displaying the categorized data graphically, and describing or comparing the categories. Because the process of describing or comparing categories usually involves number or measurement, number and measurement are central to data analysis, and data analysis provides a context to which number and measurement can be applied.
The collection of data should ideally start with a question of interest to children. For example, children in a class might be interested in how everyone got to school in the morning and might wonder what way was most popular. To answer this question, children might divide themselves into different groups according to how they got to school in the morning (by bus, by car, by walking, or by bike). The children could then make “real graphs” (graphs made of real objects) either by lining up in their categories or by each placing a small toy or token to represent a bus, a car, a pair of shoes, or a bike into predrawn squares, as shown on the left in Figure 2-13 (the predrawn squares ensure that each object occupies the same amount of space in the graph). Instead of a real graph, children could display the data somewhat more abstractly in a pictograph by lining up sticky notes in categories, as on the right in the figure. Each child places a sticky note in the category for how the child got to school.
In general, pictographs use small, identical pictures to represent data. In this case, each sticky note stands for a single piece of data and functions as a small picture in a pictograph. Children can then use these real graphs or pictographs to answer such questions as “How many children rode a bus to get to school today?” or “Did more children ride in a car or walk to school today?” or even “If it were raining today, how do you think the graph might be different?” Data displays that are used in posing and answering such quantitative questions serve a purpose and help children mathematize their daily experiences. In contrast, data displays that are only