This paper discusses the implementation of challenging and non-routine questions (CNRQs), in our school's mathematics and science tutorial exercises and examination papers aimed at training students to attain higher levels of understanding and greater proficiency in the subject matter. This assessment initiative was carried out with the belief that assessment drives students' learning because "what is considered important to (be) assessed will strongly determine what is considered important to learn" (Mclellan, 2001, p. 309) and when assessment is used appropriately, it can play a powerful role in teaching students better (Popham, 2011). After two semesters of implementation, eight lecturers' and 253 students' perceptions on the assessment initiative were solicited. Examination questions were analysed using the Taxonomy Table to reflect on lecturers' perceptions of CNRQs as exemplified in the assessment items. The findings showed that all the lecturers were generally supportive of the initiative but they faced implementation challenges. While many academically able students welcomed CNRQs in their modules, the less able students expressed learning anxiety in mathematics and science classrooms. A great majority of CNRQs were classified as those requiring Cognitive Process Apply and Knowledge of Procedural and Conceptual in the Taxonomy Table. Four implementation challenges identified will be discussed followed by a set of recommendations to further improve our assessment initiative.