Teaching Mathematics and its Applications - current issue

A note on arc length

Patyi, I. — Mon, 24 Aug 2009 22:49:01 PDT

We consider how the arc length integral of the graph of a function in the plane is connected with the hyperbola and its rational parameterization.

A proof of the converse of the Pythagorean proposition

Scimone, A. — Mon, 24 Aug 2009 22:49:01 PDT

The article presents a demonstration of the converse of the Pythagorean Theorem based on the reductio ad absurdum. This is necessary to overcome the discrepancy, noticed by pupils, between the Euclidean purpose to demonstrate that the given triangle is right-angled and the auxiliary figure by which the given triangle is drawn as if it were already a right-angled one. To the eyes of students this does not make the Euclidean reasoning clear.

The impact of the mathematics support centre on the grades of first year students at the National University of Ireland Maynooth

Bhaird, C. M. a., Morgan, T., O'Shea, A. — Mon, 24 Aug 2009 22:49:01 PDT

In this article, we consider the mathematics grades of first year students at the National University of Ireland Maynooth and the influence that the Mathematics Support Centre (MSC) has on these grades. We will consider the evidence to suggest that the MSC has a positive effect on the grades of the students who attend the centre. It seems to be particularly beneficial to students with weak mathematical backgrounds. As these students are most at risk of failing or dropping out of University, the positive impact of the MSC on their grades is very encouraging.

An application of calculus: optimum parabolic path problem

Atasever, M., Pakdemirli, M., Yurtsever, H. A. — Mon, 24 Aug 2009 22:49:01 PDT

A practical and technological application of calculus problem is posed to motivate freshman students or juniory high school students. A variable coefficient of friction is used in modelling air friction. The case in which the coefficient of friction is a decreasing function of altitude is considered. The optimum parabolic path for a flying object for which the work done by variable coefficient air friction force is minimum is determined. If a flying object follows the determined path, energy requirement would be less compared with other parabolic or linear paths.

An integrative learning experience within a mathematics curriculum

Melendez, B., Bowman, S., Erickson, K., Swim, E. — Mon, 24 Aug 2009 22:49:02 PDT

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 develop a final presentation that included a committee consensus on how to approach the problem in a practical way. As a result, students learned how mathematics plays a role in other disciplines and how insight from different points of view affects the approach taken to a complex problem.

Teaching mathematics understandings for transfer

Jones, J. L., Jones, K. A., Vermette, P. J. — Mon, 24 Aug 2009 22:49:02 PDT

Promoting student understanding for transfer is an illusive hallmark of effective mathematics instruction. While much research has shown the necessity of promoting understanding for transfer, less attention has been paid to actual pedagogical strategies that can be used to promote transfer of mathematical ideas. Using Fogarty et al. (1992, How to Teach for Transfer, The mindful school, Palatine, Illinois: Skylight Publishing) ‘ten tools for teaching for transfer’ as a model, the authors of this piece provide numerous suggestions designed specifically for promoting transfer of concepts in secondary mathematics.

The immortal ant and the expanding balloon

Griffiths, M. — Mon, 24 Aug 2009 22:49:02 PDT

In this article we consider, via a specific modelling example, the educational benefits to be gained from running mathematical activities with our sixth-form and undergraduate students that, in modern parlance, might be termed ‘rich tasks’. The idea for this modelling activity arose while the author was reading a popular-science book on cosmology (in particular, on the possible shapes of the universe). Light travelling around the universe was likened to an ant crawling around a balloon. A statement in the book regarding the ant's progress around the balloon did not entirely ring true with the author, and his subsequent investigations led to the activity described here. We explore several scenarios associated with the model in order both to pre-empt possible paths taken by the students and to be able to provide some guidance when necessary. Suggestions are given as to how the activity may be extended, and then, after highlighting the numerous educational benefits, we consider the potential pitfalls and difficulties associated with the delivery of tasks such as these.

Real world graph connectivity

Lind, J., Narayan, D. — Mon, 24 Aug 2009 22:49:02 PDT

We present the topic of graph connectivity along with a famous theorem of Menger in the real-world setting of the national computer network infrastructure of National LambdaRail. We include a set of exercises where students reinforce their understanding of graph connectivity by analysing the National LambdaRail network. Finally, we give suggestions for using this module as a project in an undergraduate mathematics course.