Welcome to the 11th Carnival of Mathematics! 11 is a great number, because it consists of two 1s, and we have two firsts to brag about. First, mathematical readers will note that 11 is the first double-digit prime integer. Second, this is the first time that the Carnival of Mathematics has been hosted 3 times in a single month!
Speaking of 11, a good place to start is the 11th in a series of quotations over at Let's play math. This is a great quote about how students mistakenly see math, and how to solve the problem of how math is viewed.
Just what are the numerous ways to get students interested in math? Laurie at Trivium Pursuit has helped one teacher, who has had a great experience in delaying math.
Over at Math Notes, you can see how a mathematical magic trick was used to get a young girl interested in algebra.
If you haven't explored this site before, you may not realize that I'm a great proponent of making math fun and interesting. Here on Grey Matters, you can watch some amazing math videos, or lean how to perform some amazing feats yourself over in the Mental Gym section (I especially recommend Mental Shopper).
Once students understand that math is more than just disembodied numbers, they can better prepare for more advanced and abstract concepts. At Math Notations, we learn not only how to teach recursive sequences and function to grades 7-12, but how to use the Rule of Four to teach other mathematical concepts, as well. If you're no longer in school, don't think you're getting off easy, because there's a geometry challenge waiting for you at Math Notations, as well.
Mark at the Universe of Discourse uses the example of square and triangular numbers to show how learning from your mistakes can be valuable.
Speaking of learning from experience, JD2718 tries to find the right wording and image for a bonus question for a pre-calc exam and gets some great advice on the problem. As it turns out, few of the students even made it to that question, but provided interesting answers to another question. These last three posts are great lessons in not limiting yourself, and trying to solve problems by changing your point of view.
Even when math is completely abstracted from numbers, it can still provide fascinating and relevant lessons.
The Unapologetic Mathematician discusses categorification and its importance. It's quite interesting, not only because it uses abstraction from numbers, but also employs the abstract notion of the concept of numbers!
When Enigmania examines the notion of finite and infinite collections, leading into a discussing of the concept of potential infinity, and even takes it in new directions.
The 12th Carnival of Mathematics will be held on July 13th over at the Vedic Maths India blog. Send your submissions via the submission tool. Also, contact Alon if you wish to host the Carnival of Mathematics August 24th or later.