Emphasis on problem solving and mathematical modeling has gained considerable attention in the last few years. Connecting mathematics to other subjects and to the real world outside the classroom has received increased attention in mathematics programs. This article describes an application of simple differential equations in the field of…

Traditionally, students learn arithmetic throughout their primary schooling, and this is seen as the ideal preparation for the learning of algebra in the junior secondary school. The four operations are taught and rehearsed in the early years and from this, it is assumed, "children will induce the fundamental structure of arithmetic" (Warren &…

A series of simple games can be analyzed inductively to determine strategies. Students explore possibilities, hypothesize solutions, prove their solutions correct, and then generalize to more complex games. (SD)

Complex decision-making environments often demand that a range of alternative strategies be identified and compared for their shared value in achieving desired ends. Simple parametric statistical procedures such as analysis of variance and discriminant function analysis can be used in such situations to compare (using selected criteria) the value…

It is noted that helping children learn how to solve problems has become a major goal for school mathematics. However, many children are not very successful at deciding what operation is appropriate for solving a given problem, and teachers often have difficulty describing or explaining how to identify the key features of a particular problem that…

This paper notes three objections to the use of hand-held calculators in schools: they would (1) block reasoning, (2) make individuals machine-dependent, and (3) broaden the gap between developed and underdeveloped nations. Each is addressed, with specific examples used to refute them. The belief is strongly expressed that calculators can aid in…

Flow-diagrams, algorithms, decision logic tables, and concept maps are presented in detail as methods for teaching practical procedures, problem solving, and basic concepts in microbial genetics. It is suggested that the flexible use of these methods should lead to an improved understanding of microbial genetics. (Author/MA)

Described are various common misconceptions about the nature of mathematics and suggests that courses or activities based on model building might help change these. Two examples are offered. (SD)

Three models are compared in terms of detail, scope, attention to individual differences, and how they deal with qualitative change and semantic processing. Two are information-processing models of arithmetical word problem-solving performance, and the third is a model of children's counting types and thinking strategies. (MNS)

Over 600 pupils in grades five, seven, and nine in Italian schools were asked to choose the operation needed to solve 26 multiplication and division word problems. The findings seemed to confirm the impact of the repeated addition model on multiplication and of the partitive model on division. (MNS)

How children can be guided to see and feel the power of thinking with and about mathematical symbols is discussed. A strategy to help them bridge the gap between manipulative models and symbols is detailed. (MNS)

A method is described for representing quadratic functions by three-dimensional wire models. This enables one to form a simple geometric concept of the location of imaginary zeros. (MNS)

This paper develops and illustrates a latent trait approach to constructing an item bank when responses are scored in several ordered categories. This approach is an extension of the methodology developed by Choppin, Wright and Stone, and Wright and Bell for the construction and maintenance of banks of dichotomously scored items. (Author/PN)

To examine how conceptual knowledge about fraction magnitudes changes as students' learning progresses, 5th and 7th-grade students were asked to solve fraction magnitude problems that entailed finding a fraction between two given fractions and then to evaluate solutions for similar problems that were modeled for them. When the given fractions…

The University of Maryland offers a physics course as part of the Maryland Collaborative for Teachers' Preparation (MCTP) project. One of the course aims is to promote the learning of the concept of a function through the learning of physics. Students learn in small groups through problem solving and with the aid of microcomputer-based…