Many children do not appear to see any need to worry about the conventions for ordering operations or using brackets in algebra problems, due to the "intuitive" mode of approach they use in mathematics. The need to teach pupils the necessity of such conventions is discussed. (MP)

A lesson on a basic logarithmic property is presented, using geometric representations and limits of sequences. (MP)

Data indicate that relatively advanced science-oriented college students can experience serious difficulties in symbolizing certain meaningful relationships with algebraic equations. Reversal errors in formulating equations were seen to stem from two main sources: (1) a syntactic word order matching process and (2) a semantic static comparison…

Materials designed to promote student investigation of factoring quadratic polynomials over the integers through using a physical model are presented. Pupils are expected to discover regularities that will permit them to factor such polynomials at the symbolic level. Worksheet masters designed for classroom use are provided. (MP)

The use of a computer to help honors second-year algebra students graph quadratic and higher-order polynomials is discussed. Sample computer programs are included. (MP)

The uses of random number generators are illustrated in three ways: (1) the solution of a probability problem using a coin; (2) the solution of a system of simultaneous linear equations using a die; and (3) the approximation of pi using darts. (MP)

Three teaching ideas are presented: how to present changes between scientific notation and decimal form that eliminate some student confusion; an analysis of an incorrect algebra equation that produced a correct answer; and aspects of a standard calculus problem dealing with minimum and maximum values. (MP)

A college-level intermediate algebra course with an applications theme is described. (MK)

Determining which whole numbers can be expressed as the difference of two squares and which as the sum of two squares forms the basis of two discovery exercises. (DT)

Presents an activity that connects area with cutting brownies which are in different shapes for different numbers, uses algebraic equations, and fixes the exact dimensions of brownies. Concludes with four different solutions from six people for the class of 16 and a trapezoidal brownie. (ASK)

Presents several examples of investigations which demonstrate the following: (1) algebra is connected to other mathematical topics; (2) algebra is an effective tool for representing patterns and relationships; and (3) algebra is an effective tool for analyzing patterns. (DDR)

Presents a solution of the three-sailors-and-the-bananas problem and attempts a generalization. Introduces an interesting way of looking at the mathematics with an idea drawn from discrete dynamical systems. (KHR)

Illustrates a modeling approach used by Singapore educators to teach mathematical skills and concepts in a problem-solving environment. (Contains 11 references.) (YDS)

Presents action research in the classroom that involves a semantic feature analysis task to help students develop reasoning skills. (YDS)

Helps students develop new insights into mathematical relationships through alternative representations. Examines patterns, symbolic, and functions approaches. (Contains 11 references.) (YDS)