Discusses the properties of the equation y"+ay=0, a basic equation in differential equations classes which is well known to have periodic solutions. Explores similar but more complicated equations using a graphing calculator to ask questions about the nature of the solutions and to generate conjectures from examples. Lists some equations and…

Presents the use of children's literature to teach mathematics, encouraging children to identify, discuss, and extend "math morals" of the stories. Provides examples of using literature and classroom activities to identify principles regarding incomplete information, the need for standard units, commutative operations, and the rapidity of…

Presents the problem of doubling dough by creating a mixture of dough that doubles in volume every minute when placed in a warm oven. Discusses ways of proposing this question in the classroom. (ASK)

Addresses the initial understanding that advanced undergraduate mathematics students exhibit when presented with a new concept in an environment requiring self-generation and self-validation of examples of the concept. Concludes that students who used an example generation learning strategy were more effective in attaining an initial understanding…

In an article from the July 1995 issue of Educational Studies in Mathematics, Even and Tirosh claim that the quantity (-8)1/3 is undefined. This article presents arguments as to why the reasoning of Tirosh and Even is flawed. Attempts to convince educators of the importance of applying a mathematical definition precisely. (AIM)

Suggests that the cross product of two vectors can be more easily and accurately explained by starting from the perspective of dyadics because then the concept of vector multiplication has a simple geometrical picture that encompasses both the dot and cross products in any number of dimensions in terms of orthogonal unit vector components. (AIM)

Describes common misconceptions with decimals and suggests activities that can strengthen connections between decimal concepts and fractions, place value, and physical models, such as the number line. Encourages reasoning, communicating, and problem solving. (TO)

Children with arithmetic learning disabilities (n=16) and normally achieving controls (n=16) in grades 3-5 were administered a battery of computerized tasks. Memory spans for both letters and digits were found to be smaller among the arithmetic learning disabled children. Implications for teaching are discussed. (Author/CMS)

Describes a classroom problem of probability as follows: How many people do you need in a group to ensure that the probability of at least two of them having the same birthday is greater than one-half? Answer: 23. The probability principles needed are simple enough to be accessible to advanced high school students. (PVD)

Presents a graphing activity to show transverse and longitudinal waves using spreadsheets. (Author/NB)

Discusses the use of mathematics, specifically spreadsheets, to study apportionment in the U. S. House of Representatives. Topics include the interdisciplinary nature of the study, how population changes affect the distribution, different methods for apportioning representatives that have been used throughout history, and analyzing the data. (LRW)

Derives two sufficient conditions for a finitely generated Lie algebra to have the nilpotent hypercenter. Presents a relatively large class of generalized soluble Lie algebras. Proves that if a finitely generated Lie algebra has a nilpotent maximal subalgebra, the Fitting radical is nilpotent. (DDR)

Examines classroom situations which allow for learning of rules of mathematical reasoning. Findings indicate that debate about mathematical rules can be generated amongst students ages 12 to 13 through the study of a mathematical problem. Argues that it is necessary for the teacher to conclude the debate. Contains 10 references. (JRH)

Used software environment to examine algebra students' attempts to reformulate narratives using verbal and iconic lexical sets. Described how natural language text turns into a script of events and processes, how the qualitative graphic description of the script is sketched using iconic notations, and how the graph turns into a subject for…

Offers a Tangram Teaching Guide that provides a five-step developmental sequence for teaching tangramming to young children. Includes teaching resources and a checklist summarizing the teaching sequence. Asserts that tangram experiences help children develop positive attitudes toward geometry, further their shape identification and classification…