Spatial Literacy

The development of mathematical literacy hinges upon a spatial understanding of the three dimensional world. These photographs portray an aspect of math literacy, called spatial literacy, which revolves around the way humans see the world and in turn, the way humans represent this 3D world mathematically. Understanding mathematical concepts through representations (symbols, graphs, diagrams, maps, words, numbers, etc. ) is pivotal to math literacy.

One such representation, a map, displays a relationship between independent elements, or variables, and a dependent variable. Typically, the use of maps in math link a place (the independent variable) to a characteristic of that place. Thus maps are directly related to the study of functions. In conjunction with a scale, maps can be used to visualize our understanding of the scientific qualities of the Earth. The creation of the spherical globe is a perfect example of how humans have developed and used maps to understand and visualize our world more accurately. (Remember, humans used to believe that the Earth was flat!)

These photographs depict a particular type of map, called a contour map. Contour maps display a function of one or more variables at constant output values. The most common type of contour map is an elevation map, which displays the height of the land in relation to locations. However, many types of contour maps exist. The photograph above left is the most readable contour map, requiring the least amount of experience and background knowledge. Located in the University of St. Thomas' Geology department, this is the first printed geological map of Minnesota, showing the location of the various types of rock in the state. Upon reading the scale, the viewer understands that the colors correlate to the type of rock. She must simply look at the map to determine where these rocks exist in order to "read" the map. While most of us have seen contour maps depicting elevation, temperatures, weather patterns, or geological composition, our understanding of what these maps represent in our 3D world often times have not been developed. In other words, we may be able to "read" such maps, but do we truly understand what they represent and where they came from?

The photograph on the right might help to fine tune this understanding. Displayed is a computer screen with an incredible computer program entitled Mathematica. Just like the languages of math and french, for example, computer programs require a sophisticated and accurate use of language, requiring yet another system of translation between one concept or representation to another. This system of language enables students to visualize math concepts in a more concrete manner. For example, the top three images depict three different vantage points of a function of two variables, resulting in a ribbon-like graph. Imagine this function depicts elevation. What is the land doing here? Is it flat land? Or is it rolling hills? After making your conjecture, study the map just below these three images. Can you guess how this relates to the first three graphs?

As you may have guessed, the bottom graph shows a contour map of the original function, and the varying colors play a crucial role in reading this graph. While the contour map makes the land look flat, the colors indicate that the elevation indeed is changing. If an individual had never seen a contour map before, however, she might guess that the land indeed is flat. This shows how important being able to decode and read maps is in the development of spatial literacy, the ability to view the 3D world through various representations, and hence, in the development of math literacy.