This paper examines various cognitive strategies applied while CAS (Computer Algebra System) are used in undergraduate-level engineering mathematics teaching and learning. We posed some questions in relation to such CAS use: What kind of tools can CAS offer to enhance different cognitive strategies of students? How can the use of CAS widen the range of students' cognitive strategies and affect pragmatic, heuristic, and epistemic thinking schemes? How can CAS enhance metacognition and cognitive self- efficacy? How can CAS-enhanced curricula benefit from the examination of various cognitive strategies? How can the examination of CAS-related cognitive strategies assist modularisation of topics and thickening the "knowledge-representation network"? In this paper, we offer some examples to illustrate issues raised by the questions above. (Contains 9 figures.)