Topics from graph theory are introduced at an informal level and thereby made accessible to the majority of secondary school students. Three worksheets are included. (MNS)

An educational psychologist visited a Japanese fifth-grade mathematics class that was discussing and solving the problem of how to divide two into three parts. Students learned to devise and describe methods for solving mathematics problems and to defend and explain their problem solving. American educators are adapting some methods that the…

Fourth-grade students (n=45) either with or without learning disabilities and achieving or not achieving at grade level in math were asked to explain strategies used to solve computational problems. Strategies were classified as reproductive or reconstructive (which varied in applicability and efficiency). Significant group differences were found.…

Describes a scheme designed to guide prospective teachers beyond the point of proficiency as a student solving given problems. Provides a mechanism whereby prospective teachers advance toward assuming the role of a teacher posing his or her own problems. (13 references) (Author/MKR)

Content analysis of 7 mathematics textbook series, grades 1-8, found that textbooks published after 1989 (when NCTM Standards were published) showed shifts of emphasis among content areas; changes in amount of content development, drill, word problems, and problem solving; and increased use of estimation and calculators. (13 references) (MKR)

Proposes a teaching model to teach mathematics represented as a triad of three components: (1) management of learning; (2) mathematical challenge; and (3) sensitivity to students. Describes the three components and relates them to a constructivist perspective of learning. (MDH)

Examines infinite sets and cardinality classifications of empty, finite but not empty, and infinite through discussions of numbers that fall into particular categories. Categories discussed include perfect numbers, Mersenne primes, pseudoprimes, and transcendental numbers. Discusses the Null Or Infinite Set Effect (NOISE) and infinitude resulting…

This paper reviews the present state, recent trends, and prospective lines of development concerning applied problem solving, modeling, and their respective applications. Four major trends are scrutinized with respect to curriculum inclusion: a widened spectrum of arguments, an increased universality, an increased consolidation, and an extended…

Clarifies the meaning of writing across the curriculum and writing to learn mathematics, and describes formal and informal approaches for incorporating writing into the mathematics classroom. Concludes that writing in mathematics can identify math anxious students and help discover students' misconceptions. (11 references) (MDH)

Describes three approaches teachers can use to help students understand the computation of numbers: calculator explorations, problem solving, and discussion topics. Specific examples are provided for primary and upper grades. (MDM)

Describes a learning module designed to help students use the factor labeling method in problem solving. (ZWH)

Presents a problem in which the incorrect application of the Law of Sines leads to an erroneous solution. Demonstrates that the commission of this error by an ophthalmologist using laser trabeculoplasty could lead to patient injury. (MDH)

Students do not associate traditional word problems with their own experiences because they describe situations textually, rather than contextually, and seem artificially geared to specific number operations and single correct answers. Aided by a state grant, elementary teachers in one Minnesota district are using video anchors to simulate…

Another way to add and subtract, in which the mental regrouping strategy is applied to an original 10-structure, is presented. Pupils use a visual model, called "little person," to move from counting to visualization. Originally designed for use with pupils with learning disabilities, this method has wider applicability. (KR)

Presented are two teaching methods: an algorithm for determining area; and identifying cubic polynomials with three integral zeros, integral maximum and minimum points, and integral inflection points at the advanced placement calculus level. Examples for each are given. (CW)