The last entry talked about providing multiple illustrations of overriding themes within a subject. A closely related concept is providing views of the same or similar material, but when viewed through a different lens. In most cases the math, art, history and science curricula are developed in isolation. In reality there is significant overlap and meaningful interaction among these fields. Was Brunelleschi an artist, an architect, or an engineer? Was Leonardo da Vinci an artist or a scientist? Especially with da Vinci, how did these interests interact to produce a greater whole? In a more modern setting, Paul Graham's Hackers & Painters "points out that the similarities between hackers and painters are endless". James Burke's Connections has as a central theme of unexpected connections among technological advances, science, and economics. The Metropolitan Museum of Art even has a science department.
I have, for example, a strong memory of visiting the Fogg Museum at Harvard and seeing connections between studies and sketches to design patterns and iterative development development in computer software.
Remember that the recurring theme for this set of posts is making education more effective in the sense of making it more likely to be employed when encountering real world problems outside of the context of the classroom. Viewing material from multiple viewpoints is highly effective in this cause. Most directly, repetition is known to improve learning and recall of the subject matter. Presentation of material from multiple viewpoints and in multiple contexts increases both the ease with which it is incorporated into the student's existing knowledge base, and the depth of their understanding. It is important that the instruction emphasize that these are related presentations of the overarching theme. As always the students should be deeply involved in discussions about the relationships among the different contexts.
It is best if the repetition is separated in time. For example covering the development of the steam engine from an engineering perspective, then a couple of months later covering it from an economic perspective.
In addition to promoting both a deeper and broader understanding, this approach also strengthens motivation for understanding fields not obviously related to a student's central interests. A student interested in economics might ask why they should study physics. Now this style of teaching would show that economic concerns frequently set the tone for scientific progress, and that scientific progress frequently enables entire new economies. High speed communications enables corporations to be distributed over the entire planet, and brings many cultures closer together. Efficient transportation allows the distribution of manufacturing, and also the distribution of resources - especially in a time of crisis.