A surviving notebook of Kiselev's indicates that, for example, in 1915 alone his earnings from 'Arithmetic' and 'Algebra' were ten times greater than his annual pension (which was, it should be noted, almost a general's pension).

... structured in accordance with the views on the exposition of this subject that have been expressed by the authors of the latest French and German handbooks, particularly the former.

Kiselev's textbooks came out on top because they were exemplars of a teacher's common sense and experience. The well-known Russian mathematics educator Ivan Andronov (1941) once wrote that Kiselev knew his strengths and did not undertake that for which his strengths might not have been sufficient. Kiselev's textbooks are well-organized and logical (later, they were found to contain not a few logical gaps, but all of these were beyond the understanding of the ordinary student). In the course in geometry - Kiselev's most popular course - practically all of the assertions are grounded and proved. But Kiselev never tried to offer a strict axiomatic course with complete indication of axioms and all of the references that a professional mathematician would have considered necessary.

The most shining example is Kiselev's treatment of the circumference and π. Circumference is defined as the limit of the perimeters of regular polygons inscribed into the circle when the number of sides is doubled indefinitely. Doesn't that sound impressive? But consider then that Kiselev precedes the definition with a reasonably developed theory of limits. The book gives a very clear introduction into the theory of limits which, although not 100% rigorous, neither noticeably cuts corners. For example, the book does prove that the limit (which is the circumference) exists. This comes after a thorough discussion of similarity. In particular, he proves that regular polygons with the same number of sides are similar, and their sides have the same ratio as their radii. Combining this with the theory of limits he derives the fact that the ratio of the circumference to the diameter is the same for all circles and thus introduces π.

On the whole, the economy of presentation is nothing short of remarkable. Just to take one example: Cavalieri's Principle. Kiselev rightly observes that to justify it one needs methods that would go beyond elementary mathematics. However, the principle is elegant and useful and mentioning it supplies an engaging historical background along with a viable demonstration of the continuity of the evolution of mathematics over time. So, based on the theory of limits developed in the first part (Planimetry), Kiselev proves (although without ever employing the symbol lim) the principle for triangular pyramids and uses the occasion to mention Hilbert's third problem. Later on, he applies the principle to determine the volume of a ball (but now without proof) and makes use of the opportunity to mention the work of Archimedes and of the recovery of his tomb by Cicero.

I am happy that I lived to see the days when mathematics became the property of the broad masses. Is it possible to compare the meagre circulation of pre-revolutionary times to the present. And it's not surprising. After all, the whole country is now studying. I am glad that in my old age I can be useful to their great motherland.

At that time, the liberally-minded public took a decisive stand against examinations as a practice that constrained students, engendered a regime of rigid control, and so on. Kiselev spoke about the various "aberrations" in the schools: the fact that classes were overcrowded, the fact that there was not enough time properly to interview and assess all of the students in a class, the fact that school schedules were poorly designed, as a result of which there were "empty" lessons at the end of the year, which students spent playing games. He spoke about the importance of independent work and examinations as a means of instigating students to engage in such work, and he pointed out that an examination is often the teacher's only opportunity thoroughly to evaluate the students. He concluded his report, however, not by urging that examinations be preserved, but merely by recommending that no support be given to petitions for their elimination, leaving the decision to others.