A manipulative model for the addition, subtraction, and multiplication of integers is described in which a carpet square with a hole in it and the plug that fits in the hole are "opposites" of each other. Several other models for integer multiplication are briefly described. (MN)

Described is the development of a simulation, or model of an existing congested pedestrian crossing situation by elementary school students in order to conduct trials of their solutions. (MN)

An alternative explanation is presented for the pattern of relative difficulty of arithmetical word problems to that suggested in a 1983 article. It is argued, that for many problems, much of the symbolic manipulation is accomplished externally, not internally. (MNS)

An example of how geometry serves as a model in the real world is outlined, with suggestions on how it might be used at the high school level. (MNS)

Mastering the basic number combinations involves discovering, labeling, and internalizing relationships, not merely drill-based memorization. Counting procedures and thinking strategies are components, and it may be that using stored procedures, rules, or principles to quickly construct combinations is cognitively more economical than relying…

The author first corrects Baroody's description of the network retrieval model for basic number facts, in which facts are stored in memory and retrieved as needed. He then indicates weaknesses in Baroody's argument. (MNS)

This paper addresses the developments of a class of fifth-grade children as they worked modeling problems during the first year of a 3-year longitudinal study. In contrast to usual classroom problems where students find a brief answer to a particular question, modeling activities involve students in authentic case studies that require them to…

This set of transparencies shows how the manipulation of combinatorial structures in the context of modern combinatorics can easily lead to interesting teaching and learning activities at every level of education from elementary school to university. The transparencies describe: (1) the importance and relations of combinatorics to science and…

Methods of effectively teaching algebraic thinking in elementary schools as well as secondary schools is the topic of the following 19 papers. Papers include: (1) "Transforming Algebra from an Engine of Inequity to an Engine of Mathematical Power by 'Algebrafying' the K-12 Curriculum" (J. Kaput); (2) "Developing a Coherent and…

Mathematical modelling and an example used with undergraduates were presented in part 1 (v17, n5, p212-18, 1982). A second example, Power from Windmills, is provided which has considerable potential for development both as a model and as a series of modelling experiences of increasing difficulty for students with different backgrounds. (Author/JN)

Describes the heating of a baby's milk bottle (an exercise in modelling) and the interaction between lecturer and students as they formulate the problem, produce a tentative solution and interpret the solution. (Author/JN)

Mathematical modeling is defined. Examples are used to show that there are models available which illustrate both the traditional use of mathematics in the physical science and its newer use in nonphysical disciplines, and which are at a suitable level for teaching in schools. (Author/MK)