Described are features of a methods course in elementary school mathematics at Colorado State College. An essential purpose of the course is to orient the prospective teacher to the utilization of discovery processes in classroom learning situations. (RP)

Diagnostic evaluation is a major way to help students overcome errors. How such evaluation can be done is discussed, with comments on what should be checked and recorded by the teacher. (MNS)

Two successful procedures for evaluating problem-solving performance in the classroom are shared. Five goals for teaching problem-solving are noted, followed by a discussion of evaluating a child's performance through joint use of: (1) analyzing written work; and (2) observing and questioning students. (MP)

In teaching mathematics to preservice elementary teachers, the author presents classroom incidents for which each student must write what he or she would do in the situation. The write-ups are then discussed in small groups. This technique seems to help students apply the mathematics they are learning to the classroom. (SD)

Discussed are "moves" in teaching mathematics that can serve as a basis for defining understanding. How to characterize and use moves is discussed, with specific examples and research evidence. (MP)

Correction is given to problem involving number grids presented in May, 1969, Arithmetic Teacher. (RS)

A rational presentation of the so-called long division method for extracting the square root of a number. Diagrams are used to show relationship of this technique to the binomial theorem. Presentation exposes student to many facets of mathematics in addition to the mechanics of funding square root and cube root. Geometry, algebraic statements,…

A technique is presented that gives a quick approximation of square roots of whole numbers. (MP)

The author discusses some unique and non-routine ways of developing the multiplication facts. (CT)