Two specific cases involving Pascal's Problem of the Points are discussed, followed by a solution in the general case. (MNS)

Mental skills developed through the study of mathematics are identified, and ways in which this information can shape the role of teachers of algebra are suggested. (MNS)

Explores meanings of "generic" and "generality" as they are found both in everyday language and as they confront mathematics students. Considers everyday occurrences of the idea of generic (leading to the notion of a generic example of a class) and some ramifications in elementary algebra. (JN)

A method used by the ancient Babylonians to solve quadratic equations is presented. Illustrations are included from one Babylonian tablet. (MNS)

A number problem is presented and analyzed. (DT)

The problem of determining the distance that an object fell is analyzed. (DT)

Using an incorrect conjecture as a learning activity in mathematics is discussed. The example used is from transformation geometry. (DT)

A programming problem on calculating the roots of a quadratic equation is used to illustrate the inexactness of computation with a digital computer. (DT)

This article shows that the recognition of the dualities in equality (operator-equivalent) of the minus sign (unary-binary) and the zero (nullity-totality) during the transitional process from arithmetic to algebra by 12-13 year-old students constitutes a possible way to achieve the extension of the natural number domain to the integers. (Contains…

The study of linear functions is important as it provides students with their first experience of identifying and interpreting the relationship between two dependent variables. This paper, which builds on previous research, reports a study undertaken with 64 year 9 students from two Australian schools. Linear functions were introduced to these…

This study investigates student understanding of the part-whole concept in mathematics at an independent two-year post-secondary institution in New Mexico. The mathematics portion of the Tests of Adult Basic Education (TABE) Summary Form was used as the evaluative instrument. Evidence for a lack of part-whole concept understanding as a hidden…

When students confront arithmetic or algebraic word problems, they develop ideas and notations during the processes of solving them by using various arithmetic strategies. Those ideas and notations are the basis for solving that type of problems. Is it possible to aid the development of students' algebraic thinking during their transition from…

In this study, we explore six students' conceptions of Z[subscript n] in an effort to understand students' conceptions of quotient groups in general. We discovered that there were three different ways our students thought about Z[subscript n], namely as infinite sets, element-set combinations, and representative elements. We explore how…

This paper presents some ideas on how to utilize TI-83 Plus calculators to perform division of one polynomial (the divided) by another polynomial (the divisor) and how that procedure might be incorporated into a college algebra lesson. Four ways to obtain the quotient and remainder when dividing a polynomial by a first-degree polynomial are…

This paper focuses on student understanding and learning of the algebraic concept--rate of change. Teachers' knowledge about their students and current literature on students' understanding is used to design and assess the instruments. Data were obtained as part of two-year research program that focused on how the study of students' understanding…