Technology-active mathematical modelling

Ferrucci, Beverly J.; Carter, Jack A

doi:10.1080/0020739031000148921

Cited by 7 publications

(6 citation statements)

References 9 publications

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“…There seems to be no agreed definitions of mathematical models and modelling (Ferrucci & Carter, 2003). A convenient way through the variations available may simply be to view a mathematical model as the representation of some aspect of the world-as-experienced by the use of mathematical techniques in such a way that predictions can be made about it.…”

Section: Mathematical Modelsmentioning

confidence: 98%

The Contribution of Visualisation to Modelling-Based Teaching

Gilbert

Justi

2016

Models and Modeling in Science Education

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Both the creation of models and their communication to other people involve visualisations. These are, respectively, 'internal' (or mental) and 'external' (or public) representations, with the latter confusingly also being called visualisations. Perceptions by one of the five senses provide external representations. The modes of external representation of particular importance in science education are the: gestural, concrete, static visual (pictures, diagrams, graphs, mathematical and chemical equations), dynamic visual (drama, animation, simulation), oral and auditory. The skills and abilities that constitute meta-visual competence in the modes are reviewed in this chapter, for they enable the central element of modelling -the design and conduct of thought experiments -to take place. Consequently, the skills and abilities of both modelling and of visualisation are mutually developed and employed during MBT. The Growing Importance of VisualisationSince the dawn of 'the age of science', arguably about 1400 CE, evermore detailed phenomena in the world-as-experienced have been studied, producing increasingly complex and detailed models of their behaviour and constitution. In order to be accepted as contributing to scientific progress, these models then have to be communicated by their creators to other scientists for critical review and, given sufficient support, for general publication in scientific journals and use in other research. Creating, seeking approval for, and disseminating these models inevitably taxes the imaginations of scientists, tasks for which every help is no doubt much appreciated. With the somewhat parallel growth of systematic science education, in Europe and North America from about 1850, one problem that rapidly emerged was how to successfully promote an understanding of the ever-expanding range of established models in students. More recently, in order both to support the development of more scientists and to facilitate greater creativity, as well as providing insight for the general public into how models are devised and evaluated, a greater emphasis has been placed in science education on the skills of modelling. Visualisation plays a central and increasing role in all three of these activities: the creation of models, their evaluation by the scientific community, and their communication to students of science of all ages. 122A visualisation, also commonly called 'what is seen in the mind's eye', is a colloquial way of referring to the result of the formation of a 'mental image' or 'mental model'. Visualising, the formation of a visualisation, is a quasi-perceptual experience, in that it resembles perceptual experience, but is one which can occur in the absence of the external stimuli (Thomas, 2014). The steadily increasing social pressure to create and communicate visualisations has gone hand-in-hand with an expansion of the availability of support for doing so. Whilst early efforts were largely confined to sketches and line drawings, the advent of high-quality reprographics and ...

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Section: Mathematical Modelsmentioning

confidence: 98%

The Contribution of Visualisation to Modelling-Based Teaching

Gilbert

Justi

2016

Models and Modeling in Science Education

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“…In addition, the solution of the model provides students with opportunities to exploit the potential of technology or computer tools, as advocated by Ferrucci and Carter [13].…”

Section: Discussionmentioning

confidence: 98%

Real-life application of a simple continuum traffic flow model

Ang¹,

Neo²

2005

International Journal of Mathematical Education in Science and

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A numerical solution to a simple continuum model for traffic flow is discussed. Real traffic data are used for an in-depth study and the implementation of a finite difference scheme is described in detail. The results show that predicted traffic flow conditions agree well with the observed data provided boundary conditions are treated properly. This modelling exercise provides an excellent example of applying mathematics to a fairly complex real life problem. It serves to provide insight into the processes involved in deterministic modelling using a realistic and relevant example.

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“…Computer models allow students to experiment with concepts that are often underpinned by a level of mathematical sophistication beyond their experience or interest [7]. This may be particularly important for the ecology student, who may be discouraged from learning key concepts because of a perceived, and possibly real, mathematical hurdle.…”

Section: Mathematics and The Ecologistmentioning

confidence: 99%

SLAC: A tool for addressing chaos in the ecology classroom

Hamilton¹

2005

International Journal of Mathematical Education in Science and

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Until the early 1970s, ecologists generally assumed that erratic fluctuations observed in natural populations were a product of stochastic noise. It is now known that extremely complex dynamics can arise from basic deterministic processes. This field of study is generally called chaos theory. Here, a computer program, SLAC (Stability, Limits, And Chaos), is described, which facilitates the study of a simple deterministic model known as the logistic difference equation. It is designed to familiarize the biology student, who may not be mathematically inclined, with the fundamental concepts of population dynamics, especially the not-so-intuitive notion that complexity can evolve from deterministic mechanics. In addition to the program, pedagogically significant issues associated with the derivation of the equation and its parameters, and population dynamics in general, are highlighted.

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Technology-active mathematical modelling

Cited by 7 publications

References 9 publications

The Contribution of Visualisation to Modelling-Based Teaching

The Contribution of Visualisation to Modelling-Based Teaching

Real-life application of a simple continuum traffic flow model

SLAC: A tool for addressing chaos in the ecology classroom

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