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2 Fixed the link

Let's say you choose 2. This is a sort of motivation-less course, naturally - all the things that will be proven, or at least many of them, are somewhat obvious to people who have lots of math experience, which the typical person to make it that far in the math curriculum will be (see David Bressoud's talks, of which that is one, for some fairly troubling statistics).

Okay, but you can turn that on its head. The reason such things are obvious (early in such a course, for instance, one usually proves that if $p|n^2$, then $p|n$) is because one has played with numbers a lot. So giving students something new in which to develop context and intuition is a great idea. Graph theory is a standard place to do this - proving easy things about colorings or connectivity - but one could introduce the groups $\mathbb{Z}_n$ or something with a little more structure than one initially thinks.

I saw a great talk where proving things about the decimal expansion of numbers was a big part of such a course. This can get into primitive roots, surds, etc., if you're ambitious - or just provide something a little off the beaten path.

Now, this doesn't look like an answer to your question, but it is. Namely, now that no one knows quite what the right answer is, the whole class can work together to make a proof that they all believe (and if they're wrong, you put it on the test). This isn't quite Moore method, but is of course influenced by it. Or you can make a journal for such things and give them feedback, or whatever you like. It's not the usual technique for teaching proof-writing, but is more realistic and can be easily complemented to the techniques you're currently studying (e.g., some graph theory stuff pretty much has to be proved by induction).

And something they've created from scratch is going to be much more effective in figuring out how to attack a proof. The key is that this will not be successful without doing it fairly consistently - not necessarily every day, but providing a consistent (perhaps weekly?) opportunity to do this.

1 [made Community Wiki]

Let's say you choose 2. This is a sort of motivation-less course, naturally - all the things that will be proven, or at least many of them, are somewhat obvious to people who have lots of math experience, which the typical person to make it that far in the math curriculum will be (see David Bressoud's talks, of which that is one, for some fairly troubling statistics).

Okay, but you can turn that on its head. The reason such things are obvious (early in such a course, for instance, one usually proves that if $p|n^2$, then $p|n$) is because one has played with numbers a lot. So giving students something new in which to develop context and intuition is a great idea. Graph theory is a standard place to do this - proving easy things about colorings or connectivity - but one could introduce the groups $\mathbb{Z}_n$ or something with a little more structure than one initially thinks.

I saw a great talk where proving things about the decimal expansion of numbers was a big part of such a course. This can get into primitive roots, surds, etc., if you're ambitious - or just provide something a little off the beaten path.

Now, this doesn't look like an answer to your question, but it is. Namely, now that no one knows quite what the right answer is, the whole class can work together to make a proof that they all believe (and if they're wrong, you put it on the test). This isn't quite Moore method, but is of course influenced by it. Or you can make a journal for such things and give them feedback, or whatever you like. It's not the usual technique for teaching proof-writing, but is more realistic and can be easily complemented to the techniques you're currently studying (e.g., some graph theory stuff pretty much has to be proved by induction).

And something they've created from scratch is going to be much more effective in figuring out how to attack a proof. The key is that this will not be successful without doing it fairly consistently - not necessarily every day, but providing a consistent (perhaps weekly?) opportunity to do this.