The ordered partition model is described as an extension of the partial credit model, its relationship to other models is discussed, and two examples are presented. The model is designed for a measurement context in which categories of response to an item cannot be completely ordered. (SLD)

Applications in engineering, science and technology within undergraduate programmes can be difficult for students to understand. In this paper, new results are presented which go some way to demonstrate and explain the problems faced by students in linking mathematical models to real-world applications. The study is based on student responses to…

A inquiry-based approach called the "modelling discussion" is introduced for structuring beginning modelling activity, teaching new mathematics from examining its applications in contextual situations, and as a general classroom management technique when students are engaged in mathematical modelling. An example which illustrates the style and…

Development of mathematical problem solving skills is an age old problem in mathematics. This paper details the design of a component of a first year university mathematics course in which group work and mathematical communication skills, especially writing skills, are used as a tool to develop non-routine problem solving skills. In this design…

The integration of history into educational practice can lead to the development of activities through the use of genetic "moments" in the history of mathematics. In the present paper, we utilize Oresme's genetic ideas--developed during the fourteenth century, including ideas on the velocity-time graphical representation as well as geometric…

Suggestions are provided for activities involving the construction of mathematical models to solve "real-life" problems. (SD)

Presents a method of solving decision problems in conditions of incomplete knowledge of the probabilities of the states of nature. It uses all available information in order to delimit the region of ignorance as closely as possible. (Author)

Three self-instructional episodes for use in physical science classes were written and tested with ninth grade students. The development was based on Piaget's learning theory leading students from actions with physical apparatus to the formulation of a mathematical equation. The episodes concerned: (1) equilibrium in a balance; (2) the oscillation…

The nature of insight is discussed as it relates to mathematical models. Intuition and the intuitively obvious are argued to have no necessary connection with models. (MP)

This article examines the Pythagorean Theorem from a geometric point of view by suggesting some natural extensions of the theorem. The use of a more general theorem to prove a difficult one is suggested, where possible. The article includes figures and proofs. (Author/MA)

Presents a simple model whereby the work per cycle done on an external agent, and a sand reservoir, by a reversible heat engine can be analyzed explicitly. (Author/SL)

Timing stoplights and trying to determine the best way to allocate cycle time to the two directions is discussed. The simple case and improving the model are both considered. (MNS)

A mathematical model of a soccer-league competition results is set up and investigated using simple randomization techniques. The hypothesis that winning the league championship was purely luck was statistically tested. (JP)

When an engineering researcher changes from his work on things to research on people, he faces an array of new ethical questions, and a new view of scientific objectivity must be developed for the study of man and society. (IR)