The article describes the performance of several individual students in a college algebra/precalculus course that focuses on the development of conceptual understanding and the use of mathematical modeling and discusses the likely differences in outcome if the students took a traditional algebra-skills focused course.

In this paper we will present the methodology and pedagogy of Elementary Mathematical Modeling as a one-semester course in the liberal arts core. We will focus on the elementary models in finance and business. The main mathematical tools in this course are the difference equations and matrix algebra. We also integrate computer technology and…

Glycated haemoglobin (HbA1c) is regarded as the gold standard of glucose homeostasis assessment in diabetes. There has been much discussion in recent medical literature of experimental results concerning the relative contribution of fasting and post-prandial glucose levels to the value of HbA1c. A mathematical model of haemoglobin glycation is…

A complete quantitative account of P. Wason's (1966) abstract selection task is proposed. The account takes the form of a mathematical model. It is assumed that some response patterns are caused by inferential reasoning, whereas other responses reflect cognitive processes that affect each card selection separately and independently of other card…

The fraction 16 over 64 has a well known, interesting property. If one incorrectly cancels the sixes, a correct answer of 1 over 4 is obtained. This is an example of a lucky fraction. In this article, the author presents several examples of lucky fractions and proves two interesting properties of these fractions. This article provides students the…

This submission contains the Proceedings of the 2013 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at Brock University in St. Catharines, Ontario. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the…

For nine-week periods during two consecutive years, sixth-grade students at the same school were taught identical mathematics content using two different instructional approaches. Year 1 involved low achievers, whereas Year 2 was mixed ability students. The experimental treatment was a problem-centered approach (PCL) where potentially meaningful…

Debt limits, interest coverage ratios, one-off balanced budget requirements, pay-as-you-go rules, and tax and expenditure limits are among the most important fiscal rules for constraining intertemporal transfers. There is considerable evidence that the least costly and most effective of such rules are those that focus directly on the rate of…

We developed four separate scenarios focusing on the connections between mathematics, biology, and social sciences. This structure facilitated the coordination of faculty from seven academic departments on campus. Each scenario had students from different majors build mathematical models, gather information from their respective disciplines, and…

A localist, parallel constraint satisfaction, artificial neural network model is presented that accounts for a broad collection of attitude and attitude-change phenomena. The network represents the attitude object and cognitions and beliefs related to the attitude, as well as how to integrate a persuasive message into this network. Short-term…

Lecturers in mathematical modelling courses are always on the lookout for new examples to illustrate the modelling process. A physical phenomenon, documented as early as the nineteenth century, was recalled: when a wineglass "sings", waves are visible on the surface of the wine. These surface waves are used as an exercise in mathematical…

The solutions of the discrete logistic growth model based on a difference equation and the continuous logistic growth model based on a differential equation are compared and contrasted. The investigation is conducted using a dynamic interactive spreadsheet. (Contains 5 figures.)

This paper revisits the demonstration of Lenz by dropping magnets down a non-magnetic tube. Recent publications are reviewed and ideas for undergraduate laboratory investigations are suggested. Finally, an example of matching theory to observation is presented. (Contains 4 tables, 5 figures and 3 footnotes.)

Modelling of statistical data is a well established analytical strategy. Statistical data can be modelled to represent, and thereby predict, the forces acting upon a structure or system. For the rapidly changing systems in the world of education, modelling enables the researcher to understand, to predict and to enable decisions to be based upon…