Many institutions regularly conduct surveys of students. In some cases these provide descriptive statistics about students' actual use of course components and the descriptive statistics are discussed using ordinary language. A number of refinements to these surveys are proposed. It is argued that mathematical modeling as used in the discipline of…

The authors explored the effects of teaching conceptual model-based problem-solving instruction on students' ability to solve problems in various situations. Participants were 3 4th-and 5th-grade students with or at risk for mathematics disabilities. The authors used an adapted multiple-probe across-participants design to assess the functional…

In this article, the authors share an episode from an after-school program and focus on eight of the twenty-four urban, sixth-grade students who volunteered to work on mathematical problem solving. When students are given a supportive environment, open-ended tasks, and thoughtful teacher questioning, their reasoning can develop naturally. By…

In this study, psychometric properties of the test of the three-mathematical minds (M3) were investigated. The M3 test was developed based on a multidimensional conception of giftedness to identify mathematically talented students. Participants included 291 middle-school students. Data analysis indicated that the M3 had a 0.73 coefficient as a…

For over a decade, research studies of mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. To deliver on the promise of common standards, the standards…

At United States Military Academy, a unit on biological modeling applications forms the culminating component of the first semester core mathematics course for freshmen. The course emphasizes the use of problem-solving strategies and modeling to solve complex and ill-defined problems. Topic areas include functions and their shapes, data fitting,…

The teaching of mathematical modeling to undergraduate students requires that students are given ample opportunity to develop their own models and experience first-hand the process of model building. Finding an appropriate context within which modeling can be undertaken is not a simple task as it needs to be readily understandable and seen as…

The goal of this study was to determine how the fear relevancy of outcomes during probabilistic classification learning affects behavior and strategy use. Novel variants of the "weather prediction" task were created, in which cue cards predicted either looming fearful or neutral outcomes in a between-groups design. Strategy use was…

This article describes how sixth-grade students developed concrete models to solve division of fractions story problems. Students developed separate two-step procedures to solve measurement and partitive problems, drawing on invented procedures for division of whole numbers. Errors also tended to be specific to the type of division problem…

At least 3 different types of computational model have been shown to account for various facets of both normal and impaired single word reading: (a) the connectionist triangle model, (b) the dual-route cascaded model, and (c) the connectionist dual process model. Major strengths and weaknesses of these models are identified. In the spirit of…

This paper offers some reflections on the difficulties of teaching mathematical modeling to students taking higher education courses in which modeling plays a significant role. In the author's experience, other aspects of the model development process often cause problems rather than the use of mathematics. Since these other aspects involve…

The oxygen dissociation curve (ODC) of hemoglobin (Hb) has been widely studied and mathematically described for nearly a century. Numerous mathematical models have been designed to predict with ever-increasing accuracy the behavior of oxygen transport by Hb in differing conditions of pH, carbon dioxide, temperature, Hb levels, and…

People tend to perceive ongoing continuous activity as series of discrete events. This partitioning of continuous activity may occur, in part, because events correspond to dynamic patterns that have recurred across different contexts. Recurring patterns may lead to reliable sequential dependencies in observers' experiences, which then can be used…

This paper reports on the implementation of a self-directed learning process in a circuit theory course, incorporating dynamic training elements which were designed on the basis of a cybernetic model of cognitive process management. These elements are centrally linked in a dynamic learning frame, created on the monitor screen, which displays the…

AN INQUIRY INTO RECRUITMENT OF APPRENTICES TO SKILLED TRADES IN WESTERN AUSTRALIA INDICATED LITTLE CORRELATION BETWEEN THE NUMBER OF NEW APPRENTICES AND THE LEVEL OF INDUSTRIAL EMPLOYMENT OR THE TOTAL NUMBER OF APPRENTICES. THIS ARTICLE ATTEMPTS TO OUTLINE A MATHEMATICAL MODEL OF AN APPRENTICESHIP SYSTEM AND DISCUSS ITS IMPLICATIONS. THE MODEL, A…