For years, I've been explaining the "Muslim World map" fallacy. Many maps first posit the existence of a "Muslim World" in their title, and show that world with a map shaded according to the percentage of Muslims in each country (often only in the eastern hemisphere). The concept of the Muslim World is itself problematic, since it implies a kind of uniformity of belief and practice across all Muslim populations. See an example here, at Wikipedia.

A map presented in this way shows a Muslim core in the Middle East, with, for the most part, less concentrated Muslim populations as you move further away from the region. Using only this kind of map, focused only on the percentage rather than the number of Muslims in a country, can unintentionally reinforce a common stereotype--that Arab = Middle East = Muslim. While the map shows one aspect of world Muslim populations, it does not show the diversity of Muslim societies around the world, or even accurately reflect where most of the world's Muslims live.

Until now, maps showing different perspectives on the world's Muslim populations were few and far between. However, a brand new Pew Forum demographic study of Muslim societies gives us some very interesting data and two very cool maps, which can constructively be used in comparison with the type of map above.

The first map shows the actual populations of Muslims in various countries by a graduated circle, with the largest circles marking the largest actual populations of Muslims, not the proportion. This map looks very different from the map above, with much more weight on south and southeast Asia and sub-Saharan Africa rather than primarily on the Middle East. This encourages us to think about the cultural diversity that underlies the religious practice and daily lives of Muslims in very different societies.

The second map is a cartogram, which allows even closer comparison of the numbers of Muslims in various societies (and prompts one to imagine a class exercise to develop a cartogram of other world religions).

The two most important take-aways from using these maps in the classroom are (1) the ethnic and cultural diversity of Muslim populations and (2) the concept that no map contains the whole truth about what it is mapping. The cartographers' choices of what data to highlight and what data to omit can create very different results.