Children's learning about the real world in projects usually involves both of the following two important processes: investigation and representation. Investigation involves formulating questions and finding out about something. Representation involves describing phenomena to oneself or communicating descriptions or ideas to others. As investigation and representation are undertaken young children involved in real world studies seem inevitably to be developing skills and concepts which are associated with several curriculum subjects at once.

Here is an example of the ways in which both investigation and representation were involved in the work of two children studying the disappearance of puddles in the school yard. The description is followed by an analysis of the learning opportunities provided by the teacher and the perspectives offered by different curriculum subjects.

Brief description of the investigation in progress

"It has rained earlier in the day. Two children are drawing chalk lines around puddles in the school yard and measuring the distance across the puddles in various directions. The puddles are drying up and at half hour intervals the children draw new chalk lines recording the evaporation rate of the water during the morning. They also draw the puddles' decreasing surfaces on paper so that they will be able to tell the other children about their work at the class meeting at the end of the morning." (Chard, 1992)

The importance of puddles

The fact that it had been raining earlier in the day gave the activity particular relevance for the children. When it rained it was much less pleasant for them to go to school. They had to dress for the wet weather and watch out for puddles on the pavement. When it rained it also meant that recess would not be outside in the school yard in the fresh air. The children may have to spend all day in their classroom. The children's current experience with puddles also included the fact that they disappear over time though they may not have known how this happened. For instance, they may or may not have asked someone how long it takes a puddle to dry up or ever been given any explanation as to how and where the water went. Even if a child had asked this question maybe the parent or other child may not have had time, or been able to give a satisfactory answer. In the school context, as teachers, we are well placed to help children pursue puzzling questions about everyday experience.

At this point a nagging question might enter the reader's mind: isn't school for more important things? Should parents not be worried to hear that their children are active in the school yard when learning math? How does the teacher account for why such everyday things as puddles would be a worthwhile focus of research for children? In the case described above the teacher reasoned that the children's interest in such a study would enable them to focus their energies on applying a variety of useful mathematical skills at the same time as developing their understanding of some very important scientific concepts. The children would be applying their current understanding of evaporation to the planning of the research, and looking for evidence to explain the phenomenon more fully.

Investigation

In the case described here the starting point for the inquiry arose from the children's wish to know if the puddles would be gone by recess time so that they would be able to go outside. The teacher encouraged the children to think about how they might predict the time it would take the puddles to go. They discussed possible explanations; do they `dry up' or `get sucked down' into the ground, for instance? The teacher and children talked about various ways they could learn more about how puddles disappear and about the factors which might be contributing to the rate at which this happens.

The practical investigation developing from the discussion about the disappearance of the puddles involved the children in considering the following concepts: change, process, cause and effect, the weather, evaporation and the water cycle. The investigation process required the children to apply the skills of tracing carefully, measuring, recording in written notes, making diagrams and using units of time and length. In the process of carrying out the work the children were involved in prediction, close observation, discussion, hypothesizing, reasoning, explaining and justifying their explanations of what they observed. The teacher had been able to check in with the students at various points during the activity to hear and discuss their findings with them. All the learning implicit in these processes was achieved through work for which the children were accountable to the teacher and to their fellow students. They had learned from previous project work of this kind that it was expected that they would explain how they carried out the study.

Representation

The accountability of students to share their work with the rest of the class involves them in processes of representation. The students researching evaporation in the school yard had first to represent to each other what they had been doing in order to give a clear account of their work to others. They had to be able to see the progression of their investigation. This progression started with the first questions they had asked about where and how the water disappears. It continued through the means of investigation they undertook, the observations and recording they did. Then finally the process culminated in the children's conclusions and the explanation of these to other children who had not been involved in the study.

