Classrooms that used different instructional approaches to mathematics were observed, contrasting instruction that aimed to promote conceptual understanding rather than algorithmic skill with more conventional instruction. Results with 6 second-grade classrooms (135 students) suggest that relationships between teaching and learning are a function…

Based on a two-tiered epistemological model (preliminary physical concepts and emerging mathematical concepts), studied the construction of number among 91 kindergarten students in France, Canada, and the United States. Subjects' cognitive numerical structures were surprisingly similar despite differences in language and culture. (SV)

Develops the Pythagorean Theorem in the context of the Van Hiele levels by presenting activities appropriate for each level. Activities point to preparatory development (level 0), give 3 different versions of Euclid's proof (levels 1, 2, and 3), give some generalizations of the theorem (level 3), and explore the Pythagorean relationship in other…

Presents the computation and estimation strands of the "National Statement on Mathematics for Australian Schools." Recommends that the computational curriculum in schools reflect a more balanced time allotment among written, mental, estimating, and calculator computations. (MDH)

Provides descriptions of how five teachers in various content areas (mathematics, art, French, physics. and English) at one high school in Illinois feel about the importance of writing. Explains how these teachers incorporate their belief into everyday instruction in their areas. (HB)

Two groups of adolescents (n=36) with learning difficulties in mathematics were taught problem-solving skills under two conditions: standard word problems or contextualized problems on videodisc. Both groups improved their performance, but students in the contextualized problem group did significantly better on the contextualized problem posttest…

Describes the guess-and-check method and discusses the advantages of using computers to apply the methods to solve mathematics problems. Provides two examples that use BASIC programs to illustrate the method. (MDH)

A University of Redlands (California) calculus course was redesigned to include computer demonstrations and homework assignments in which the computer could play an important role. Comparison of results of this instruction with that using traditional methods suggest the approach using computers has merit. (MSE)

A multisensory program using a counting technique was effective in teaching math skills to three elementary students with mild disabilities. Results showed significant gains in acquisition of target skills as well as maintenance and generalization to novel math problems. (Author/DB)

Entering a value into a calculator and repeatedly performing a function f(x) on the calculator can lead to the solution of the equation f(x)=x. Explores the outcomes of performing this iterative process on the calculator. Discusses how patterns of the resulting sequences converge, diverge, become cyclic, or display chaotic behavior. (MDH)

Presented is a class activity, modeled after the game of bingo, which can provide a review of mathematics skills through constructive use of the last few minutes of a class period. Introduced are examples suitable for both middle school and high school mathematics classes. (JJK)

Described is an instructional method that makes use of an electronic spreadsheet for the numerical and graphical introduction of the fundamentals of Taylor polynomials. Included is a demonstration spreadsheet using the expansion polynomial to evaluate the cosine function. (JJK)

Described is a programing application of the software, Mathematica, which allows students to explore the various cases involved in minimizing the sum of squares for the best fit of a regression line. Several examples are included with appropriate software commands. (JJK)

Project SEED is a successful program that teaches elementary school students advanced math. Specialists conduct 45-minute lessons, asking questions designed to help students discover mathematical logic. Students respond with a system of SEED hand signals which allow everyone to participate and be monitored at once. (SM)

Student comments about having time in class to think and solve problems are presented. Stressed are teaching methods which allow students to familiarize themselves with the problem, think about solution processes, work through the solution process, and reflect while solving a problem. (CW)