Thomas Kuhn (1962/2012) introduced the term "paradigm shift" to the scientific literature to describe how knowledge in science develops. The aims of this article are to identify paradigm shifts, or revolutions, that have occurred in mathematics, and to discuss their relevance to teaching mathematics in schools. The authors argue that…

Developing an understanding of place value and the base-ten number system is considered a fundamental goal of the early primary grades. For years, teachers have anecdotally reported that students struggle with place-value concepts. Among the common errors cited are misreading such numbers as 26 and 62 by seeing them as identical in meaning,…

Children enjoy playing a game based on addition module seven. The system can be applied to questions concerning the days of a week. (SD)

Tests for divisibility in bases 2 through 10 are presented. Two strategies used by a group of fourth-year students are described. (MNS)

An activity providing practice with whole number addition and subtraction, as well as enlarging on the idea of numeration systems, is described. (DT)

Number bases other than ten can be introduced effectively by presenting fictional civilizations which use them. (SD)

Addition and subtraction of integers can be approached through the use of chips of two colors. (SD)

Activities involving set union and intersection, graphing solutions of open sentences, and negation are described. These activities afford students with opportunities for computational practice as well as instruction on equations and inequalities. (SD)

The "basic fact bug" is a diagrammatic device for use in reinforcing addition or multiplication skills. It is self-checking. (SD)

On a scale of "moja" to "kumi", African math studies rate "kumi" with kids. (Editor)

Instruction on properties of whole numbers, the meanings of operations on whole numbers, symbolic representation and algorithms for completing these operations is discussed. Many activities appropriate to each of these topics, and suitable for primary school children, are presented. (SD)

A series of activities designed to help primary school children understand the meaning of the term "fraction," the symbolization, and equivalence of fractions are presented. Identification of units and pictorial representation are stressed, as is the uses of concrete materials. (SD)

Several topics concerning numeration systems that are appropriate for small group projects are suggested. (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)

A method of identification of pigs used by farmers is described as an application of a base three numeration system. (MP)