The traditional teaching approaches are generally teacher-directed where students are taught in a manner conducive to sitting and listening. It is true that traditional philosophies often allow us to continue with the lecture-based model with some useful results. However it is often argued that the traditional approach may not provide students with valuable skills. The teaching of mathematics that is usually referred to or called non-traditional uses constructivist philosophy as its basis; this implicates strategies in which an individual is making sense of his or her universe. So the student is an active participant, which may help develop, construct or rediscover knowledge – a major goal that can be a time consuming process if taken literally for each student; alternately, there is also a philosophical position known as social constructivism suggests group work, using a specialist language of the field, and discourse learning its cultural framework; social intercourse and problem solving being the most important part of learning process. It is argued that the nontraditional teaching is done using a problem solving or inquiry based approach; where the learner is the problem solver. Therefore, e-learning is considered to be more in line with the non-traditional approaches than the traditional. This paper critically reviews the literature on mathematics and engineering learning in terms of these approaches and compares them. The paper specifically examines the advantages/disadvantages of the approaches as well the manner in which they influence performance of students in mathematics and engineering courses.