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I believe that three key elements need to be in place for a super strong math project or lesson. Real World Authenticity, Mathematical Rigor and 21st Century Swagg. If there is a hearty balance of these three things in my experience that's when I bring the learning to the next level. A traditional classroom would fall into the Mathematical Rigor category, but lacks Real World Relevancy or 21st Century Swagg.
Having students design a car on a computer, without a solid math foundation (or for an appropriate grade level) is a prime example of Real World Authenticity absent Mathematical Rigor or 21st Century Swagg.
|21st Century Swagg Personified!|
A lack of 21st Century Swagg may be the product of using a blurry ditto from 1981. Presentation matters. The look of the assignment matters. Humor, if possible, matters. Student interest matters! I can't count how many problems I use from textbooks that start with "In 1991". Most of my students this year were born in 1998. While what happened in 1991 may be important, there are also important things that happened in 2011 that textbook companies just can't keep up with.
Of course there is not necessarily an Authentic Real World project for each math topic you teach. That doesn't mean it's impossible to make one. You just may need to up the dosage of Mathematical Rigor or 21st Century Swagg. My popular CSI projects are examples of this. With the engaging CSI puzzle solving framework (extra 21st Century Swagg) and Mathematical Rigor, a project for any topic is possible. Of course there are Authentic Real World problems in these puzzles, but perhaps nothing meaty enough to expand to a full-blown project.
I would argue you can't do without any of these ideas. Many might say you can cut out the 21st Century Swagg. Perhaps that's possible, but if student interest isn't there, student engagement may not be.
Real World Authenticity -- Mathematical Rigor -- 21st Century Swagg. Your might be your new bff. Or it might not be. Go make cool stuff for your kids!