A hungry worm is looking for something to eat according to very specific rules, and the path he takes is a graph. The problem is detailed in Applesoft BASIC using low resolution graphics for worms that turn 90 degrees and high resolution for worms that can turn 45 degrees. (MP)

Results of interviews with students regarding their conceptual understanding of fractions are discussed. Fewer than 10 percent had acquired an adequate conceptual base. (MP)

Geometry is revealed as one of the most universal and useful tools in all parts of mathematics, with the idea of a "pure" geometry divorced from algebra an historically recent idea. (MP)

Problems focusing on number theory that can make good use of the calculator in discovering and proving simple theorems are proposed. The focus is on the properties of subtracting the smaller of a three digit number and its mirror number from the larger in a process that leads to zero. (MP)

Children are seen to need positive experiences with spatial words in order to be successful at understanding the concepts. If teaching methods used are mindful of the intricacies of understanding spatial communication, pupils will have the necessary positive initial experiences. Teaching suggestions for achieving positive effects are detailed. (MP)

A model that can be effectively used to develop the notion of function and provide varied practice by using "real world" examples and concrete objects is covered. The use of Popsicle-sticks is featured, with some suggestions for tasks involving functions with one operation, two operations, and inverse operations covered. (MP)

Learning activities using a two-pan balance to teach the concept of equality are described. Construction of a poster board balance is illustrated. (MP)

Results of the second mathematics assessment of the National Assessment of Educational Progress (NAEP) are analyzed with regard to the performance of 13- and 17-year-olds on probability exercises. The results suggest that this area has been neglected in mathematics instruction. (MP)

Some patterns in prime numbers and their implications for general theorems are presented. Much of the material is taken from "The Strong Law of Small Numbers," an unpublished paper by Richard Kenneth Guy. (MP)

Discussed are the results of the second National Assessment of Educational Progress (NAEP) mathematics assessment concerning children's ability to solve verbal problems. The data indicate that the commonly held view that children cannot solve word problems may be an oversimplification. (Author/TG) Aspect of National Assessment (NAEP) dealt with in…

Described are graphing activities which can be instrumental in introducing the mathematics concepts of counting, sorting, grouping, and comparing on the primary level. On the intermediate level, these activites can be used to introduce collecting and sorting unorganized data, and creating graphs to represent the data. (Author/TG)

Two major periods of development in proportional reasoning are identified by analysis of a 23-item experiment given to subjects between 6 and 16 years of age. (MP)

An approach which seeks to stimulate interest in mathematics by enabling a student to use his knowledge in a nontrivial application is discussed. An example of how the approach was implemented is presented with an assessment of the results as measured by student reactions. (Author/TG)

Rule learning in mathematics among elementary school children is described. Samples of dialogue between experimenters and children are presented, and the concept of rule learning is described in relation to two subgroups, gifted children and "regular" ones. (MP)

The task of finding the least number and the size of weights necessary to weigh every integral number of pounds from one to 40 is presented as a problem solving activity for elementary classrooms. (MP)