This paper is divided into three parts. Part I connects the reality of the classroom with the idealism which arises from some of the problem solving literature. It is argued that a broader concept of problem solving is needed to provide a perspective for bridging the gap between the conceptions of problem solving in the literature and typical…

Describes an algorithm that provides more rapid convergence for more complicated forms of phase separation requiring the use of a digital computer. Demonstrates that this "inside-out" algorithm remains efficient for determination of the equilibrium states for any type of phase transition for a binary system. (CW)

Five-frames are proposed as manipulative material to increase children's ability to identify the number of objects without direct counting. How to use frames and beansticks to construct basic facts without counting is discussed. (MNS)

A framework is presented for integrating use of a microcomputer into a statistics unit. Descriptions of some programs suitable for the Apple microcomputer and ideas for lessons are included. (MNS)

Pumpkin seeds are counted after students convert pumpkins to jack-o-lanterns. Among the activities involved, pupils learn to count by 10s, make estimates, and to construct a visual representation of 1,000. (MP)

The need for communication between mathematics and physics teachers is discussed. Suggests that there is a problem among students of these subjects, in transferring their knowledge of mathematical terminology from mathematics to physics. (SA)

The focus is on using mathematical concepts and operations to decode holiday messages. Worksheets are provided for levels one-two, three-four, five-six, and seven-eight. (MNS)

A primary math activity teaches students counting and classifying using a book about a mother and child who tour a farm at midnight. An intermediate math activity teaches logical reasoning through a story problem in which students must use information from a story to figure out an answer. (SM)

This paper provides a pragmatic view of efficient use of graphics calculators. Efficiency is described in terms of quick and easy calculation, as debated and evidenced in a Year 12 calculus class. Students' methods of calculation are analysed in terms of the algebraic understanding and technical skills that underpinned them. Patterns in students'…

One area of science education that is, at times, neglected involves lessons on technological concepts of these principles--designing, testing, and quality control. Instead, a focus upon science concepts from a pure, and unapplied, perspective is the norm. Thus, while students may learn the equation "mass divided by volume equals…

Teachers who believe "practice makes perfect" may engage students in repetitive, perhaps timed, computational exercises. If educators teach students to understand the procedures they practice, however, they will not need as much drill and they will have more flexible use of the computations they perform. Three-quarters of a century ago,…

Teachers can use pedometers to facilitate inquiry learning and show students the need for mathematics in scientific investigation. The authors conducted activities with secondary students that investigated intake and expenditure components of the energy balance algorithm, which led to inquiries about pedometers and related data. By investigating…

This is the teacher's manual to accompany part 2 of the workbook for grade 5 pupils in the Comprehensive Instructional Management System, a teacher-designed unified mathematics curriculum for kindergarten through grade 7. It is composed of a curriculum, a testing component, and a computer-managed reporting system. The curriculum is organized into…

Some recent research findings with implications for improving mathematics instruction are reviewed in this report. The focus is on two topics: computation, in particular subtraction and estimation, and problem solving. Findings about each are listed, with references for each cited study included. Effective algorithms and strategies used by…

Parents have many opportunities every day to develop, nurture, and refine their children's mathematics skills. This pamphlet was designed to help parents become aware of these opportunities and to encourage them to participate in their children's learning process. Estimation is the skill of making a reasonably accurate guess and is prominently…