorems and "proving" them. Moreover, the study found a correspondence between participants"™ diagrammatic reasoning skills and certain behaviors attributed to van Hiele levels. However, the van Hiele levels attained by the participants were consistently higher than their diagrammatic reasoning skills would indicate.


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More About This Work

Academic Units
Mathematics Education
Thesis Advisors
Vogeli, Bruce R.
Ph.D., Columbia University
Published Here
January 25, 2012