Describes how a measure of problem difficulty (problem complexity) can be developed. Explores factors that may affect the difficulty of mathematics problems by focusing on ninth-grade student test responses (n=125), mathematics teacher questionnaire responses (n=29) in Hong Kong (China), and using a computer. Identifies four problem difficulty…

Nine freshmen in a ninth-grade accelerated algebra class were asked to solve five nonroutine combinatorial problems. The four mathematically gifted students were successful in discovering and verbalizing the generality that characterized the solutions to the five problems, whereas the five nongifted students were unable to discover the hidden…

Research findings concerning student learning difficulties in algebra are discussed. A teaching approach which takes into consideration these findings is suggested. Encouraging students to see patterns and to develop flexibility in their thinking are stressed. (CW)

Discussed is the use of magic squares as examples in a first year course in linear algebra. Four examples are presented with each including the proposition, the procedure, and a proof. (KR)

Discussed are the idea, examples, problems, and applications of convexity. Topics include historical examples, definitions, the John-Loewner ellipsoid, convex functions, polytopes, the algebraic operation of duality and addition, and topology of convex bodies. (KR)

Described is an approach to teaching algebra in a meaningful context by using problem solving to motivate students and increase their retention. Examples of this approach are given. (CW)

Ideas which apply language concepts to the study of algebra are presented. Discussed are algebraic notation, vocabulary, vocalization, and written assignments. The careful use of algebraic language in mathematics classes is emphasized. (CW)

Outlines an instructional plan working within the existing structure of most colleges that produces higher levels of student achievement through the manipulation of time. Described are the objective-based unit design, group instruction, initial test, corrective procedures, and retest. Lists 10 references. (YP)

Presents four worksheets designed to introduce middle school students to the use of diagrams to solve real world problems. Describes instructional usage of the worksheets with answers to all worksheets. (YP)

An approach to finding the rational roots of polynomial equations based on computer graphing is given. It integrates graphing with the purely algebraic approach. Either computers or graphing calculators can be used. (MNS)

Describes a model for teaching early algebraic concepts using manipulative materials for elementary school students. Presents a rationale for the model. Provides activities for solving algebraic equations using envelopes and counters. (YP)

The theorems and proofs presented are designed to enhance student understanding of the theory of infinity as developed by Cantor and others. Three transfinite numbers are defined to express the cardinality of infinite algebraic sets, infinite sets of geometric points and infinite sets of functions. (DC)

Some appearances of pi in a wide variety of problems are presented. Sections focus on some history, the first analytical expressions for pi, Euler's summation formula, Euler and Bernoulli, approximations to pi, two and three series for the arctangent, more analytical expressions for pi, and arctangent formulas for calculating pi. (MNS)

Compares the trends of women's and men's world records for the 800-meter run using the linear and power regression capabilities of a graphing calculator. (MDH)

Computer-Intensive Algebra (CIA) focuses on the use of technology to help develop a rich understanding of fundamental algebraic concepts in real-world settings using computing tools for easy access to numerical, graphical, and symbolic representations of mathematical ideas. (MKR)