Examples from some area tasks indicate that misconceptions about linear measurement can be carried over to area measurement; children will occasionally count points rather than length units or area units. (MP)

This essay discusses the sketching and transformation of parabolas and other curves as areas where learners can exercise and develop control of their mental imagery. (MN)

Examined are the arguments related to whether traditional or new mathematics curricula better prepares students to write proofs. Analyzed are "proofs" presented by students; the author argues that the ability to produce a proof depends upon the cognitive level of the student. (SD)

A system for categorizing components of geometry class discussions is described. The unit of observation is the teacher question; responses are coded at four cognitive levels. The system is easier to use than many in the literature; use of it can help teachers develop questioning techniques. (SD)

Seven papers presented at a research conference on space and geometry are contained in this monograph. The first paper gives an historical sketch of the development of geometry and discusses several considerations for selecting geometric content for the elementary school. Two papers deal with Piaget's research into the child's development of space…

Thirteen different research reports related to mathematics education, plus a set of five studies by one investigator and his associates, are abstracted and analyzed. The set of five studies is primarily concerned with how students deal with ratio. Of the other studies, one focuses on the longitudinal effects of inservice teacher training; five…