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Learning Maths Outside the Classroom - The Royal Statistical Society in Treswell Wood


This page has been archived. The content was correct at the time of original publication, but is no longer updated.
Created on 28 April 2008 by ncetm_administrator
Updated on 21 October 2010 by ncetm_administrator

Natural EnvironmentNatural Environment
 

The Royal Statistical Society in Treswell Wood

Statistics is a practical subject about the real world. The aim of the project was to demonstrate statistics teaching through practical activity based on a real question, using the data handling cycle.  

In June 2007, a practical day was held for pupils from four Nottinghamshire schools along with education staff, volunteers from the Nottinghamshire Wildlife Trust and 2 members of the Royal Statistical Society (RSS). The following is a report from Chris du Feu, one of the RSS members involved in the day.

The full report can be found in Significance Vol 4(3), which is a journal published by the RSS - see http://www.rss.org.uk/main.asp?page=1712 for more details).  An online subscription or single article purchase is required to access this article:
Photographs used by kind permission of Dave Valentine.

Treswell Wood, is an ancient, coppiced woodland. Coppicing provides a variety of habitats with ample opportunity for very natural comparisons of the same species growing within very different, but adjacent, areas. We decided it would be interesting to compare plant growth in shady and sunny areas.  I visited all four schools in the two days before the event. At each school, I gave a brief illustrated talk about the wood itself, the nature of coppicing and the impact on the environment. At that point I posed the question and asked for children’s opinions.

Most considered leaves in the sunlight would be larger, a few suggested smaller, and a handful of very wise children said they did not know. The reasons given were varied and often perceptive - more light leads to more growth as growth depends on light; water in sunny areas will evaporate and so plants will not be able to grow so well; plants in sunny areas have more competition so suffer and grow less well; plants in sunny areas have more competition and so have to grow more strongly in order to survive; plants in shady areas do not grow as well because any water which falls is taken by the larger trees; plants in shady areas grow larger leaves as they need to gather all the sunlight they can.

There seems to be a general fear of using real data in teaching statistics - it is considered unclean, messy and fraught with problems. In fact, the natural world, when treated carefully will provide very robust data sets which will reveal underlying truths. The messiness that is so often feared can provide further insights into the world, into variation and into statistical processes.

We decided to make the data collection process relatively simple since these were quite young children. They were divided into groups, and given a hoop and a number. In each of the areas were numbered stakes – the pupils had to drop the hoop over the stake with their number and then find the largest 10 leaves within the hoop.  They were provided with some leaf to take measurements of the lengths. Click here to see leaf gauges.

The numbers on the gauges were the class mid-points and were the same as those written on the x-axis of the chart.  For the analysis we decided to use the leaves themselves as the building blocks of the distribution charts. The blank charts were pinned to softboard ready for pupils to pin their measured leaves onto the graph.

We were surprised by how rapidly the data collection took place. (Teachers who complain that data collection is too time-consuming for statistical coursework which forces children have to rely on ready-made, contrived, downloadable datasets, should know that our data collection was done almost as quickly as you can say ‘Mayfield School’.) 

Next, the data analysis. Each child took one leaf from their group's sampling bag with eyes closed. This introduced to them the idea of random sampling and ensured that most leaves in the goody bags could go back to school for follow-up work without the very largest leaves having been systematically pillaged. The children then pinned their selected leaves to the chart. It might be thought that the fact that leaves were of different sizes would distort the appearance of the chart. Certainly, smaller leaves had more white space around them. However, the benefits of using the leaves themselves are very great. They are much more tangible than a measurement which is then just represented by shading a black rectangle on the chart. Although I am a strong supporter of appropriate use of computer technology, I would suggest that for this type of situation, using physical models is often far more effective than the abstraction which happens when data are entered than magically turned into (often inappropriate) charts by the computer.

We need not have worried about real data. Look at the well-formed and clearly different distributions of leaf lengths. Use of these versatile display boards allowed comparisons of the distributions side-by-side or, as shown, one above the other. This was by far the most effective way of seeing the differences between the distributions. The conclusion was clear to the children. Children made other observations too - from the display it was clear that, in addition to any size variation, there was colour variation too. Leaves from shady areas were a much darker green (giving another question to address).

James then drew out the difference between what we knew from the statistics (that the leaves in shady areas were larger) and what we did not know (why there is this difference). Statistics has, so far, done part of the job. Suggestions were made about how to discover why there is difference - these included experiments, interrogation of experts or else published material in books or, probably more likely, electronic sources. (Yes, children of this age are very familiar with internet searches.)

This particular day required considerable advance preparation because it involved a number of schools and transport to the wood.  The logistics of doing something similar with a single class, particularly if there is a suitable wooded area near the school, would be considerably reduced.  The pupils gain insight into mathematics and statistics as an integral part of environmental issues, and we felt the experience they gained was very worthwhile.

Contact Details
Anne-Marie Edwards
Email - aedwards@nottswt.co.uk
Nottinghamshire Wildlife Trust
Goodbody’s Mill, Albert Road, Retford  Nottinghamshire DN22 6JD
(Tel. 01777 860 666)

The Royal Statistical Society runs an outreach programme in which a number of presenters will visit the school on a day and run activities that are designed to illuminate the use of statistics in a variety of contexts and at different levels of complexity.  The organisers work with schools to produce a programme at a level suited to the age and ability of their students from upper primary to sixth form.

Background information on the RSS education workshops can be found at http://www.rss.org.uk/main.asp?page=2205 or email d.hurcomb@rss.org.uk or j.r.nicholson@durham.ac.uk Tel. 020 7614 3934
 
 
     
 
 

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