It is difficult to ensure that incoming students enrol in first year courses at a level that is commensurate with their ability. Not only do students come from a diverse range of backgrounds, but mathematics at university is, in general, more rigorous and conceptual than it is at high school, and success at high school does not always guarantee…

The paper discusses the interaction between intuitive biases of probabilistic thinking and mathematical knowledge. It would appear that students may answer numerical problems correctly but falter on simple descriptive solutions. Students appear to relinquish formal knowledge for simpler heuristics when attempting to describe the outcome of an…

The main objective of this study was to gauge preparedness in math with achievement in first semester math for the fall 2005 intake of Manufacturing Sciences Division post-secondary program students. The data used to measure this level of preparedness was gleaned from students' high school Grade 12 (new and old curriculum) or Ontario Academic…

In part 1 of this work we showed how modern mathematical research could, with a suitably chosen problem, be included in the first year curriculum of undergraduate mathematicians. With the use of Computer Algebra Systems, even the average undergraduate mathematician can aspire to discover interesting yet still unexplained behaviour in many areas of…

Semantic retrieval (SR) and executive-procedural (EP), but not visuospatial (VS) skills, have been found to be uniquely predictive of mathematical calculation skills in a sample of clinically referred college students. This study set out to cross-validate these results in an independent sample of clinically referred college students (N = 337) as…

The narrative in this article begins with a simple remark about a heavenly body to a class, and then winds its way through a lot of mathematical topics.

David Gale was one of the mathematicians responsible for the modern form of the theory of duality in linear programming and the associated proof of the minimax theorem in the theory of games. He is a member of the National Academy of Sciences and is Professor Emeritus of Mathematics and Operations Research at the University of California at…

How does artificial gravity affect the path of a thrown ball? This paper contrasts ball trajectories on the Little Prince's asteroid planet B-612 and Arthur C. Clarke's rotating-drum spacecraft of 2001, and demonstrates curve balls with multiple loops in the latter environment.

We show that there is a link between a standard calculus problem of finding the best view of a painting and special tangent lines to the graphs of exponential functions. Surprisingly, the exponential function with the "best view" is not the one with the base "e." A similar link is established for families of functions obtained by composing…

For a long time, the medieval university maintained relative consistency throughout Europe in teaching topics and methods. But between 1550 and 1650 this came to an end. The evolution concerned the content of the courses and, to a lesser extent, the way the field was taught. The impact of these changes varied greatly from place to place, and new…

Online collaboration exercises were used as part of a diverse assessment package for an undergraduate differential equations course. Online collaboration served as a highly effective method for promoting and assessing generic graduate capabilities such as writing in a context-relevant manner and the development of self-awareness with regard to…

Effective statistical collaboration in a multidisciplinary health research environment requires skills not taught in the usual statistics courses. Graduates often learn such collaborative skills through trial and error. In this paper, we discuss the development of a biostatistical collaboration course aimed at graduate students in a Health…

As a response to the "Mathematics Problem" many universities introduced mathematics support provision. These additional learning opportunities were invariably in a specific physical location and available at certain times. In order to increase the number and types of students who could access support e-learning resources were made…

Many students in U.S. schools have trouble understanding fractions and Algebra II, the one difficultly occurring at the end of elementary school, the other in high school. One reason is that schools generally focus on one aspect of mathematics--calculation--and often fail to address the second aspect--interpretation. Also responsible is the…

Popular culture provides many opportunities to develop quantitative reasoning. This article describes a junior-level, interdisciplinary, quantitative reasoning course that uses examples from movies, cartoons, television, magazine advertisements, and children's literature. Some benefits from and cautions to using popular culture to teach…