Academic scholars face a difficult challenge when attempting to grasp the intricate world of mathematics. The complexity of mathematical concepts often lies hidden beneath layers of formulas and procedures, obscuring their true essence. Traditional educational resources often fall short in conveying the profound meaning behind these concepts,…

Suggestions for teaching the concept of division by zero are given. (MK)

The use of flow charts in the teaching of college mathematics enhances students' understanding of mathematical processes. Used appropriately in elementary and secondary schools they could also nurture understanding of algorithms. (SD)

The author proposes that computer programs which are designed to make algorithmic structures accessible and comprehensible be employed as advance organizers in mathematics instruction. These programs would bring clarity and structural integration to mathematical, instructional, and cognitive structures important to the mastery of mathematical…

The author develops a four-stage model for concept-internalization. The stages are: (1) concrete structure; (2) linguistic structure; (3) algorithm; and (4) mastery. The model is related to teaching methods and the teaching of long division is examined in detail. (SD)

The need for incorporating algorithmics into mathematics instruction is presented. The proliferation of computers is seen to have made the designing of algorithms an essential skill. Examples are given, and the view that mathematics will lose much prestige and importance if algorithmics is not integrated into it is presented. (MP)

The ideas and techniques involved in learning about fractions were investigated with students in grades 1-12, in the first 3 years of colleges, in community college mathematics courses, and in graduate school. Also included were some high school mathematics teachers, some mathematicians, and some retired persons. Part I provides the rationale and…

In spite of current sentiment to the contrary, the wellsprings of mathematics are not utility and relevance, but creativity, imagination, and an appreciation of the beauty of the subject. This has implications for the teaching of mathematics. (PK)

How graph paper has been used to illustrate the algorithm for division of fractions is presented. The combined use of graph paper and an overhead projector can make the presentation even more convincing. A review of whole number division is recommended prior to the lesson. (MP)

This paper presents a theoretical framework for investigating the role of algorithms in mathematical thinking using a combined ontological-psychological outlook. The intent is to demonstrate that the processes of learning and of problem solving incorporate an elaborate interplay between operational and structural conceptualizations of the same…

Activities are given to assist students in seeing a rationale for the difficult algorithms we teach for fractions. Both interpretations of fractions and operations with fractions are discussed. (MNS)

The uses of programable calculators in the mathematics classroom are presented. A discussion of the "microelectronics revolution" that has brought programable calculators into our society is also included. Pointed out is that the logical or mental processes used to program the programable calculator are identical to those used to program…

Described are four classroom activities that may be interspersed into a curriculum or offered as homework. Systematic procedures, alternative strategies, and trial and error are emphasized in these counting exercises. (KR)