An addition "trick," an analysis of why it works, and steps in constructing other problems of the same type from the basis of a discovery learning activity for addition. (DT)

Presented are several methods of introducing nondecimal numeration systems to elementary grade students. Various activities for grouping and/or visual displays are used. Games which incorporate nondecimal grouping ideas are also presented. (JP)

The author describes various classroom activities for teaching basic number skills under the headings (1) Understanding facts, (2) Relating facts, and (3) Mastering facts. The activities are designed to involve children in the making of models of the operations of arithmetic and the interpretation of these models with number sentences. (MM)

Evidence gathered in a study of 106 students in a course in elementary school mathematics methods shows that work with a nondecimal numeration system involving entirely new number symbols and names can lead to heightened awareness and appreciation of difficulties that children might have in understanding base ten numeration. (Author/CM)

An unusual way of using the long multiplication algorithm to solve problems is presented. It is conceptually harder, since it involves negative numbers but is easier to perform once mastered, since the size of the multiplication table required is smaller than the standard one. (MP)

These worksheets will provide students with experiences in identifying largest and smallest single-digit numbers, in writing names for single-digit numbers, in tests of divisibility, and in writing number sentences. (MP)

Presents examples of 3-by-3 and 4-by-4 magic squares. Proves that the numbers 1 to 10 can not be fitted to the intersections of a pentagram and that the sum of the 4 numbers on each line is always 22. (YP)

Discusses how to express an n factorial as a product of powers of primes. Provides two examples and answers. Presents four related suggestions. (YP)

Discusses a primary teaching method for the concept of negative numbers. Describes some activities for teaching the concept. (YP)

Measurement experiences can promote and illustrate number work in an intuitively satisfying way. Some current practices that are counterproductive for developing number sense and some alternative strategies that are more constructive are included in discussions of the approximate nature of measurement, realistic measurement, and work with rational…

The question is raised: What comes first: rules of calculation or the meaning of concepts? The pressures on the teacher to teach and simplify knowledge to algorithms are discussed. The relation between conceptual and procedural knowledge in school mathematics and consequences for the teacher's professional knowledge are considered. (DC)