The earlier sections of this account are concerned with some standard properties of pure recurring decimals. These include the cyclic property, illustrated for example by the decimals representing the six proper fractions with denominator 7, each of which has a period using a cyclic permutation of the digits 142857 It was a question concerning this property, raised by a student, which led to the writer's interest in the properties considered in the later sections. References are given in Dickson's History of the Theory of Numbers, Vol. I, Ch. 6.

The question about the teaching of Mathematics considered most frequently and with most detail is How? This is the main preoccupation of the Mathematical Association Reports on separate subjects : it is of special interest to note that in the Report on the Teaching of Calculus oft repetition of the phrase “ the teacher will know ” implies that the topic is as rich as human nature. Yet for writers in the Mathematical Gazette, and for most scholarship winners, the question is superfluous, though all appreciate a good teacher. (For these too the answer to Why? is simple—the urge of joy or duty.) On the other hand, it would scarcely be denied that for more than two-thirds of the pupils in our schools the question How? is unanswerable under present conditions : for them we are attempting the impossible.