Describes an approach to the initial teaching of composite functions that relies primarily on mapping representations. (MKR)

Three open-phrase games are presented which offer interesting experiences with substitution of numbers. Four open-sentence games are also described, two dealing with the initial stages of finding a partial solution and two requiring students to find the complete solution of an open sentence. (MNS)

An example is discussed in which a drill exercise, initially involving whole number addition, can be used to develop concepts in equations of many variables. (MP)

Presents a teacher's guide and reproducible student worksheets to develop the procedure for finding the inverse of a function. (MKR)

Presents a technique for teaching logarithms using function notation. (MKR)

This paper describes student difficulties in first-year calculus classes and suggests some instructional strategies to address these difficulties. Participants in this study were 200 low socio-economic background freshmen majoring in business in Brazil. Results show that the main difficulties are related to lack of understanding of algebraic…

Classroom related topics discussed are: cryptics and statistics; understanding absolute value; recognizing quadratic equations with no real roots; and two derivations of a formula for finding the distance from a point to a line. (MP)

The focus of this document is on students' understanding of symbolization processes in algebra, and specifically their understanding of semantically laden letters. In the first four sections, four inappropriate ways in which many college students use semantically laden letters are described. Evidence from clinical interview protocols demonstrate…

A structured system of visual features is seen to parallel the propositional hierarchy of operations usually associated with the parsing of algebraic expressions. Women more than men were found to depend on these visual cues. Possible causes and consequences are discussed. Subjects were secondary and college students. (Author/DC)

Discusses the use of technology to investigate what graphs represent as well as how to interpret graphs. (MKR)

Discusses the use of activities demonstrating connections between algebra and geometry, which helps students gain a conceptual understanding of important calculus ideas and gives a historical appreciation of how mathematics evolves. Uses distance, speed, and time problems as an example. (MKR)

Results of empirical research relating computer programming instruction and understanding of the concept of mathematical variables is unclear. While some studies have found a positive relationship, others have reported nonsignificant results. The purpose of this study was to investigate high school students' (n=36) understanding of the concept of…

Discusses a visual programming language, Function Machine Lab, which helps students with the concept of function using the function machine image. (MKR)

A brief overview is given of a research project funded to investigate the cause and cure of errors in ratio and proportion, algebra, and fractions. Choosing pertinent information, interviewing students, listing significant features, developing lessons, and testing the materials are considered. (MNS)

A collection of student distortions, represented by student-invented variations of theorems, are presented. They were drawn from examination papers of 17-year-old students in Israel. (MNS)