I present an operational model of how students simplify trigonometric expressions. The model has three main components: recognising, recalling and doing. This paper describes the interaction between these components and links this model to other models of doing mathematics. (Contains 2 figures and 1 table.)

This textbook, designed for at least one and one-half year's work in algebra, is intended for the use of those schools which find a one-book course best adapted to their needs. Experience thoroughly justifies a careful review at the beginning of the third half year's work. As the first twenty-three chapters contain the greater portion of the usual…

This textbook combines the material of the "New First Course in Algebra" and the "New Second Course in Algebra" in a form convenient for use in courses of more than a year in length. A large amount of review material is to be found at the point where the second year of work commences, since it was felt that there should be an…

Spirolaterals, figures derived from a logically constructed set of rules involving patterns of lengths and of turns through specified angles, are explained and analyzed, and unsolved problems are discussed. (DT)

Illustrated is the use of arithmetic modulo 2 for finding the truth values of logical statements. (MM)

This article suggests using mathematical terms (rationals, integers, naturals) to designate ability groups of students in a class. (MM)

Results of using platonic solids for probability experiments are presented. (JG)

Reprinted is "Shanks, Ferguson and pi" by T. A. A. Broadbent. It describes the historical development of the mechanical calculation of the number pi. (CT)