This article summarizes research conducted in Gifted Algebra I and Gifted Precalculus classes in a public, suburban high school in spring 2002, which investigated the importance of reading and writing in understanding mathematical principles. The classroom teacher supplemented traditional numerical problem solving with vocabulary quizzes, reading…

This document is concerned with developing an understanding of problem solving by providing tasks to help students with their problem solving strategies. These tasks were used by Vermont teachers during the pilot years of the High School Mathematics Assessment and were selected by attendees of the June, 1995 Research Scoring meeting. Tasks are…

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)

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)

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)

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)

Examines teachers' judgments of the difficulties of algebra problems. Offers classroom-tested instructional approaches that build directly on students' mathematical intuitions and inventions. (KHR)

Describes the successful use of a computer algebra system (CAS) with a student as he worked on a problem involving functions far more difficult than he had previously encountered. (Author/NB)

Presented is a example that shows why a certain technical lemma is necessary for a valid proof of Galois Theory. The usual proof of Galois' Theory is included as well as one using the lemma. (KR)

Describes how Suzuki's methods of teaching young pupils to play the violin can be combined with Polya's ideas on problem solving to teach mathematics to elementary school pupils. Six references are listed. (YP)

Describes learning difficulties students may have with the basic notions of linear algebra and three phases of abstraction. Discusses results of a program based on the abstraction process. (YP)