"Although there are some subjective opinions supporting the hypothesis that geometrical and topological topics are teachable at the elementary school level there is the need for definitive research which can answer the following questions: 1. What factors relate to a student's achievement with geometrical and topological topics? 2. At what grade levels are certain topics learned with a high degree of efficiency in terms of time and expended effort? 3. Which geometrical and topological topics are appropriate at various grade levels in terms of these topics serving to clarify and simplify other types of mathematical concepts? The primary purpose of this study was to investigate some factors which might serve as predictors of pre-determined levels of success with respect to some selected topics in geometry and point set topology, when taught to fifth-, sixth- and seventh-grade pupils via a programmed text"--Introduction. / Typescript. / "August, 1963." / "Submitted to the Graduate School of Florida State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy." / Advisor: E. D. Nichols, Professor Directing Dissertation. / Includes bibliographical references.