LEARN NC was a program of the University of North Carolina at Chapel Hill School of Education from 1997 – 2013. It provided lesson plans, professional development, and innovative web resources to support teachers, build community, and improve K-12 education in North Carolina. Learn NC is no longer supported by the School of Education – this is a historical archive of their website.

Now that we understand a little of what it takes to create visual representations of data, let’s look at the other end of the process. What are the skills necessary to “read” or interpret visual representations of data?

Understanding representations

First, a student reading a map has to understand the idea of representation. This seems obvious, but it isn’t a skill that children are born with. Toddlers learn only gradually that objects in a photograph, for example, are two-dimensional rather than three-dimensional.1 To find their seats on our classroom map, for example, students will have to understand that they’re looking for physical desks, not rectangles drawn on the floor with letters inside them. That’s not a problem (we’d hope) for high school kids, but it isn’t going to work for kindergartners.

Figure 5-1. Reading even something as simple as a seating chart requires an understanding of visual representation.

seating chart, lettered

Even some seven- and eight-year-olds have trouble understanding representation. In one study, children watched an adult add green dots to a map to represent hiding places, then watched another adult adding red dots to a map to make the paper more colorful. When asked which map would be more helpful in finding hidden toy fire trucks, young children typically picked the map with the red dots, because fire trucks are red. In reading geographic maps, children may think that a road drawn in red will be red in real life, or that a road colored blue is actually a river, or that a region shaded green has a lot of trees — or that the cow on a map indicates not a dairy-producing region but a single giant cow. 2

To some extent, children naturally come to understand representation as they grow older. But most students will, at some point, need deliberate instruction to understand the idea of representation. Fast-forward to eighth or ninth grade, when they’re struggling to learn algebra: Kids who have no trouble with basic arithmetic may fall to pieces when you start throwing x and y around, because they’re not prepared for that level of abstraction. But that, too, is a kind of representation.

Visual representation, too, can get awfully complicated. As the concepts we’re communicating and learning grow more complex, so do even our best efforts at simplifying those concepts. Worse, not every map is well-designed or well-explained. Probably we’ve all had the experience of staring at a graphic in a newspaper or magazine trying to figure out just what the heck is being represented. It’s not always our fault that we can’t figure it out, but it becomes our responsibility when we have to make decisions based on badly designed visual representations.

Spatial thinking

In order to read geographic maps, students also have to understand how space is represented — what Jean Piaget called Euclidean spatial concepts, the ability to conceptualize space through an abstract system like a coordinate grid. Those concepts are necessary to understand scale or to measure distance and angle.

Students must also have what Piaget called projective spatial concepts. They must, for example, be able to interpret the angle from which a map depicts the earth’s surface and “project” that to their own perspective. Most maps are drawn from overhead, but that’s rarely how we actually see the earth’s surface.

Even our classroom seating chart depicts the classroom from the perspective of a fly on the ceiling, whereas students will have to find their desks by walking on the floor. When I drew that chart, I didn’t label the front of the room, but you probably assumed the front — the teacher’s perspective — was at the bottom. (Why?)

Google Maps, interestingly, helps to bridge that gap, by combining traditional map views with street-level photography. For example, here’s a helpful view of the Raleigh Convention Center:

Figure 5-2. Google Maps combines birds-eye views with street-level views. (Pretty, isn’t it?)

View larger map

These abilities emerge in the early elementary years and continue developing through middle school and beyond — which means that teachers can’t take them for granted. Until children develop these abilities, they rely on topological spatial concepts.3 Topological characteristics are those that don’t change when a surface or space is distorted. If, for example, we twisted our classroom seating chart, like this:

Figure 5-3. Warping our seating chart into a horseshoe shape preserves topological characteristics but changes distance and direction.

seating chart warped into a horseshoe shape

…some desks appear to be farther apart than others, and Anastasia would no longer appear to be sitting “behind” Lerlene. Direction and distance have changed. But Candi’s desk is still next to Josepha’s.

“Next to” is a topological characteristic, and something that young children grasp more easily than other spatial concepts. As a result, they can see that two objects next to each other on a map would be next to each other in real life, even when they can’t determine how to get from one to the other or how big they are.