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.…

This paper proposed the question "How do we teach logical thinking and sophisticated mathematics to unsophisticated college students?" One answer among many is through the writing of computer programs. The writing of computer algorithms is mathematical problem solving and logic in disguise and it may attract students who would otherwise stop…

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

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…

Considers possibility of developing a computer tutor around an explicit concept-learning theory derived from machine learning techniques. Some problems with using the focusing (and similar) algorithms in this role are discussed and possible solutions are developed. Design for a guided discovery learning system for tutoring concepts is proposed.…

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)

It is suggested that the reasons for teaching the standard written algorithms for calculations are not out of date. Alternative algorithms, such as mental algorithms, calculators, and nonstandard written methods, are discussed. (MP)

The question is raised: What comes first: rules of calculation or the meaning of concepts? The pressures on the teacher to teach and simplify knowledge to algorithms are discussed. The relation between conceptual and procedural knowledge in school mathematics and consequences for the teacher's professional knowledge are considered. (DC)

Provides the transcript of an interview with Dr. Lev Landa that addressed issues related to his algorithmico-heuristic theories of learning and instruction, called Landamatics. Highlights include teaching thinking versus knowledge; algorithms; instructional design; improving training and performance in industry, business, and government;…

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)

One teacher's struggle with conveying a concrete realization of the subtraction algorithm to students leads to a discussion of elementary mathematics instruction in general. (MP)

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…

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)