The absolute-value scale, a manipulative that students can construct from a sheet of ruled notebook paper, helps to promote conceptual connections between the number line and the notion of absolute value as distance. This manipulative technique is particularly suited to students who are struggling with transitional abstract cognitive development.…

Computer spreadsheets, computer graphing software, and programable graphing calculators are each demonstrated in the computational process of numerical iteration as a problem-solving method. Examples, illustrations, practical tips, and a typical calculator program are included. (JJK)

Presented is the ancient Egyptian algorithm for the operations of multiplication and division of integers and fractions. Theorems involving unit fractions, proved by Fibonacci, justifying and extending the Egyptian or Ahmes' methods into the Hindu-Arabic numeric representational system are given. (MDH)

University students (n=158) were examined to determine whether first describing a mathematical relationship by a written English sentence would affect success in constructing an algebraic equation. Students using common idiomatic forms of English that could not be directly translated into mathematical notation were found to be the most successful.…

Presented is an exploration of a number of ways these quantities can be demonstrated and some interconnections between them. Discussed are triangular numbers, sums of squares, sums of cubes, table squares, and counting rectangles. (CW)

Described is an approach to the derivation of numerical integration formulas. Students develop their own formulas using polynomial interpolation and determine error estimates. The Newton-Cotes formulas and error analysis are reviewed. (KR)

Illustrated is the use of computer algebra software to assist in both a computational and theoretical way to develop the underlying theory of polynomials and the partial fraction decomposition of a rational function. Background information and a discussion of theoretical considerations are provided. (KR)

Argues that teachers and lecturers need to identify essential skills which are technology-independent and need to determine the most effective use of new technology in the classroom. Examines prospects for change using the newer technology of graphing calculators for mathematics courses. Contains 15 references. (ASK)

Describes a simple cooling experiment that can be conducted in class at the college algebra, precalculus, calculus, or differential equations level whose aim is to determine the best exponential function to fit the experimental data. (Author/ASK)

Investigates four seventh-grade teachers' awareness of students' tendency to conjoin or "finish" open expressions and teachers' ways of coping with this tendency. Concludes that two experienced teachers were aware of this tendency, whereas the novices were not, and teaching approaches related to this tendency differed considerably. Contains 24…

Describes some basic difficulties in early algebra and their causes and presents some strategies for overcoming them. Lists five areas as being essential foundations for learning algebra: (1) seeing the operation, not just the answer; (2) understanding the equals sign; (3) understanding the properties of numbers; (4) being able to use all numbers;…

Suggests ways researchers can use international comparisons to improve student learning, using math performance of U.S. and Chinese sixth-graders on four types of tasks. Chinese students did better on computation; U.S. students excelled at process (open performance) assessment tasks. U.S. kids need to develop symbolic and algebraic thinking. (MLH)

For students to develop an understanding of functions, they must have opportunities to solve problems that require them to transfer between algebraic, numeric, and graphic representations (transfer problems). Research has confirmed student difficulties with certain types of transfer problems and has suggested instructional factors as a possible…

We present here results of a case study examining the classroom practice of one thirdgrade teacher as she participated in a long-term professional development project led by the authors. Our goal was to explore in what ways and to what extent the teacher was able to build a classroom that supported the development of students' algebraic reasoning…

This article describes an investigation making connections between the time on an analog clock and the angle between the minute hand and the hour hand. It was posed by a middle school mathematics teacher. (Contains 8 tables and 6 figures.)