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.