Murray Black, Farida Kachapova and Ilias KachapovThe paper gives a brief overview of the relations between procedural and conceptual knowledge and emphasizes the importance of developing effective mathematical techniques. The paper describes and analyses some teaching strategies used by the authors in a classroom in order to improve students? learning of some mathematical techniques and their understanding of the relevant concepts. We show how the substitution method can be applied to some classes of mathematical problems where traditionally other methods are used. The problems are completing the square, solving quadratic equations, evaluating the limits of indeterminate form 0/0 and integrating rational functions with a quadratic in the denominator. We also analyse how the method of probability trees is used in problems about conditional probability and the ways to improve this teaching strategy.