Ang Keng Cheng

This paper describes our experience in incorporating Maple into a traditional First Year Undergraduate Mathematics course. We describe our approach to the overall organisation of the course, illustrating the use of Maple in specific topics. We also report on the results of a student survey on the use of Maple, noting a few areas for improvement. Overall, the non-intensive approach has had a positive impact on the course. Although this report is on a First Year Undergraduate course, the principles of the approach may be applied to the teaching of Mathematics at other levels as well.

In today’s Information Technology age, educators at all levels are using the power of IT to enhance learning. This paper describes our experience in incorporating the use of a Computer Algebra System (CAS), Maple V, into a traditional First Year Undergraduate Mathematics course. It gives a summary of our approach to the overall organisation of the course, illustrating the use of Maple as a tool to aid the teaching and learning of specific topics. The effects of using Maple were measured by a student survey, conducted at the end of the course. We report and discuss the findings of the survey in this paper. Overall, the approach has had a positive impact on student learning. Although this experiment is on a First Year Undergraduate course, the principles of the approach may be applied to the teaching of Mathematics at other levels as well.

Undergraduate mathematics courses in most universities would consist of numerous modules or subjects. The definitions, theorems and concepts taught in one module are very often based on what has been introduced in previously taught modules. This is especially true for the more advanced modules. Although there is usually a prescribed syllabus for each module, it is impossible to list all the details in the syllabus. This may lead to significant differences when a module is taught by different lecturers. One way to address this problem is to provide an easily accessed and linked set of notes for all fundamental modules in reasonable detail. This may serve to prevent omission of certain topics in earlier modules and repetitions in later modules. In this paper, we describe our experience in developing an integrated set of online undergraduate course notes. In addition, we shall also explain how Maple worksheets are merged into the system for students to explore the mathematical concepts dynamically.

In this paper, we examine the use of a simple stochastic di erential equation in the modelling of an epidemic. Real data for the Singapore SARS outbreak are used for a detailed study. The model is solved numerically and implemented on matlab, with further analysis and re nement. This article is built around several matlab programs and serves to provide a practical and accessible introduction to numerical methods for a stochastic model for epidemics.

Mathematical modelling is an important part of Higher 3 Mathematics,a new mathematics syllabus for pre-University students under the GCE Advanced level curriculum in Singapore. In this paper, how technology may be exploited to facilitate learning and investigation of certain key concepts in the topic is discussed. Examples such as the logistic equation and modelling of epidemics are presented in some detail. Some implications on its impact in the classroom are also discussed.

We have developed a simulation model that describes the spread of dengue fever in Singapore. The population of the host is divided into compartments representing disease status (susceptible, exposed, infectious and resistant) whereas the population of the vector is considered as a whole because it is difficult to determine the dengue virus status in the vector. Larvae density is used as an index of the vector population. In our model, the flow between compartments is described by a set of differential equations and the change of vector is represented by means of a piece-wise function over time. The resulting model is stochastic as well as deterministic. We took into account the majority of factors that known to influence dengue epidemiology. Compared with the deterministic model developed by Newton and Reiter (1992), our model is more realistic and suitable to the local situation. This model also demonstrates the successful use of Maple V, a commonly used computer algebra system, in such modelling techniques.

The purpose of this paper is to examine the possibility of introducing the teaching of mathematical modelling to the secondary school curriculum in Singapore. As well, the benefits of teaching and learning mathematical modelling are discussed. Examples to illustrate the process of mathematical modelling using only basic mathematical ideas and concepts are presented. These serve to illustrate that school mathematics can be used to provide experiences of the process of mathematical modelling in the classroom. Some implications on the teaching and learning of mathematics using such an approach are examined and discussed.

We study the SIR model of transmission of dengue fever with two pathogen strains. A model is constructed to study the effects of different factors on the course of the epidemic. The difference between the two strains is not discussed. Instead, we focus on the trends of primary infection and secondary infection. Our analysis shows that factors related to the host (such as host population) do not change the pattern the spread significantly. In contrast, factors related to the vector (such as vector population, vector life span and biting rate) have a more significant effect on the outbreak of secondary infection.

This paper posits that teachers’ pedagogical content knowledge in mathematical modelling instruction can be demonstrated in the crafting of action plans and expected teaching and learning moves via their lesson images (Schoenfeld, 1998). It can also be developed when teachers shape appropriate teaching moves in response to students’ learning actions. Such adaptive development of teachers’ pedagogical content knowledge may in turn be supported by their knowledge of the mathematical modelling process and Ang’s (to appear) proposed framework for planning mathematical modelling instruction.

Queuing theory is usually introduced to students from second year onwards in a university undergraduate programme, as the mathematical principles governing queues can be fairly demanding, making it challenging to introduce any earlier. However, we often see queues and experience queuing in real life. It would therefore be appropriate, relevant and useful to introduce the concept of queuing theory to preuniversity students or first- year undergraduates. The approach suggested is through simulation models supported by suitable technology. In doing so, students can understand some basic probability theory and statistical concepts, such as the Poisson process and exponential distribution, and learn how queues may be modelled through simulation, without the need to know all about classical queuing theory. In this paper, we will discuss the role that simulation can play in a classroom to create real world learning experiences for students. To provide a concrete illustration, a set of real data collected in a simple ATM queue will be used to explain how students can systematically be engaged in a modelling activity involving queues. Following that, queues at cinema ticketing counters are studied to discuss the modelling of a more complex queue system.