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"This theory says, "For math to be engaging, it needs to be real. The fake stuff isn't engaging. The real stuff is." This theory argues that the engagingness of the task is directly related to its realness. This is a limited, incomplete theory of engagement. There are loads of "real" tasks that students find boring. (You can find them in your textbook under the heading "Applications.") There are loads of "fake" tasks that students enjoy." I agree completely that there are plenty of REAL tasks that aren't engaging, but in my personal experience as a math student and as a teacher that occasionally creates math lessons, I find the most engaging problems are those that have a real application to my personal interests and life. Personally, I believe that if teachers present "real" tasks to the students that they are passionate about and have fun teaching, that rubs off on the students.

"There's a contest called Math-O-Vision, which your students should enter. Here's the premise: The Neukom Institute for Computational Science, at Dartmouth College, is offering prizes for high school students who create 4-minute movies that show the world of equations we live in. In 240 seconds, using animation, story-telling, humor, or anything you can think of, show us what you see: the patterns, the abstractions, the patterns within the abstractions." Two interesting things going on in this short blog post: 1. It introduces a contest which might be interesting for some of your students. I looked at the winning video from last year (linked in the post) and know that our students are capable of making something of similar quality. 2. The articles provides an interesting insight on math as a "product." This is quite an interesting discussion when thinking about how/why to assign this type of activity to your students.