On the basis of the findings it would appear that mathematics instructors should consider seriously the use of Structure-of-Intellect factor tests for selection and placement of students. (Authors)

Focuses on modifying personalized systems of instruction (PSI) by using competency unit testing instead of mastery testing. The algebra service courses at the University of Arizona are described. Includes data on student achievement. (MNS)

People are noted as intrigued for centuries by interplay between algebra and geometry with many important advances viewed to have come down through some sort of linking of the two. Examples are given of advantages to learning and discovery that can be found in an investigative approach combining them. (Author/MP)

Five problems are given which are designed to challenge gifted students while giving them opportunities to use algebraic concepts. Solutions are provided. (MNS)

Analogies between topics in algebra and in arithmetic are noted. It is suggested that algebra teachers should consider how to take advantage of student backgrounds in arithmetic by exploiting these analogies. (MP)

The subtraction ideas presented are designed for elementary and junior high school children, yet are felt to be flexible enough to offer some challenge for high school students, particularly in algebra. (MP)

An approach to the instruction of maxima and minima problems that works with tools of geometry and algebra is presented. The focus is on a classic pie-cutting problem, which is viewed as an interesting and instructive task that is an excellent application of transformation geometry. (MP)

Describes a study which explores the feasibility of implementing a "didactical shadow" seminar in abstract algebra. Includes the effect of the seminar on prospective secondary mathematics teachers' (N=17) attitudes and on their understanding of concepts and principles of abstract algebra and algebra of the real number system. (DS)

Some methods of proof of traditional algebra problems using geometric methods are explored. The techniques used come from the original Greek approaches to these mathematical questions. (MP)

The development of the new mathematics curriculum of the late 1950s is examined in light of current calls for changes in the instructional program. Thoughtful, imaginative reform that offers radically new models of approach to teaching mathematics is called for. (MP)

Worksheets for duplication are provided for this activity designed for students in grades 6-10. The objective of the activity is to have students discover generalizations about the patterns formed. (MK)

Presents 12 questions related to a given real-life situation about a man shaving and the number of hairs in his beard in order to help students see the connection between mathematics and the world around them. (ASK)

Outlines a course at the University of Glamorgan in the United Kingdom in which a computer algebra system (CAS) teaches mathematical modeling. The format is based on continual assessment of group and individual work stating the problem, a feature list, and formulation of the models. No additional mathematical word processing package is necessary.…

Presents a quilting problem that engages students at many levels, has multiple possible solution paths, lends itself to a variety of representations, and connects many mathematical ideas. (KHR)

Describes a low-tech, hands-on activity to improve student understanding of irrational numbers. Each student creates a number line from adding machine tapes and uses a square and a precisely folded triangle as the only measuring device. (KHR)