This booklet is a sample activity from an individualized instruction unit in mathematics. Agreement between the performance specified in the units' objectives, the performance taught in the instruction activity, and performance required on the posttest was a key criterion during the development of this material. The student is told what he is…

Although recent writings indicate the importance of personal contact structures in diffusing innovations and in determining perceptions, the internal contact structure of the school faculty remains unexamined. This study applies directed graph theory, a new branch of mathematics, to analyzing school contact structure. Sociometric data and…

The operation of rounding is shown to lead into an investigation of an abstract mathematical system. Properties of the system are discussed and graphs of the rounding function are drawn. Some questions for discussion are given. (MP)

A magazine article is shown to contain material that could lead to discussions of several topics in mathematics. The article and the related mathematics are discussed in detail. (MP)

A mathematical derivation is given, developing the cardioid as an epicycloid locus. Curve-stitched designs are given for a family of epicycloids. (MP)

How tedious algebraic manipulations for simplifying general quadratic equations can be supplemented with simple geometric procedures is discussed. These procedures help students determine the type of conic and its axes and allow a graph to be sketched quickly. (MNS)

Four different types of problems from graph theory are presented and discussed. (MK)

A diagrammatic approach to invariants of knots is the focus. Connections with graph theory, physics, and other topics are included, along with an explanation of how proofs of some old conjectures about alternating knots emerge from this work. (MNS)

This article describes an activity for secondary school students that may constitute an appropriate opportunity to discuss with them the idea of proof, particularly in an algebraic context. During the activity the students may experience and understand some of the roles played by proof in mathematics in addition to verification of truth:…

This paper suggests that mathematics teacher educators should listen carefully to what their students are saying. More specifically, it demonstrates how from one pre-teacher's non-traditional geometric representation of a unit fraction, a variety of learning environments that lead to the enrichment of mathematics for teaching can be developed. The…

The purpose of this study was to determine whether there were significant differences in students' performances amongst conceptual, algorithmic and graphical questions tests. Seventy-one eleventh-grade students were involved in this study. In order to assess students' performance, conceptual, graphical and algorithmic questions tests were…