Recently, abstracted quantitative structures (AQS), a construct from quantitative reasoning, has been offered as a means to conceptualize and study mathematization during mathematical modeling. Extending this theoretical work, we provide empirical evidence that an intervention targeting participants' AQS can assist in aligning modelers' models…

In this work, we review and share some useful technology for mathematics educators that can help to enhance their pedagogical practices to motivate students to improve their further understanding of differential equations after an initial exposure to the topic in an undergraduate class. In particular, we present some innovative ways to employ…

This article is based on data from two major research projects that investigated students involved in mathematically demanding courses during their transition through college and into university. It explores the nature of modelling as a mathematical practice in this important transition phase for students. Theoretical considerations are informed…

How far does the back end of a bus swing out as the driver makes a turn at an intersection?'' is the problem discussed. (MM)

The approaches taken to psychological research are discussed. Studies are classified as axiomatic, classical, stochastic or statistical, or structural. The mathematical models used in each type of study are discussed. (SD)

The meaning of an "application" of mathematics is examined and sample real-world mathematical problems are given. (DT)

Elementary differential calculus is used to analyze and to discuss some complex economic situations. (JT)

The author uses mathematical models that involve only algebra and a few basic ideas in discrete probability to describe the frequency of conception in large human societies. A number of calculations which can be done by students as exercises are given. (MN)

Mathematical observations are made about some continuous curves, called transitions, encountered in well-known experiences. The transition parabola, the transition spiral, and the sidestep maneuver are presented. (MNS)

A course in mathematical model-building is described. Suggested modeling projects include: urban problems, biology and ecology, economics, psychology, games and gaming, cosmology, medicine, history, computer science, energy, and music. (MK)

After considering the growth in the use of mathematics in the past 25 years, this report makes four major recommendations regarding the undergraduate curriculum: (1) The mathematics department should offer a course or two in applied mathematics which treat some realistic situations completely, including the steps of problem formulation, model…