If you go down to the woods today ... you’re sure of a big statistical experience. You might run into Chris Du Feu giving 9-year-olds their first lesson in statistics. Tasks for the teacher? One, clear nettles; two, make sure that leaves will stay firmly stuck in place on the bar-chart…
What is the best age to start formal teaching of statistics? The Royal Statistical Society (RSS) has a well-established programme of statistics workshops for secondary schools. A team will descend for a day on a school and give some sort of statistical experience to pupils, usually of year 9 (13- and 14-year-olds) or older, and also provide training and support for the teachers. It has been the intention, for some time, to extend this programme to primary schools. (See also the RSS Schools Lecture (The Guy Lecture)).
On a rare sunny day in June, in a wood deep in rural Nottinghamshire, we held the first RSS workshop for primary schools. It differed in several ways from previous secondary workshops. The children were younger, for one thing: this was a class of nine-year-olds. The initiative for this pilot activity came from the RSS team rather than from schools; and it was to be held in the field—or, to be more accurate, in the wood— rather than at a school. Why? For three very good reasons.
For one thing, it would be more interesting for the children. It would be a different, enjoyable day for them, and anything they experienced would be likely to remain in their minds. Second, it would be more pleasant, memorable and stimulating for the teachers. The third reason, however, is far more important. Statistics is a practical subject about the real world. If you begin its teaching in a real, practical context you have a better chance of long-term success with the students.
On the day there were to be two of us from the RSS workshop team—I and James Nicholson, who coordinates the workshop programme. We invited pupils from four local schools and also asked education staff and volunteers from the Nottinghamshire Wildlife Trust (NWT) for assistance on the day. The event was advertised as a joint RSS–NWT activity—the location being Treswell Wood, one of the NWT’s reserves.
We know that 5- and 6-year-olds can understand frequency data in two-way tables.
The aim of the day was to demonstrate statistics teaching through practical activity based on a real question. We also hoped to see how much young children are capable of understanding if material is handled in an appropriate manner. The activity was based around the data handling cycle that underlies the National Curriculum (NC). Happily, this cycle also underlies good statistical practice. Unhappily, with the test- and target-driven regime in schools, the good intentions of the NC are not always made manifest in statistics teaching in schools. In the data handling cycle a question is posed, a plan for addressing the question is devised, data are collected and analysed, and the original question answered. This will, in most cases, lead to further questions being asked. What is so controversial about that? Why is this not the pattern for all teaching of statistics in all schools instead of the endless sterile calculations of means of fictitious, contrived and utterly pointless data?
We needed a question which could be understood and addressed by 9-year-old pupils and which could be dealt with in one field session. We also wanted something that would be beyond the normal limits of what is demanded by the NC for pupils of that age. With practical work done in the past with 5- and 6-year-olds in one of the schools involved, we knew that they could interpret and understand frequency data in two-way tables. Comparing numeric frequency distributions was a natural next step. Typically, this will be done in schools only when children have had practice with calculating means, medians and modal classes and ranges of grouped frequency data. Some of these things are clearly beyond the ability of most 9-year-olds—so why not try anyway?
There seems to be a general fear of using real data in teaching statistics—it is considered unclean, messy and fraught with problems. Consider the alternative, though—fictitious data. It is a fundamental principle of logic that false assumptions cannot give well-founded conclusions. Any conclusions, therefore, drawn from fictitious data are ill founded. Is it any wonder that so many pupils view statistics as a waste of time? In fact, the natural world, when treated carefully, will provide very robust data sets that will reveal underlying truths. The messiness that is so often feared can provide further insights into the world, into variation and into statistical processes. Given the choice of the rich opportunities provided by real, natural world data or death by lack of motivation by contrived data sets, I think it wise to avoid the death option.
Our base for the day, Treswell Wood, is an ancient, coppiced woodland. Coppicing is a woodland management system that has been in use, in some places, since Neolithic times. Small areas of the wood are cut each year, on a rotational cycle which can be between 5 and 30 years in length. With coppiced woodland we have different areas with coppice regrowth of different ages—ranging from newly felled right through to deeply-shaded, mature woodland. This variety of habitats gives 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.
