Visualization in Calculus

Recent curricular efforts have placed increased emphases on establishing bridges between visual and analytic representations of fundamental calculus concepts. The role of visual thinking is so fundamental to the understanding of calculus that it is difficult to imagine a successful calculus course which does not emphasize the visual elements of the subject (Zimmerman, 1991). However, as outlined in Eisenberg & Dreyfus (1991) , there seem to be valid reasons as to why students have difficulty thinking in visual frameworks. Understanding these reasons should help in the development of suitable materials and learning strategies to promote visual thinking. This project will investigate several hypotheses, ambiguities, and needs generated by research on in mathematics, the relationships of visualization skills to specific concepts in calculus, and the potentials of spatial training in enhancing mathematical understanding. The specific research questions are as follows:

• What is the role of visualization in understanding the fundamental calculus concepts?
• What effects does spatial training have on college students' calculus achievement and spatial visualization ability?
• Are there gender differences in calculus achievement and use of visualization?
• Does spatial training affect men and women differently?