The Guide one book in three volumes

This is a book of reasons. Every rule of arithmetic it teaches comes from something the child has first done with her hands, and then it is given its reason. It is written for you, the parent at the kitchen table or the teacher with a class, and it teaches a child from about six, one short sitting at a time, over six years. A sitting is work on one idea, done with real objects: ten to fifteen minutes in grades 1 to 4, and twenty to thirty in grades 5 and 6. You need no more mathematics than you learned at school: every rule is explained in full before you teach it.

Each section starts with the argument, for you to read the evening before. It gives the reason in full, so that you can answer a question the book did not foresee. Then comes the sitting for the child, at every grade that meets the section: what to set on the table, what to say and ask, and the sentence to listen for.

Taught twice. The book follows the Russian school it comes from, which taught arithmetic in two passes. In grades 1 to 4 the child does arithmetic with sticks, cubes and coins, and nobody asks her for a definition or a proof. In grades 5 and 6 she meets the same arithmetic again, and every rule is given its reason. That second pass is A. P. Kiselev’s course, which gives the thirty chapters their order. So a section often has two sittings, one that teaches the skill with objects and one, in grade 5 or 6, that says why it works. A grade means the year of the course, not the child’s age.

The three volumes

The volumes each grade needs