As we wanted to present a complete, well-prepared activity for the children, we selected a particular plant species, a method of assessing size, a sampling regime and a method of analysis. The plant species? Enter dog’s-mercury—a spectacularly unimpressive plant, even when it is in what passes for full bloom. However, it is an abundant ground cover plant in woodland and the leaves are distinctive. Its leaves remain green from late winter until late autumn, so we would not suffer problems of short or unpredictable flowering periods. With year-to-year differences in flowering time, it is not possible to predict far in advance whether particular flowers will be in bloom at any time, so it was the species’ long leafing period which would give a predictable subject for study. So, here was the question: do dog’s mercury leaves grow larger, the same size, or smaller in shady areas than they do in sunny areas?
Sampling was a major problem: how can you choose random samples of leaves from plants? (Answers on a postcard please.) We decided that it would be better to choose, deliberately, the largest leaves that could be seen—after all we were looking for largeness of leaf. We also decided to use leaf length as a measure of size. Some pupils of this age could have difficulty in measuring lengths with any degree of reliability so we prepared some leaf gauges (Figure 1). The numbers on the gauges were the class mid-points and were the same as those written on the x-axis of the chart. These blank charts, in best Blue Peter style, we also prepared earlier. The operation did, of course, involve some prior work to ensure chart and gauge covered the range of leaf sizes likely to be encountered. 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 on the basis that it is easier to see a picture than to describe it.
It is important to ensure children are well prepared, so 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. (The teachers did not know the answer either—although one was willing to wager 50p, but not £50, on leaves in shady areas being larger.) You might wish to consider your own response before reading on.
On the day, we marked sampling points—clumps of the plant—with stakes. Naturally, in the few days after my final check there had been rain and hot sunshine—the nettles, goosegrass and brambles had nearly smothered some clumps so some quick overgrowth clearance was needed. It is always well worth checking immediately before such events that nature has not changed the situation from what it was even a few days before. For sampling, children dropped a hoop over the stake and then selected the largest 10 leaves they could from within the sampling area delineated by the hoop. The process was repeated in the sunny area. 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 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 great. They are more tangible than a measurement which is simply represented by shading a black rectangle on a 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 that happens when data are entered, then magically turned into (often inappropriate) charts by the computer.
It is always worth checking before such events that nature has not changed the situation.
Our classroom was a clearing in the wood. The woodland floor provided seating. The only imported classroom props were two very old desks used as stands for the charts. Once the charts were constructed, James led the discussion of conclusions. We need not have worried about real data. Look at the well-formed and clearly different distributions of leaf lengths in the photograph below. 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. Our fi rst job done—children aged nine are quite capable of comparing numeric frequency distributions if they are dealt with in a real context. Children made other observations also—from the display it was clear that, in addition to size variation, there was colour variation also. 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 was our first primary-school workshop, our first in the open air. We were trying work beyond both the children’s experience and our own. There was plenty of opportunity for things to go wrong. In fact, my wife said she had never seen me so worried about anything ever before. It might have rained—analysis would have been possible in a small, open shelter but it would have been difficult. With the rain we had suffered beforehand and the local flooding shortly afterwards, we were remarkably fortunate to have had such a pleasant day. There were natural hazards in the wood. Nettles and brambles were cleared just before the children arrived. The insects behaved well with no irritating midges or mosquitoes. Only one hornet was seen (although these magnificent beasts are very docile compared with wasps, which were not in evidence at all). Success of the operation depended on familiarity with the particular wood itself. Even in a similar woodland, it would be difficult to do the same exercise without preliminary visits to find suitable places where the plants grow (if indeed they are present there at all). As it was, we had James to do the statistics, two NWT education officers and NWT volunteer Dave Valentine who provided technical assistance, particularly in the nettle location and eradication department. The NWT staff felt that the children had gained an insight into a small but real bit of woodland ecology, as well as a day among nature, which cannot be a bad thing. They hope to build on this event and to introduce similar things into their programme of educational activities. We of the statistical team felt that the children had gained a real and a realistic introduction to statistics. Will the children remember the day? Will they absorb the lesson? Will they have a more positive attitude towards statistics?
Overall then, it was a very successful event, albeit with much work and worry beforehand. Will we hold more workshops for primary schools? We certainly hope so.
Chris Du Feu formerly taught at Queen Elizabeth’s High School, Gainsborough. He now specialises in ornithological statistics.