Karrass Margaret author Teachers College. Mathematics Education Vogeli Bruce R. thesis advisor Teachers College. Mathematics, Science, and Technology Teachers College. Mathematics Education originator text Dissertations 2012 English 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. Ph.D., Columbia University. Mathematics education http://hdl.handle.net/10022/AC:P:12378 NNC NNC 2012-01-27 15:13:57 -0500 2012-05-24 14:16:24 -0400 6375 eng