Schools are facing increasing demands to prepare students for rapid economic, environmental and social changes, for jobs that have not yet been created, for technologies that have not yet been invented, and to solve social problems that have not yet been anticipated. Underpinning the E2030 project is the premise that education needs to do more…

Attempts to describe a notion parallel to number sense, called symbol sense, incorporating the following components: making friends with symbols, reading through symbols, engineering symbolic expressions, equivalent expressions for non-equivalent meanings, choice of symbols, flexible manipulation skills, symbols in retrospect, and symbols in…

Teaching which does not in any significant way address the genesis of mathematical ideas hides the fact that mathematics is created by people; that it involves intuition, exploring, conjecturing, and reasoning; and that it is purposeful. Such teaching can give students appearance that much of mathematics is very arbitrary; it just falls from the…

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

This response to Usiskin's editorial comment on calculator use in the May 1983 issue considers why arithmetic is taught. The belief that mathematics improves thinking and the humanist position that it is part of our cultural heritage are noted. The role of mathematics in the curriculum should be reconsidered. (MNS)

The author presents and elaborates on a division algorithm devised by his 9-year-old son. (MK)

Based on Piaget's theory that children acquire number concepts by constructing them from within, the authors conclude that teaching algorithms harms mathematics learning. A better approach is allowing them to construct their own logico-mathematical knowledge and invent their own efficient procedures. (JOW)

An algorithm is first defined by an example of making pancakes and then through discussion of how computers operate. The understanding that human beings bring to a task is contrasted with this algorithmic processing. In the second section, the question of understanding is related to learning algorithmic performance, with counting used as the…

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…

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…

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)

Three types of arithmetic algorithms are discussed and compared. These are algorithms designed to get the right answer, computer algorithms, and algorithms designed to get the right answer and understand why. (MP)

Three different methods of teaching fraction computation were compared using community college student scores on measures of fraction computation, fraction understanding, and attitude towards mathematics. One method used conventional algorithms; the second, a control for the effect of using a calculator, used conventional algorithms and…

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)

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)