Two complementary processes involved in mathematical modelling are mathematising a realistic situation and applying a mathematical technique to a given realistic situation. We present and analyse work from two undergraduate students and two secondary school teachers who engaged in both processes during a mathematical modelling task that required…

In recent years, there has been some dispute over the appropriate way to model decision making in professional sports leagues. In particular, Szymanski and Kesenne (2004) argue that formulating the decision-making problem in a noncooperative game leads to radically different conclusions about the nature of competition in sports leagues. The author…

This project was developed as an interdisciplinary application of the optimization of a single-variable function. It was used in a freshman-level single-variable calculus course. After the first month of the course, students had been exposed to the concepts of the derivative as a rate of change, average and instantaneous velocities, derivatives of…

There is an international trend in mathematics education of antiauthoritarianism, emphasising cooperative learning and students' autonomous search for knowledge. In Sweden, this is framed by "students' independent work", characterised by only limited amounts of teacher-student and student-student interaction and communication and a low…

This contribution reports about a seven-month long video-based study in two regular Flemish sixth-grade mathematics classrooms. The focus is on teachers' approaches towards problem solving. In our analysis we distinguished between a paradigmatic-oriented (focus on the mathematical structure) and a narrative-oriented (focus on the contextual…

Recent drug studies have investigated the incidence of blood clots among patients using the Ortho Evra[R] birth control patch. In this article, the author describes an investigation of oestrogen levels in the body resulting from the application of the Ortho Evra[R] birth control patch versus daily use of Ortho-Cyclen[R] birth control pills.…

Many students have some difficulty with calculations. Simple dimensional analysis provides a systematic means of checking for errors and inconsistencies and for developing both new insight and new relationships between variables. Teaching dimensional analysis at even the most basic level strengthens the insight and confidence of students, and…

General equilibrium models now play important roles in many fields of economics including tax policy, environmental regulation, international trade, and economic development. The intermediate microeconomics classroom has not kept pace with these trends, however. Microeconomics textbooks primarily focus on the insights that can be drawn from the…

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…

The newly revised mathematics curriculum in Singapore has recently factored Applications and Modelling to be part of the teaching and learning of mathematics. Its implication is that even children should now be involved in works of mathematical modelling. However, to be able to implement modelling activities in the primary mathematics classroom,…

This paper draws on a one year study of three secondary school classrooms to examine the nature of student-student-technology interaction when working in partnership with computer algebra systems (CAS) on mathematical modelling tasks and the classroom affordances and constraints that influence such interaction. The analysis of these data indicates…

This project is one of four that were issued to first semester sophomore undergraduates at the United States Military Academy as part of an integrated learning experience at the end of their Calculus II course work. This project was used during a short, seven lesson block of instruction that was intended to capitalize on their recent academic…

In this paper we describe a teaching approach focusing on modelling in physics, emphasizing scientific reasoning based on empirical data and using the notion of multiple representations of physical phenomena as a framework. We describe modelling activities from a project (PHYS 21) and relate some experiences from implementation of the modelling…

The simplest age-structured population models update a population vector via multiplication by a matrix. These linear models offer an opportunity to introduce mathematical modeling to students of limited mathematical sophistication and background. We begin with a detailed discussion of mathematical modeling, particularly in a biological context.…

The final report of the Williams committee (DCSF, 2008: 68) argues that the revised mathematics Framework (DfES, 2006) "should be reconsidered to achieve a more suitable, user-friendly form." It might also have added that there is not much help and support in it for early years teachers. A much more useful document is the "Practice guidance for…