I’ve already put up some magic tricks on MathPickle, but I’d like your input.  What place does magic have in the classroom?

Mathemagic is great.  Some teachers use it to increase their coolness factor, but the primary reason to use mathemagic should be to generate discussion and enliven the class.  In most cases the mathemagic should not be left as a mysterious hole, but should be broken by the students – perhaps with help. The debunking of mathemagic is similar to debunking a false proof.

…but the mathemagician is purposefully trying to hide her tracks…

Yes, but the debunking is the same whether the error is hidden on purpose or by oversight.

I know that you feel proof and problem solving cohabit the heart of mathematics education.  Does that mean that magic is there at the heart.

I would not go that far.  Magic is one way for a wrong proof to be presented to a class.  It is optional, but it can be a nice option!
Blog - Magic 1

As an example of setting up and then debunking mathemagic, I like your video of the 64 = 65 magic trick.  However, you don’t need to rush into a resolution with your class. 

Blog - magic2

There is nothing wrong with leaving students perplexed for a week and I can see that that is your intent with your first Tweedledee and Tweedledum video. 

The difference between the two is that the curricular material can be covered in the Tweedledee and Tweedledum grade 3 video without the students debunking the magic… whereas in the high school problem, the curricular material was only covered during the debunking.

I didn’t know the 64 = 65 mathemagic video was for high school.  It does fit well, but some of the students may already have seen it by that time.

One last question – is it ever appropriate not to debunk a mathemagical trick?

“Keeping students in the dark!” does not sound like a great teaching motto, but it might be defensible if the mathemagic leaves students in a state of WONDER.