I really appreciate Dan Meyer’s post on real world vs fake world and getting the MTBOS to help define what makes a problem “real world.” He put a call out to Mathalicious (specifically), which is a team of highly-skilled designers of “real world” math problems. Mathalicious states in a post concerning the purpose of two types of tasks problem solving tasks and application tasks:
While the purpose of problem solving tasks is to help students develop a deeper understanding of math, the purpose of application tasks is to use math to develop a deeper understanding of how the world works. It’s pretty Radiolab like that. [Link to Radiolab added.]
As math teachers, we need to be able to integrate both types of tasks into our courses. I am making an effort to use both by using Dan’s 3-Act tasks (which have a more problem-solving flavor) and Mathalicious.com (which have the ever-expanding real-world tasks). My battle is with how much time I devote to these types of tasks, which, as you can imagine, take a lot of class time. Mathalicious rightly states this toward the end of the post:
Instead of discussing which type of activity – procedural, conceptual, or applied – we should use, a more constructive conversation would be about how often and when. For instance, is it more effective to start a unit on linear functions with an open-ended problem (e.g. Dan’s Groceries), an application activity (e.g. our Domino Effect), or a procedural task (e.g. Khan Academy’s activity on slope-intercept form)? Also, within the unit, how much time should we allocate to each type of activity, i.e. how much time should we spend in each world?
I highly encourage everyone to read Dan’s original post (including the comments!) and Mathalicious’s reply.