The focus is on multi-step problems, with suggestions on helping students understand the mathematical relations, decide which computational procedures to use, and identify the sequence in which computations should be performed. An activity to aid understanding of variables is also included. (MNS)

The conceptual difference between understanding and algorithmic performance is examined first. Then some dilemmas that flow from these distinctions are discussed. (MNS)

Some strategies for avoiding misconceptions about the greatest common factor and the least common multiple are presented. Several alternative methods for computing each are given. (MNS)

Several activities are suggested in which children practice computation as a purposeful part of that activity. (DT)

This paper introduces the reader to the concepts of binomial probability and simulation. A spreadsheet is used to illustrate these concepts. Random number generators are great technological tools for demonstrating the concepts of probability. Ideas of approximation, estimation, and mathematical usefulness provide numerous ways of learning…

The Purposeful Algebraic Activity Project is concerned with the development of algebraic activity in pupils in the early years of secondary schooling. Here we report on the different ways in which we have observed children articulating generalisations during semi-structured interviews which are being used to gain snap-shots of this development. We…

A strategy to make the transition from manipulative materials to a written algorithm for division is outlined in dialogue form. (MNS)

Results of this study indicated calculator algorithms can serve as an effective alternative instructional strategy where computational skill is an instructional goal. (MP)

Five calculator activities are described that are designed to explore ordered operations. Suggestions are given on mathematical objectives, strategies for solving, and possible extensions or follow-up activities. (MP)

This article focuses on the aspect of mental arithmetic that uses thinking strategies that are effective with large numbers as well as basic facts. Two activities are suggested for lack of the four operations. (MK)

Reactions to a two-week workshop are given. Conclusions are that chisanbop has presented a misleading picture and is highly overrated. (MP)

The use of different colored quizzes for different skill levels is suggested as an aid for motivation in a mastery learning setting. (MP)

Discusses the importance of mental mathematics beyond the middle school. Presents sample objectives for different courses or strands, and teaching ideas to make mental mathematics an important, ongoing goal in secondary mathematics instruction and beyond. (KHR)

Encourages teachers to allow opportunities for students to present alternative algorithms, whether the students invent them or learn them, then lead a discussion about the meaning of the operations with the goal of students understanding why the algorithm works. Teachers with students of similar racial and ethnic backgrounds should encourage the…

Presents an activity using a number grid to challenge second grade students' concepts related to counting change. (KHR)