I cannot accept that mathematics be taught in a vacuum. Yes, mathematics is beautiful, be it pure or applied. However, in our age of immediacy for students we need to move more of our efforts to teaching mathematics in context, in touch with the real world. We should incorporate more modeling and applications in our mathematics courses to richly support and motivate our students in their attempts to learn mathematics and we should support colleagues who seek to use this approach.
Over the course of time I have moved to this position. At first I used applications of mathematics in course lectures, e.g., error correcting codes in algebra, cryptology in number theory, life sciences in calculus, and engineering in differential equations. Then I assigned students to read articles in other disciplines and share these applications in class. Finally, I incorporated projects in which students could see and practice the application of mathematics. Introducing a modeling scenario makes the mathematics immediate; what do I do right now? Students desire to address the problem at hand, which is real to them, primarily because it intrigues them and piques their curiosity. Thus the mathematics becomes a necessary tool they are ready to learn. I eventually used the application to motivate the learning of the mathematics before introducing that mathematics. This is a “flipping” of content.
Some students are a bit shy, even resistant, to this approach. However, in an active and supportive learning environment in which students work in small groups and the teacher works the room by watching, visiting, listening, and assisting the groups, students do amazing things. Sometimes they get off a workable track, but colleagues and teachers bring them along. Students make mistakes, but as we know, learning from mistakes is an important part of learning [BrownEtAl2014]. Indeed, we do it all the time ourselves and call it conjecture and research. Continue reading