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)

Described are activities and games incorporating a technique of "one step" which is used with children with learning difficulties. The purpose of "one step" is twofold, to minimize difficulties with typical trouble spots and to keep the step size of the instruction small. (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)

A special calendar chart is presented that can be used to find out what day of the week any date falls on during the 1980s. (MP)

Three methods of proof are analyzed as a means of aiding teachers in presenting arguments for certain number concepts. These are: (1) proof by contradiction, (2) Venn diagrams, and (3) method of exhaustion. (MP)

An appeal is made for a more formal treatment of the topics of estimation and reasonableness of answers in the school mathematics curriculum. (MP)

A "flipping" clown figure can be used on a number line to help students conceptualize operations using negative numbers. (SJL)

Two studies sought to determine the developmental relationship between the child's use of counting as a notational symbol system to extract, compare, and reproduce numerical information and the development of number conservation. Subjects were four- to six-year-old children in Study 1 and seven- to nine-year-old learning disabled children in Study…

The article includes a short history of polygonal numbers, a method for finding the root of a polygonal number, and suggestions for using polygonal numbers in the classroom. (MK)

Examples of opportunities for undergraduate students to engage in mathematical research are demonstrated. All examples are partition identities. (MK)

Results of a study of children's ability to perceive grouped vs. ungrouped objects representing the numbers 1 through 9 showed that perceiving elementally grouped objects was significantly easier than nonelementally grouped objects, and elementally grouped objects in a pattern were significantly easier than non-patterned groupings. (DT)

Illustrates how many key algebraic concepts can be informally developed within the number and operations strand taught in the primary grades. Discusses expressions and equations, properties and conventions, relationships between operations, and variables from this perspective. (ASK)

Presents three number games for mathematics classrooms designed to improve the learning of number concepts. Game topics include determining products, arranging mathematical signs, and factoring. (ASK)

This constructivist teaching experiment investigated the role of whole-number knowledge in fraction learning. Two nine-year-old students worked for one year with a computer program (Copycat) and demonstrated that the development of whole-number knowledge and rational-number knowledge is interdependent. Contains 59 references. (KMC)

Presents an investigation, applicable for grades 3-6, that focuses on the concept of randomness and encourages children to conjecture and to conduct experiments which verify or contradict their intuitions. Involves using hands-on explorations, collecting data, and drawing conclusions on the basis of the information. (JRH)