The adaptive use of approximate calculation was examined using a verification task with 18 third graders with mathematics learning disabilities, 22 typically achieving third graders, and 21 typically achieving second graders. Participants were asked to make true-false decisions on simple and complex addition problems while the distance between the…

What students need to know in a world where most computations are done by machine is discussed. Needed changes in the mathematics curriculum are then detailed in relation to mental arithmetic, numeration, decimals and fractions, paper-and-pencil computation, order of operations, problem solving, and instruction on calculator use. (MNS)

More mental computation and organized and enjoyable activities to practice such skills are advocated. Suggestions for brief sessions involving challenging questions and quick recall of number facts are presented. The author presents and comments on several sample lessons designed for a wide range of student abilities. (MP)

Assessed attitude, computational preferences, and mental computational performance of 176, 187, 186, and 206 Japanese students in grades 2, 4, 6, and 8, respectively. Found wide ranges of performance on mental computation, that visual modes of presentation increased performance levels, and a narrow range of strategies. Contains assessments. (37…

A math teacher describes an approach to help special education students solve addition and subtraction problems through a system involving finger counting. The systems for subtraction and addition solve the problem faced by students unable to memorize facts and unable to use their fingers when numbers exceeded five. (Illustrations of the approach…

The heliocentric, or Sun-centered model, one of the most important revolutions in scientific thinking, allowed Nicholas Copernicus to calculate the periods, relative distances, and approximate orbital shapes of all the known planets, thereby paving the way for Kepler's laws and Newton's formation of gravitation. Recreating Copernicus's…

The origins of this paper lay in making beds by putting pieces of plywood on a frame: If beds need to be 4 feet 6 inches by 6 feet 3 inches, and plywood comes in 4-foot by 8-foot sheets, how should one cut the plywood to minimize waste (and have stable beds)? The problem is of course generalized.

Hadamard's two integral inequalities are generalized and the quadrature formulae associated with them are demonstrated.

Students analyze a photograph to solve mathematical questions related to the images captured in the photograph.

This issue of the journal contains abstracts and critiques of 11 research reports. They concern: a case study of one child's strategies for mental addition; children's understanding of fractions; computation routines prescribed by schools; models in verbal problem solving; predicting eighth-grade algebra achievement; the effectiveness of…

This article presents a study in which applications were integrated in the Multivariable Calculus course at the Technion in the framework of supplementary tutorials. The purpose of the study was to test the opportunity of extending the conventional curriculum by optional applied problem-solving activities and get initial evidence on the possible…

Learning to question is essential for determining pathways of conservation and development in southwestern Amazonia during a time of rapid global environmental change. Teaching such an approach in graduate science programs in regional universities can be done using play-acting and simulation exercises. Multiple working hypotheses help students…

The mathematical performance of 182 third and fourth graders in 8 different areas of mathematics was examined. The children belonged to 4 achievement groups: children with mathematic difficulties (MD only), children with both mathematic and reading difficulties (MD-RD), children with reading difficulties (RD only), and normally achieving children…

This study implemented a three-stage problem-based estimation instruction scenario and combined it with mobile technology to provide elementary teachers with an effective e-tool for observing student estimation and leading effective class or group discussions on the selection and assessment of appropriate strategies for solving daily estimation…

The article suggests possible reasons for difficulties with verbal (word) problems and describes two remediation strategies: re-teaching the introductory sequence for an operation and having students write their own problems. (CL)