This study is an initial analytic attempt to iteratively develop a conceptual framework informed by both theoretical and practical perspectives that may be used to analyze non-textual elements in mathematics textbooks. Despite the importance of visual representations in teaching and learning, little effort has been made to specify in any systematic way the characteristics and roles of non-textual elements in mathematics textbooks. A non-textual element in this study denotes a visual representation that is comprised of components that are not purely verbal, numerical, or mathematical symbolic representations. Non-textual elements thus include, for example, photos, pictorial illustrations, graphs, and mathematical abstract figures. Based on the results from the iterative investigations including pilot studies (a survey of students followed by a preliminary textbook analysis), and analyses of data from interviews with teachers (11 South Korean and 10 U.S. teachers) and curriculum developers (four South Korean and three U.S. textbook authors), this study has developed the Final Framework (F-Framework) for non-textual elements, in which "accuracy," "connectivity," "contextuality," "simplicity," and "aesthetics" are the central aspects. In particular, this F-Framework suggests that "accuracy" and "connectivity" are the fundamental aspects that every non-textual element should possess; "contextuality," "simplicity," and "aesthetics" are useful aspects that may facilitate the teaching and learning of mathematics. The validity and reliability of the F-Framework were tested by examining lessons about angle, slope, and prime factorization in four South Korean and three U.S. mathematics textbooks. Through the iterative process to develop the framework, this study found theoretical and practical issues around non-textual elements that may be useful for future research. Although all the five aspects of non-textual elements in the F-Framework were considered important, curriculum developers and teachers had different interpretations and emphases on each aspect in different contexts, which were also related to their theoretical and practical concerns. Continuous dialogue between teachers and curriculum developers is needed to explore ways in which the effects of non-textual elements on student learning can be improved. The results from the textbook analysis suggest that textbooks may provide different opportunities to learn different mathematical ideas, which may affect students' understanding of mathematical concepts. This study provides useful implications on curriculum development, teacher education, and educational policy. Further investigations about how non-textual elements are used in other topics of mathematics textbooks as well as how to improve non-textual elements should be followed. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]