Presented are five short articles which describe innovations in mathematics teaching. Included are "Polar Summation,""The Age of the Solar System,""Forward Homework--A Motivational Tool,""Trigonometric Identities through Calculus," and "Algorithms for Evaluation of Polynomials." (CW)

Assesses the competence of children (N=215) between the ages of 5 and 9 at addition by asking them to estimate the answers to addition sums. Reports that children at higher levels tend to produce more reasonable estimates than children at lower levels. Discusses the existence and nature of a zone of partial knowledge and understanding. Contains 31…

Examines adults from China and Canada solving single-digit multiplication problems. Reports that Chinese adults were faster and made fewer errors than Canadian adults, and Chinese adults made more errors that reflect verbal-production processes that may occur after retrieval whereas Canadian adults made more errors that reflect retrieval…

Explores students' abilities in mental computation, finds out the strategies they use most naturally, and develops a theoretical framework by giving 60 children a questionnaire and interviewing them on a series of arithmetic operations to be solved by mental computation. Generates a classification of children's strategies. Contains 31 references.…

Presents a student module modeling knowledge states and learning skills of students in the field of Newtonian dynamics. Uses data recorded during the exploratory activity in microworlds to infer mental representations concerning the concept of force. A fuzzy algorithm able to follow the cognitive states the student goes through in solving a task…

Compares traditional mathematical models with computer simulations. Shows the strengths and flexibility of algorithmic computational simulations through a program designed to investigate and extend understanding in one of the most enduring questions in social choice research. Discusses solutions to this problem from each approach--analytic and…

Two studies involving 110 and 91 children aged 5 to 7 years show that children's knowledge of counting and addition facilitated their acquisition of a concept not taught in school, that every number has a natural successor (Successor Principle). Even the oldest children could not rank order correctly numbers that contained fractional notations.…

The relationship between verbal and visual-spatial working memory and mathematical computation skill was examined in 98 children and adults with and without mathematical disabilities. A hierarchical regression analysis, when partialing for reading ability, age, and gender influences, showed mathematical computation was better predicted by verbal…

Tested in three experiments hypothesis that coordinating saying number-words and pointing to each object to count requires use of the central executive and that cost of coordination decreases with age. Found that for 5- and 9-year-olds and adults, manipulating difficulty of each component affected counting performance but did not make coordination…

Comparison of pre- and posttest scores in mathematics computation of 2 classes of (n=91) ninth-grade students, 1 class emphasizing drill and practice and the other focusing on learning concepts, found the mean grade equivalent score for computation of the concept class increased more than 2 years and these students attempted to answer more…

Discusses two students' discovery that both of their answers to a computation for E in a chemical reaction in electrochemistry were correct, that there was not a unique answer, and that the textbook had presented only one of the possible answers to the problem. (MKR)

This article makes the case for an alternative type of mathematics instruction for students with disabilities using multiplication. It explains how educators can skip addition and subtraction in computation instruction and start with multiplication by controlling for two elements: counting through 10 and place value. Word problems are also…

Introduces a popular children's book which is the foundation for activities that introduce students to some basic concepts of probability. Recommends the use of this book to engage middle grade students in exploring patterns related to counting. (ASK)

Introduces a cost-benefit transfer model which considers a performer's perception of need, sensibility, and effort to determine the likelihood of putting to use an idea learned in training. The model predicts use through a mathematical formula: the product of need and sensibility divided by effort. Case evidence of academic physicians are cited in…

Examined whether 5- and 6-year-olds understand that addition and subtraction cancel each other and whether this understanding is based on identity or quantity of addend and subtrahend. Found that children used inversion principle. Six- to eight-year-olds also used inversion and decomposition to solve a + b - (B+1) problems. Concluded that…