This article presents some of the optics and mathematics related to what causes a rainbow, why it is brighter inside than out, and why more than one rainbow may appear. (PK)

Competence in dealing with mathematical model building requires mathematical knowledge, technological knowledge about how to develop a model, and reflective knowledge relevant for evaluation of the model building process. A general conceptual framework for identification of reflective knowledge is presented by a structural and a developmental…

Described are the rules and mathematical development of five games for teaching and practicing addition concepts. (PK)

Presented are six problems from diverse areas of mathematics that are appropriate for students of differing age and ability levels. (PK)

Presented are two sets of materials appropriate for exploring different aspects of shape. Ideas about sequences are considered. (PK)

Notes that the derivative of the area of a circle yields the circumference and the derivative of the volume of a sphere yields the surface area. Explores where these or other such relationships are generalizable. (PK)

Mathematics textbooks for grades K-9 were examined to determine how much of content was new content rather than review of old content. New content tends to decrease from grade three through grade eight with lowest amount of new content in books for grades six, seven, and eight (below 40 percent for two series). Differences among series are…

Ten remedial mathematics exercises are provided for children who have failed to integrate or apply their math skills. The exercises provide remediation through systematic experimentation, rather than abstract drills, by using number-configuration distinction with blocks, fractioned candy bars, decimal match sticks, graphed pictures, etc. (JDD)

Suggests activities which use newspapers as a source of data from which students design, read, and use tables, charts, and graphs. The activities, in reproducible worksheet format, provide teachers with both short- and long-term projects. (PK)

Twenty secondary mathematics teachers described their thinking as they solved four proportion problems, explained how they would teach two of the problems, and solved four similar problems after having been asked to use proportional strategies. Findings indicate that less formal strategies were not often used by these teachers. (PK)

Investigated the behavior of college mathematics professors as they taught a basic course. It was found that all of the teachers typically taught the class as a unit using a teacher centered approach. Compared to less effective teachers, the more effective teachers asked more product questions and covered more content. (PK)

This article describes the instructional efforts and success of two first grade teachers who cooperated in a year-long subtraction study with a university research team. Performance profiles of students in the experimental and control groups are presented, and implications for teaching are discussed. (PK)

Presents writing activities appropriate in the mathematics classroom in the five categories of direct use of language, linguistic translation, summarizing, applied use of language, and creative use of language. (PK)

Practical and classroom-tested ideas are suggested for teaching the midpoint theorem and exponents and factorials. (PK)

Presents several kinds of mathematical problems or activities which are suggested by a clock face. (PK)