Kruteskii's work on the mathematical abilities of school children is a seminal work on the nature of mathematical ability. However, the task of developing methods for the practical application of his work is still a significant problem in mathematics education. The authors have developed a practical application of Kruteskii's approach to the important problem of "initially developing components of mathematical ability in student and thereafter identifying" mathematically promising students. Examples of problems that were designed to develop ability to generalize, flexibility and reversibility of mental processes are presented. A practical guide for determining the level of development of components of mathematical abilities in individual students, in terms of specified observables, is presented as a set of structured reference tables. The authors set out a practical application protocol that combines use of the tables and sets of specially developed problems for initial development of mathematical abilities prior to identification of mathematically promising students in the general classroom. A significant motivation for this work is the desire to avoid time-consuming and resource intensive practices such as interviews and summer schools which therefore have been used successfully because these practices are now out of reach for all but very wealthy countries or highly ideologically driven systems. On the other hand, special examinations heavily depend on the level of preparedness of the students for the particular examination, and therefore some students with high abilities but with fewer opportunities to prepare could be overlooked. (Contains 1 note, 1 table, and 2 figures.)