Project work and systematic instruction

The kind of project work described here is only part of the curriculum for these children. It would almost certainly not be appropriate for children to learn all their mathematics in this way. Many skills are best acquired systematically under direction of the teacher. Teacher directed lessons in mathematics may take the form of a demonstration and explanation followed by instructions for the students to carry out some procedures for themselves to ensure that they can do them successfully unaided and that they understand how they work. The process of subtraction may require some children to work through a considerable number of practice examples before they become proficient at these kinds of calculation. However, once proficient the children can benefit from opportunities to appreciate what the process of subtraction can do for a person investigating a scientific phenomenon. For example, in the case of the evaporating puddles, the decreasing measures of the circumferences recorded at intervals can be expressed in terms of how much less distance around the puddles is observed with every half hour that passes during the course of the morning.

Whole class direct instruction is economical and likely to be the most frequent kind of math instruction children will experience in the elementary school. However, there is considerable advantage for the individual children involved and for the rest of the class to see how math skills can be applied in research of various kinds. We might also well ask what the other children were doing while two children were investigating the puddles. The teacher's description of the whole class of 24 children doing a project on `rain' also includes a group of six children working with the teacher on a science investigation to see which materials and fabrics let the water through and which are waterproof. In quantifying the permeability of the materials by water, the children were counting the number of drops of water which drip through in 15 seconds. They were also learning about the length of time that passes in a quarter of a minute. Elsewhere in this classroom three children were involved in dramatic play. They were playing in a store which had been set up for them to think about buying and selling things to do with protection from the rain such as boots, rain coats and umbrellas. One child was engaged in close observation of a toy cash register and identifying and counting coins. The other two were sorting items and grouping them together to make it easier for customers to find what they want. All of these children were involved in some form of math activity.

The other children were reading from books about the weather, water and plumbing, still others were writing or painting. Four were engaged in observational drawing of an umbrella. In the course of these other examples of project work there might also have been children who were counting or discussing time, quantity or measurement. Some activities they were engaged in involved investigation and others involved representation. Representation requires the children to use different kinds of descriptive languages. The many languages of learning include talk, drawing, painting, writing, math symbols, graphic organizers, dramatic play, work with clay or construction materials, and so on.

Representing an umbrella

Let us take the example of the close observation of the umbrella in the case described above. The children learned how an umbrella could be described in three different ways: through observational drawing, in language and mathematically. In their drawing some of the children shared what they had noticed through close observation, for instance, the point with a metal tip sticking up at the end of the dome shape of the fabric, the ribs curving down to the points at the edge of the dome, the stick emerging from the underside of the dome and finishing in a curve with a loop of cord attached through a hole in the handle. Other children wrote a detailed description describing what they could see from several different angles. The written description included information which was not featured in the drawing. For example a child might describe the function of the different parts of the umbrella. In other ways the drawn description may easily include details of shape, proportion and perspective which it might be more awkward to describe in writing.

Mathematical description offers yet more different ways to represent information. Mathematical representation is particularly concerned with accurate and precise detail. This kind of detail would be necessary if a person wanted to compare the umbrella with one they had at home or if they wanted to try to make an umbrella for themselves. The drawing may show the ribs of the dome of fabric from one side with the other side hidden. The written description may mention the ribs and how they are attached to the stick and how they move when the umbrella opens and closes. Only the mathematical description can offer precise quantities, for example the number of ribs, their length and the width of the dome shape at different distances from the tip. Then there are further representational languages which each would have their own purpose in the representation of an umbrella: design technology and physics, for instance by means of which a person could come to understand what is involved in improving the umbrella as a piece of household equipment or understanding how the folding mechanism worked.

Integrating subjects in the curriculum

When children can study different objects in relation to a topic of interest they can see the value of being fluent in the use of a number of different descriptive languages. If the academic subjects are only taught separately it may be that the descriptive power of each language is not so easily appreciated by the children. An umbrella is a good example of an object which offers alternative investigational and representational approaches. It is connected to a topic which is of concern in many communities: rain. Rain in its turn is a part of the water cycle, a weather phenomenon which is central to understanding the atmosphere on our planet earth.