What Does Cross-Curricular MEAN?Author(s): Michael HammondSource: Mathematics in School, Vol. 22, No. 2 (Mar., 1993), pp. 14-15Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30214975 .

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What does

Cross-cV

MEAN

Should data-handling be taught in a cross-curricular context?

What are the obstacles to co-operation between departments?

What can be done to improve cross-curricular links?

By Michael Hammond, Centre for Statistical Education, University of Sheffield

These are some of the issues which have been bothering me since I first started work on a cross-curricular project on data-handling.

My first idea on starting the project was to take the themes of the National Curriculum, i.e. Health, Citizenship, Economic Awareness, the Environment and Careers, and try to produce units around each one. Pupils will get the idea that they are studying, say, Health, and various individual subject attainment targets would be fulfilled as they worked through the unit. Such an approach has a lot to recommend it, artificial divisions between subjects would be broken down and pupils could see how individual skills could be used across the curriculum.

After getting feedback from trial schools I realised that this approach was not going to work. Even though these schools were specifically interested in exploring cross- curricular links, very few of them had opportunities for carying out cross curricular projects. Schools do not teach topics they teach subjects. With setting and option choices it is very unlikely that the same pupils who get together in, say, Mathematics will work together in Geography. The relationship is the reverse of what I had wanted; pupils are expected to do Economic Awareness in Mathematics, not Mathematics through Economic Awareness. (This being the case how useful is it to know that some parts of Mathematics deal with Economic Awareness? Perceptions change slowly. You could run a restaurant and serve up chips. You could call the chips "french fries" or "pommes frites" but if people think they are chips they are still chips. Likewise so many things would have to fit into place before pupils could give the new name, Economic Awareness, to the Mathemat- ics they are learning.)

I soon got the idea that cross-curricular work was going to be difficult and so I put the bulk of my energies into working with individual departments - mostly with teach- ers of science, geography, history and Mathematics. How- ever the idea of doing cross curricular work in Mathematics .still nagged at me.

Some schools, of course, do carry out wonderful cross curricular projects. This is made easier if pupils are taught in tutor groups for most of their timetable or else some special arrangement is made, e.g. taking the pupils of the regular timetable for a day or a week. In other cases strong co-operation between departments has enabled teachers carry out effective cross curricular projects. However what can the rest of us do without management support or willing collaborators?

Some teachers have got round the obstacles to cross- curricular co-operation in data-handling by contracting out

14 Mathematics in School, March 1993

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to different departments. For example, interrogating a data- base (Attainment targets 5.4) could be done in Geography rather than Mathematics and in return Mathematics teach- ers could do spreadsheets. In principle this sounds fine but the snags become apparent if we take the idea further. For example, they do quite a lot of adding up in Science could we contract out arithmetic too? Obviously not. So what makes it alright to contract out database work? What safe- guards need to be introduced? What level of co-operation is needed?

Meanwhile other teachers have suggested a cross- curricular approach in which pupils could collect data in, say, Science and interpret the data in Mathematics. Unfor- tunately this approach does not get round the timetable difficulties but even if it did, is this a proper division of roles? Why should collection of data seem less important in Mathematics than Science? How can the interaction between collecting data, and interpreting data be developed with such a rigid distinction between the two activities. After all pupils try to interpret data as they carry out an experiment and this helps inform them as to what additional data to collect.

I do not have any answers to the issues thrown up by cross curricular co-operation but I now find it useful to look for a cross curricular dimension within a single subject area. In Mathematics, any data-handling activity which uses real data is going to have this cross curricular dimen- sion as the data are generated in a real life context.

Real data are data generated by the pupils themselves, eg through a survey or an experiment, or else are taken from surveys carried out by other organisations eg a local weather station, the Government Statistical Office or MORI polls. It is not enough for the data to be authentic, pupils must perceive them as such. In one activity I asked pupils to interrogate a file which contained local weather records for all but the last day in the month of December. They were asked to write a weather forecast for the 31 December based on any trends they had observed over the previous days.

12 - 10

1u 8- aQ 6 000 a CL o

4-0 0 a00 0 E 0 gO ] a ) -2 - O o

E E -4 -

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0 10 20 30 Day

They were working with real data but their forecast showed that the data meant nothing to them.

good evening Sun might be 3 to 4 hours Wind might be 15knots Rain 5-6mm Min -7 degrees celsius Max 4-6 degrees celsius

We talked about this for some time and redrafted the forecast trying to relate their descriptions of the data with everyday language for describing the weather.

Good evening, tomorrow will probably be cloudy with some sunny spells. There could be a light breeze. There will be a very light drizzle. The lowest temperature will be below freezing, minus seven degrees celsius. It will be quite cold most of the day.

As soon as data are perceived as real, pupils are led into a cross curricular approach, Writing the weather forecast was as much about developing language skills, in particular using appropriate language for a target audience, as it was about developing data handling skills.

In another activity some Y7 pupils carried out a survey of their class attitudes to food. They had entered the results on a spreadsheet and produced various graphs of their results. They found that most boys were conscious of their weight and wanted to diet. However some of the girls were surprised about this as it contradicted their experience of seeing boys eat a lot of junk food in the playground Leila, a Y7 pupil, wrote:

We were surprised that so many boys wanted to diet but their favourite foods are junky. We think some boys are embarassed to eat fruit with friends, we also think that if a famous singer sang about healthy food, our diet would improve.

Leila was taking up the difficult notion of the validity of a survey through the cross curricular theme of health education.

In another activity pupils carried out an experiment to investigate the relationship between the speed a trolley went down a ramp and the height of the ramp.

As part of the experiment, they took readings of the time the trolley took to pass through a height gate. They entered the results on a spreadsheet and displayed a scatter graph.

1.10

- 1.00- oo S

0.90 D 0.80- E E

0.70

D 0.60- ca

S0.50 -

o ao

0.40- 0 0.30 I 1

5 10 15

Height of Ramp

This led them to ask questions such as: Are the results reliable? What would happen if the height kept on increasing? Is there a relationship between the weight of the trolley and the distance it travels?

The activity was about data-handling in Mathematics but the cross curricular links with Science were obvious.

Cross curricular themes inside a single department can only be developed so far. As a Maths teacher I would not want to develop the first activity by providing an expla- nation of what causes the weather to change; in the second activity I would not ask Leila to design health education posters and in the third activity I would not be able to offer even a lay person's view as to the causes of gravitational pull. However, when the cross curricular dimension is missing I find data handling work sterile and mechanical. When I reflect on the work I have seen in different departments over the last year I believe that in the best data handling activities pupils care about the language they use to describe data, they are curious about the data and they are asking themselves why and what if questions. These are cross curricular skills but they belong within each department.

Mathematics in School, March 1993 15

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