This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…

We have been investigating university student conceptions of mathematics over a number of years, with the goal of enhancing student learning and professional development. We developed an open-ended survey of three questions, on "What is mathematics" and two questions about the role of mathematics in the students' future. This…

In this paper, we examine the development of pre-service mathematics teachers' use of multiple representations during teaching in technology-rich environments. The pre-service teachers took part in a preparation program aimed at integration of technology into teaching mathematics. The program was designed on the basis of Technological Pedagogical…

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…

The paper presents the results of an empirical evaluation of a mathematical model of ethnolinguistic vitality. The model adds several new factors to the set used in previous models of ethnolinguistic vitality and operationalises it in a manner that would make it easier to compare the vitality of different groups. According to the model, the…

A generalized Rasch model is presented for measuring attitudes; it is based on the concepts of Thurstone's method of successive intervals. Benefits of the model are illustrated with a study of students' (N=4,035 fifth through ninth graders) interest in physics. (SLD)

To validate a proposed statistical index of instructional effectiveness, researchers identified 33 school characteristics related to instructional effectiveness and tested the relationship between these characteristics and the proposed index. The index includes two subject area indices, mathematics and reading, and is based on statistical…

Researchers have been limited in their ability to examine multiple constructs simultaneously due to the constraints imposed by traditional statistical methods. The most notable limitations include the need for a relatively large sample size while restricting the variables to a relatively small number. The application of a newly discovered…