eng Science and Education Publishing American Journal of Educational Research 2327-6150 2015-04-08 3 4 476 482 10.12691/education-3-4-14 EDUCATION20153414 article Chih Hsien Huang huangch@email.mcut.edu.tw 1 Department of Electrical Engineering, Ming Chi University of Technology, New Taipei City, Taiwan, ROC 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. http://pubs.sciepub.com/education/3/4/14/education-3-4-14.pdf calculus students definite integral representation visual thinking visualization