Calculus Students’ Visual Thinking of Definite Integral

Chih Hsien Huang^1,

¹Department of Electrical Engineering, Ming Chi University of Technology, New Taipei City, Taiwan, ROC

Cite this paper:
Chih Hsien Huang. Calculus Students’ Visual Thinking of Definite Integral. American Journal of Educational Research. 2015; 3(4):476-482. doi: 10.12691/education-3-4-14

Abstract

Visualization as both the product and the process of creation, interpretation and reflection upon pictures and images, is gaining increased visibility in mathematics and mathematics education. The use of diagrams to visualize definite integral concept, however, is problematic for many students and may actually hinder their problem-solving efforts. The purpose of this study, not only extends our understanding of students’ difficulties and strengths associated with visualization but also identifies types of visual image they utilized while solve integral problems. Through the detailed analyses of students' work and verbal protocols, the students with high visualization ability use of imagination images in high percentages along with algebraic representations and linking these two representations lead to the success of problem solving. The students with low visualization ability use of memory images. It is discovered that students can produce imagination images that play a significant role in a problem solving process. As such, a process of visualization allows an articulation between representations to produce another representation that could help students solve given problems.

Keywords:
calculus students definite integral representation visual thinking visualization

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