The forum is focused on thinking about and with algorithms as a way of unifying all one's mathematical endeavors. The lead article by Maurer presents examples and discussion of this point. Responses, often disagreeing with his views, are by Douglas, Korte, Hilton, Renz, Smorynski, Hammersley, and Halmos. (MNS)

Defines psychic intelligence as an inclination all children possess to use whatever cognitive intelligence they have for learning, adaptive behavior, and pleasure; strongly suggests that algorithmic drill usually damages the mentality of children by stifling psychic intelligence; and discusses the use of pocket calculators to prevent this effect.…

Describes the current status and limitations of expert systems, and explores the possible applications of such systems in education and training. The use of expert systems as tutors, as job aids, and as a vehicle for students to develop their own expert systems on specific topics are discussed. (40 references) (CLB)

Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…

The illustrative method of teaching employed in most undergraduate accounting courses is becoming increasingly burdensome to professors and students due to the rapid proliferation of accounting and auditing professional standards and the increased complexity of the tax law. This teaching method may be near the breaking point in upper division…

Ideas on the long-term effects of using microcomputers in mathematics are presented. The changing perception of mathematics, the role of algorithms, the use of short computer programs, the effects on mathematical understanding, implications for teaching methods, logistic problems, examinations and assessment, and planning for the future are…

Describes basic structure of a framegame, Chain Gang, in which self-instructional modules teach a cognitive skill. Procedures are presented for loading new content into the game's basic framework to teach algorithms or heuristics and for game modification to suit different situations. Handouts used in the basic game are appended. (MBR)

An attempt is made to show that algebra is rarely obvious, and merely expecting children to learn rules is an oversimplification. Sections cover: (1) The Non-visual Nature of Algebra; (2) The Apparently Arbitrary Nature of Algebra; (3) The Relationship Between Symbolism, System and Question; (4) The Complex Nature of Algebra; and (5) Some…

Some concrete examples of the use of historical materials in developing certain topics from precalculus and calculus are presented. Ideas which can be introduced with a reformulated curriculum are discussed in five areas: algorithms, combinatorics, logarithms, trigonometry, and mathematical models. (MNS)

Raises and responds to questions about what and how to teach mathematics with the availability of calculators to all students. Discusses whether students need basic facts, mechanical skills, and knowledge of computational algorithms. Argues that students need to develop number sense and analytical skills using simple, symbolic, and graphing…

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)

Discusses the differences between problems and exercises in chemistry, and some of the difficulties that arise when the same methods are used to solve both. Proposes that algorithms are excellent models for solving exercises. Argues that algorithms not be used for solving problems. (TW)

Discusses the difference between a generic chemistry problem (one which can be solved using an algorithm) and a harder chemistry problem (one for which there is no algorithm). Encourages teachers to help students recognize these categories of problems so they will be better able to find solutions. (TW)

Discusses the differences between problems and exercises, the levels of thinking required to solve them, and the roles that algorithms can play in helping chemistry students perform these tasks. Proposes that students be taught the logic of algorithms, their characteristics, and how to invent their own algorithms. (TW)

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…