Teaching Mathematics and its Applications - Advance Access

Using technology to facilitate reasoning: lifting the fog from linear algebra

Berry, J. S., Lapp, D. A., Nyman, M. A. — 2008-04-24

This article discusses student difficulties in grasping concepts from linear algebra. Using an example from an interview with a student, we propose changes that might positively impact student understanding of concepts within a problem-solving context. In particular, we illustrate barriers to student understanding and suggest technological interventions to address these barriers.

'Model your genes the mathematical way'--a mathematical biology workshop for secondary school teachers

Martins, A. M., Vera-Licona, P., Laubenbacher, R. — 2008-04-24

This article describes a mathematical biology workshop given to secondary school teachers of the Danville area in Virginia, USA. The goal of the workshop was to enable teams of teachers with biology and mathematics expertise to incorporate lesson plans in mathematical modelling into the curriculum. The biological focus of the activities is the lactose operon in Escherichia coli, one of the first known intracellular regulatory networks. The modelling approach utilizes Boolean networks and tools from discrete mathematics for model simulation and analysis. The workshop structure simulated the team science approach common in today's practice in computational molecular biology and thus represents a social case study in collaborative research. The workshop provided all the necessary background in molecular biology and discrete mathematics required to complete the project. The activities developed in the workshop show students the value of mathematical modelling in understanding biochemical network mechanisms and dynamics. The use of Boolean networks, rather than the more common systems of differential equations, makes the material accessible to students with a minimal mathematical background.

High school students can be exposed to the excitement of mathematical biology from both the biological and mathematical point of view. Through the development of instructional modules, high school biology and mathematics courses can be joined without having to restructure the curriculum for either subject. The relevance of an early introduction to mathematical biology allows students not only to learn curriculum material in a innovative setting, but also creates an awareness of new educational and career opportunities that are arising from the interconnections between biological and mathematical sciences.

The materials used in this workshop are available at a website created by the directors: http://polymath.vbi.vt.edu/mathbio2006/.

Investigating birth control: comparing oestrogen levels in patients using the Ortho Evra(R) patch versus the Ortho-Cyclen(R) pill

Laurent, T. A. — 2008-04-22

Recent drug studies have investigated the incidence of blood clots among patients using the Ortho Evra® 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® birth control patch versus daily use of Ortho-Cyclen® birth control pills. Prescribing information provided by the manufacturer and mathematical models from pharmacokinetics are used to investigate differences between the two birth control methods. Given the pharmacokinetic information on these drugs, applied calculus students are asked to recalculate the size of the patch so that the areas under the curves are equal. Their findings are compared to studies reported in the prescribing information produced by Ortho McNeil Pharmaceuticals, the manufacturers of these products.

Reorganizing freshman business mathematics II: authentic assessment in mathematics through professional memos

Green, K., Emerson, A. — 2008-02-22

The first part of this two-part paper (13) described the development of a new freshman business mathematics (FBM) course at our college. In this paper, we discuss our assessment tool, the business memo, as a venue for students to apply mathematical skills, via mathematical modelling, to realistic business problems. These memos have proven a crucial step in turning our FBM course around from a dreaded course with little connection to students’ intended careers into a course where students experience the power of mathematics for solving problems and informing decisions. Comments from students in the course throughout its 6-year history clearly point to the course's value and importance.

Matrix solution of coupled differential equations and looped car following models

McCartney, M. — 2008-02-10

A simple mathematical model for the behaviour of how vehicles follow each other along a looped stretch of road is described. The resulting coupled first order differential equations are solved using appropriate matrix techniques and the physical significance of the model is discussed. A number possible classroom exercises are suggested to help students engage with the model and its solution. The material is suitable for use as part of a first course in differential equations at undergraduate level.

Motivating the concept of eigenvectors via cryptography

Siap, I. — 2008-02-07

New methods of teaching linear algebra in the undergraduate curriculum have attracted much interest lately. Most of this work is focused on evaluating and discussing the integration of special computer software into the Linear Algebra curriculum. In this article, I discuss my approach on introducing the concept of eigenvectors and eigenvalues, which I have used for the last 3 years in my Linear Algebra course. I offer some examples on how I have attracted the interest of our students via Hill ciphering, a method of cryptography. After emphasizing the effect of a linear transformation in a vector space and the importance of eigenvectors, I show how students’ motivation and understanding towards one of the abstract concepts in Linear Algebra; eigenvalues and eigenvectors have grown positively.

The Bolyai lamp, a new math manipulative modelling the hyperbolic plane

Gyorfi, Z. — 2007-11-23

The author, Zoltan Györfi, has requested that this article is withdrawn from publication.