At the beginning of the second semester I asked my calculus students to create a brigde map using the cover of their textbook as a reference. Bridge maps are used for analogies. I prompted them by asking them to think about why the publisher of the book chose the lighthouse and stormy sea picture for the book. I asked each student to create two bridge maps. For one of them, I gave them 2 parts: 1) lighthouse, 2) stormy sea. They had to come up with two analogous parts and the relating factor. For the second bridge map I asked them to come up with all of the parts, but it had be in the context of the book cover. The first student example to the right of the book cover above is read: A lighthouse illuminates stormy seas as calculus illuminates an otherwise challenging problem. The students enjoyed the challenge and it was a good way to discuss in very general terms what the purpose of calculus is. Some students were very poetic. Light only penetrates to certain depths of the ocean as calculus only penetrates to certain depths of creativity. However, I was hoping some students would express the purpose of calculus specifically as a way of thinking that involves lots of changing variables. Instead, most all of the bridge maps were about the utility of calculus for solving problems. The bridge map helped me learn that they view calculus as a problem solving tool but not really as a way of thinking that is worthwhile as a stand alone activity.
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