Diagrams: Breaking Free from Conventional Wisdom
Two very different representations of the Periodic Table, one a grid and one a spiral.
In my previous post, I discussed how a diagram—a graphic representation of a thing, a system, or a phenomenon—can help to capture existing knowledge, provoke questions that may lead to new knowledge, and support and structure the learning of students. I used maps as a rich, everyday example of how these things to think with can have a variety of benefits.
In this post, I discuss a more rarefied example: The Periodic Table. Don’t look away—you don’t have to be a chemist to get my point here. The same principles and questions I applied to maps can be applied to discipline-specific representations and diagrams, from the most common to the most esoteric. Consider the periodic table of the elements.
This staple of science education is so immediately familiar in its overall appearance that it has sparked many humorous imitations—the periodic table of vegetables, of wine, of sandwiches, of emotions, and so on. For students who learn how to use the Periodic Table, it helps them to remember many of the features of chemical elements. Grouping them into color-coded families imparts further information about their characteristics, and by organizing the elements into rows and columns, an otherwise-overwhelming complexity is reduced.
Like a map, the Periodic Table offers an opportunity to ask what is not represented. Russian chemist Dmitrii Mendeleev first described the Periodic Law and its associated table in 1869, noting that the properties of the elements repeat themselves with increasing atomic weights. Two years later, based on the gaps in the table he had created, Mendeleev correctly predicted the discovery of ten new elements. In the century and a half after, many more have been discovered, partly on the basis of gaps and absences in the table. Because of this, the Periodic Table has evolved over time, now showing far more elements, and elements of different kinds (the rare earth and transuranium elements, for example). The Periodic Table has provoked inquiry, and as research yielded results, the tool itself has evolved.
Although the Periodic Table shown in the illustration on the left is more or less the one every schoolchild is taught, there have been a proliferation of representations of the Periodic Table since Mendeleev’s first attempt. Author Edward Mazurs surveyed the cacophony of representations and, by grouping those that are essentially similar, came up with 146 different types. Many, like Mendeleev’s original, are in tabular form, but many others use spirals, concentric circles, or figure-eight type curves on which the various elements are arrayed. Writing in 1974, Mazurs deemed the helical structure shown on the right to be “the best table for presenting the Periodic Law in all its details.”
Distinguished psychologist of art Rudolf Arnheim advocated strongly for the use of multiple representations. “The usual illustrations in textbooks…help to make a problem visible, but they also freeze it…they tempt the student to mistake accidental circumstances for essential ones.” Showing students a variety of representations of the elements is a great way to prompt inquiry. What does one representation emphasize that others do not? Which representations are most useful and for what purposes? Did you learn something from an unusual representation that you didn’t learn from the standard tabular form of the Periodic Table? Are there omissions in any of the representations, and do they all omit the same things? Modeling phenomena with diagrams is important for students to learn because it is essential to the practice of science. It has the added advantage of making student thinking visible both to instructors and to fellow learners. With a variety of mental models at their disposal, students may become more flexible in their thinking about chemical phenomena, and may also come to see that any particular representation is not fixed for all time and can be challenged.