I've been a big Dan Meyer fan for some time, and have always appreciated his real-world, participatory approach to learning. His recent post -- Literally Everything I Know About Modeling With Mathematics [SMP 4] --provides links to some of his most salient work in modeling, as well as a general summary of modeling in mathematics education.
Modeling asks students a) to take the world and turn it into mathematical structures, then b) to operate on those mathematical structures, and then c) to take the results of those operations and turn them back into the world. That entire cycle is some of the most challenging, exhilarating, democratic work your students will ever do in mathematics, requiring the best from all of your students, even the ones who dislike mathematics. If traditional textbooks have failed modeling in any one way, it’s that they perform the first and last acts for students, leaving only the most mathematical, most abstract act behind.
In his post, Dan links to one of my favorite modeling examples, Is the Checkout Line a Scam? (the answer is "yes," by the way). In it, he models several things that we can all do to bring the real world into our course design in order to make our content more relevant and the concepts we're teaching more meaningful.
- Use interesting examples from the real world -- A big part of fostering student engagement is presenting course content in relevant ways. The best and easiest way to do this is by using meaningful examples from the real world. This not only makes learning concepts relevant -- it also allows participants to make personal connections and applications.
- Get participants to think about possibilities and assumptions before the formal concept is introduced -- Contextualization of learning concepts is a critical part of student engagement. Participants want to know why these concepts matter. By sharing models from the real world, and by allowing participants to reflect on and discuss these models before ever introducing our formal learning concepts, we provide a foundation of purpose and interest for our lessons.
- Present concepts within the framework of a relevant example instead of sharing them in the abstract and then trying to link the real world to the concept at some later point -- When we lead with relevant, real-world models as opposed to formal concepts, we establish a narrative context for all subsequent information and discussions. It gives us an important anchor point for our explanations.