This study is motivated by the desire to address some of the enormous challenges faced by the students as well as the lecturer in fulfilling their respective expectations and duties demanded by the process of learning--teaching of mathematics and statistics within the framework of the constraining schedules laid down by the academic institutions and universities responsible for imparting education to students pursuing various degree programmes. The difficulties encountered in the efficient dissemination of instructions and the response of the students constitute a mechanism within which to suggest possible ways to rectify at least partially, if not wholly, the lacunae in the system and the methodology adopted by the participants engaged in this endeavour. A reasonably detailed, but by no means exhaustive, account is given of the historical developments in both mathematics and statistics primarily to arouse the interest of the students to such a level of inspiration that they draw pleasure while learning the subject. The expectations of the students as well as those of the lecturer are enumerated to a fair degree of thoroughness and possible remedial steps are suggested to minimise the differences in their perceptions using, for the first time, the famous uncertainty principle of Heisenberg, rather than employing any traditional/conventional methods that rely heavily on numerical evaluations. Wherever found essential, the scope and the goal are discussed in an environment typified by appropriate examples and similes. If followed conscientiously, the recommendations made in this paper can contribute effectively to the learning-teaching scenario with potentially significant results.