Discrete charm of the critical path
I am a non-specialist maths teacher in an 11 to 16 compre-hensive. I have been asked by a pupil who is thinking of taking A-level to explain what "decision and discrete maths" is. I am not sure I can answer this. Can you provide some examples that might be meaningful to my pupil?
Your pupil will know the difference between continuous and discrete data from GCSE. The "decision" part of A-level is about finding solutions to problems which involve sets of discrete objects.
Discrete maths is a field which has expanded greatly in the past 20 or 30 years due to the high-speed data processing available on computers. There is rarely one correct answer to a problem; it is usually a case of finding the solution which makes the most efficient use of resources.
Most decision and discrete courses cover the following topics: graph theory, networks, spanning trees, algorithms for minimum paths, critical path analysis, linear programming, network flows, optimisation. The names by themselves will probably not mean very much so it is best to give examples. For instance:
Graph theory. Given a number of towns connected by roads of various lengths, how do you find the shortest route which passes through all the towns?
Critical path analysis. When building a house, what are the earliest and latest times the builder can start certain tasks in order to finish by a given time?
Spanning trees. What routing of cables will use the minimum quantity of cabling when connecting a group of towns for a cable television network?
Optimisation. What is the maximum number of parts which a production line can produce, subject to certain constraints?
Linear programming. A fashion house might produce different styles of jeans. To maximise profit, they need to decide how many of each type they should make, given constraints such as availability of material, machinists and outlets and so on.
Problems such as these may sound simple but can become complex when the number of variables is large.
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In your column of September 26 on "Bonding games" you wrote about placing a Year 7 who had been diagnosed with dyslexia in the appropriate set. How do you spot a pupil who might have dyslexia, as opposed to just not being good at maths, when they are in a class of 30?
I spoke to Dr Steve Chinn, a specialist in maths and dyslexia, who explained that you need to look for disparities in performance, such as discrepancies in talking about a concept and then writing about it. Such pupils might have difficulty in learning number bonds and multiplication tables.
The following areas can be examined as a first stage to identifying dyslexia:
Recalling information at speed. This could be responding quickly to four-rules questions, taking longer on homework than the pupil should, difficulty recalling mathematical definitions.
Short-term memory problems. These might be identified in quick fire questions. They might avoid them, have difficulty remembering the question, or be very good at them compared with written maths. They might find two and three stage problems difficult.
Sequencing. There might be a difficulty in counting forwards or backwards in multiples or remembering the sequence in a particular algorithm.
Organisation. Their written work might be untidy. They might continually forget to bring equipment to the lesson or regularly forget homework.
Auditoryvisual perception. You might find they reverse numbers, for instance 51 instead of 15, or write in numbersletters that shouldn't be there. They might miscopy formulae. In solving equations they might write down a correct operation but on the next line carry out the inverse operation as a solution.
Having identified a pupil as possibly dyslexic, there are a number of further tests available. Information is available at these websites: www.dyslexia-archive.bangor.ac.uk a free test for primary www.dyslexiaa2z.comindex.html
Dr Chinn has written a book about dyslexia and maths, The Trouble with Maths, which will be published next February by RoutledgeFarmer.
Wendy Fortescue-Hubbard is a teacher and game inventor. She has been awarded a three-year fellowship by the National Endowment for Science, Technology and the Arts (NESTA) www.nesta.org.uk to spread maths to the masses. Email your questions to Mathagony Aunt at email@example.com Or write to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX