eng Science and Education Publishing American Journal of Educational Research 2327-6150 2015-11-24 3 12 1484 1488 10.12691/education-3-12-1 EDUCATION20153121 article Chih-Hsien Huang huangch@mail.mcut.edu.tw 1 Ming Chi University of Technology Deciding on the truth value of mathematical statements is an essential aspect of mathematical practice in which students are rarely engaged. This study explored first year engineering students' approaches to mathematical statements with unknown truth values, taking a perspective that the construction examples is an activity of problem solving. Task-based interviews utilizing the think-aloud method revealed students problem solving processes in depth. The primary data sources were the protocols of 15 students to the questionnaire, three false statements involved basic concepts about derivative and definite integral. Through analysis of the data. The findings suggest that the factors the participants failed to solves problems include: mathematical intuition and prototype example hindered the constructing of counterexamples, there are two dangers in visualizing -figures can induce false conclusions and figures can mislead our reasoning. http://pubs.sciepub.com/education/3/12/1/education-3-12-1.pdf engineering students intuition problem solving visualization