This paper presents a description of the different types of arguments that emerged as two students, working in a computerized environment, engaged in an investigation of several number theory concepts. The emerging arguments are seen as a result of the influence of the computerized environment together with collaborative learning. Using…

"How much popcorn will our classroom hold?" This intriguing question sparked a terrific integrated science and math exploration that the author conducted with fifth-and sixth-grade students. In the process of finding the classroom's volume, students developed science-process skills (e.g., developing a plan, measurement, collecting and interpreting…

Many students have difficulty finding remainders instead of quotients in the division of two numbers. Students are too quick to use technology and cannot interpret the output correctly. Moreover, many students are not accustomed to doing different yet applicable mathematics. As with all branches of mathematics, modular arithmetic and congruences…

A central component in the young child's construction of a number system is an understanding of correspondence. Although current research demonstrates that preschool children use correspondence in a variety of tasks, the nature of the relationship between the use of correspondence action patterns and the use of correspondence as a quantifier is…

A classroom activity in which numbers are assigned to words on the basis of geometric configuration of the letters is described. (SD)

Students in grades 4, 6, and 8 were interviewed using whole-number division problems, some involving division of zero by a positive whole number and some involving division by zero. Results and classroom implications are discussed. (SD)

Suggestions for using handheld calculators are given. Students can invent and check their own problems. The calculator can debug problems, provide practice, aid in developing concepts of place value, decimals, order of operations, powers of a number, and evaluation of formulas. (KM)

In this article, a continuation of SE 513 148, the author presents seven additional applications of group theory to high school mathematics. These applications can be used, not only to illustrate the group concept, but also to extend the development of ideas in the high school curriculum. (SD)

After a brief discussion of Pascal's triangle and description of four methods of hand construction, the author provides FORTRAN and BASIC programs for computer construction based on recursive definition. (SD)

A method for generating Pythagorean triples is presented and demonstrated with several examples. Its relationship to another method is shown and several interesting related facts are proven. (LS)

A chart is described which gives children an opportunity to discover prime and composite numbers and which leads to discussions of the associative and commutative laws, multiplication by 1, and powers and exponents. (DT)