This study investigated mathematical behaviors on inequality tasks using two alternative response measures in preschool subjects. (Author)

Children completed three types of equivalent cardination tasks which assessed the influence of different stimulus configurations (linear, linear-nonlinear, and nonlinear), and density of object spacing. Prior results reported by Siegel, Brainerd, and Gelman and Gallistel were not replicated. Implications for understanding cardination concept…

Material covers: (1) What Is a Mathematical Concept; (2) How are Mathematical Concepts Developed; (3) How Can Computers Help Children Learn Concepts; (4) Using Software; (5) Writing Programs; and (6) What Must We Do. Using software and writing programs are two very different experiences, but both can enhance concept development processes. (MP)

The use of exercises that students can perform independently of any calculating aids and in a reasonably brief space of time is promoted, so that pupils can concentrate on the processes involved and any relationships of interest. Some examples are presented with the goal of increasing learning promoted. (MP)

To help mathematics teachers introduce and reinforce concepts and processes by using relevant problems, several such problems are presented and discussed. (MNS)

A lesson for a sixth grade class that came out of an article in a Sunday newspaper is described. The instruction centered around an experiment in probability that was seen to provide an opportunity to add to pupil intuitive understanding of some basic notions. The lesson was viewed as worthwhile. (Author/MP)

People are noted as intrigued for centuries by interplay between algebra and geometry with many important advances viewed to have come down through some sort of linking of the two. Examples are given of advantages to learning and discovery that can be found in an investigative approach combining them. (Author/MP)

Ideas are presented to help teachers bring some excitement into their classes and help children view mathematics as an enjoyable learning experience. It is felt that the introduction of the activities can help transform mathematics classes into true learning centers, lessen mathematics anxiety, and encourage increased student involvement. (MP)

Games are promoted as useful tools that can become an integral part of the mathematics curriculum. Advantages to students and teachers are noted. Guidelines for the construction of games are provided and ways of incorporating games into a mathematics program are discussed. Active child involvement is seen as fundamental. (MP)

Concern is expressed that trigonometry is being de-emphasized at the secondary level, and that even incoming college students with excellent mathematics backgrounds and aptitudes appear to be "drawing blanks" on even the most fundamental trigonometric concepts. Teaching trigonometry as the ultimate high school subject is promoted. (MP)

Discussed are the: (1) Notion of Mathematical Objects and the Realist Approach; (2) Psychological Need for Mathematical Realities, A Psychological Point of View; (3) Formalist Approach; (4) Meaning of Mathematical Existence; (5) Relative versus Absolute Existence; (6) Psychological Need for Mathematical Realities and the Offer of Mathematics; and…