Resource material for the IT PGCE:
This page gives activities and resources for the use of computer-based modelling. Most of the examples are from Chemistry but there are a few from physics.
Most of the examples used here were devised to help 'A' level pupils and those in the first year of university to understand aspects of chemical equilibrium. They have been used in a number of European countries. A brief explanation of their uses can be downloaded as can a paper produced by an ERASMUS/SOCRATES project which explains them in more detail. The first of these downloads is from the book 'Learning with artificial worlds: computer-based modelling across the curriculum' edited by Harvey Mellar et al. (Institute library code Loz Butb MEL) which is an excellent resource for those who wish to understand this topic better. You can also download a paper giving some examples from physics.
Essentially there are two ways in which pupils can use spreadsheets for modelling activities.
Usually 'exploratory' modelling involves running a simulation - a model written by an expert - although this need not be the case. One useful classroom activity is to get children to produce their own models and then to explore each others.
A (technically) simple modelling activity that was devised for use with people studying 'A' level chemistry can be downloaded. This has been incorporated into both Nuffield and Salter's 'A' level chemistry courses to help students understand the nature of the equilibrium law and, by replacing boring repetitive but simple calculations, allows the pupils to concentrate on the science rather than the maths.
As was noted above, calculations are often a barrier to understanding in science. These barriers are of two sorts. The most obvious is where the calculations are difficult, but also just doing the same simple sum time and time again moves the pupils attention away from the concepts they are studying to the mechanics of the maths task. Automating the calculations allows pupils to concentrate on getting a 'feel' for what is happening - increasing their qualitative understanding of the process - which, contrary to most people's expectations is often the hardest thing for them to get. These examples are designed to illustrate ways in which the use of a spreadsheet can help overcome both of these kinds of barrier.
The first 6 of them have been used in the teaching of 'A' and degree level chemistry; the next two are 'fun' examples; and the final two were written for the Physics course of the Unify project, University of the North, South Africa.
The first 'exploratory' example allows pupils to explore the effect of changing concentrations and temperatures on both the position of chemical equilibrium and the equilibrium concentrations of the various reactants in the Haber process. It does this by calculating the entropy change in both the system and surroundings at any given extent of reaction - and hence the total entropy change and the position of equilibrium. The calculations involved are both difficult to understand and very tedious to do, yet the chemical ideas illustrated are both very important and often misunderstood.
This spreadsheet uses a command macro to run a simple Monte-Carlo simulation of the chemical reaction between 'a' and 'b'. The user sets the initial amounts of a and b together with the probabilities of a molecule of a changing to b and of b changing to a. The system then selects molecules at random and 'throws a dice' to decide whether they should change or not. Over time, the ratio a/b moves to be the same as that of the two probabilities - irrespective of the initial amounts of a and b present.
This example calculates the pH change as a strong acid is titrated against a strong base. Interestingly, although this is a very simple reaction, the mathematics involved in calculating [H+] is quite complicated and involves solving a quadratic equation for [H+] with complicated terms. If you wish to try working this equation out for yourself, the 'long' version of the worksheet gives the terms for a, b and c in the quadratic equation.
This example uses a function macro to calculate the pH of a solution as a weak base is added to a weak acid. (Load the macro before the 'Display worksheet.) The programme is general - the user selects all the values for the 'Initial Data' box. In this case, as there are three competing equilibria in the solution, calculating the concentration of Hydrogen ions involves solving a quartic equation - and quartic equations have no analytic solution. The function macro solves the equation using the Newton-Raphson iterative method. This would be beyond the capabilities (and inclination) of virtually all 'A' level students yet this method allows them to compare the results of a 'real' titration with that given by theory - and interesting and important concept.
This was used in the Salter's 'A' level to help pupils calculate energy changes in reactions. The idea was to get pupils to work out which was the 'best' fuel for various purposes and by automating the calculations involved, concentrate on the chemical ideas.
This has been used with younger (KS4) pupils to help them interpret the results of an experiment designed to calculate the formula of magnesium oxide.
This example has been used with 6th form pupils - but is really a 'fun' exercise designed to show how systems with feedback can move to chaotic (but deterministic) behaviour. It was used to illustrate the difference between 'exactness' and 'precision' - a distinction pupils often have trouble appreciating.
This was written as a 'fun' exercise to allow pupils to explore the general properties of Fibbonnacci sequences starting from any two numbers. Until I used it I had not realised that the ratio of successive numbers of any Fibbonnacci sequence quickly converges on the golden mean - I had never had the time to do the calculations.
This was written for the Physics course of the Unify project in South Africa and allows students first to calculate the ration r/i; then sin(r)/sin(i); and finally to compare their experimental results with the predictions of theory - without having to do lots of simple but tedious calculations.
Again, this was written for the Unify project to help make 'real' the astonishing differences between linear and exponential growth by allowing students to explore both forms.