Concerning move orders for the character 建 our teacher is adamant about starting with the left character, however Skritter does it the other way around. Which is correct?

stroke order for 建 is 聿 first and then 廴.

http://www.mdbg.net/chindict/chindict.php?page=worddict&wdrst=0&wdqb=%E5%BB%BA

Wenlin, MDBG, Nciku all have it the same way.

Stroke order is a funny thing. Even a few teachers at my school say that there are different ways that people learn to write characters (often ignoring proper stroke order). Generally speaking, they will argue that the most important thing is that a person writes a certain character the same every single time.

Thank you SkritterJake for confirming that for me. I should probably start ignoring my teacher when it comes to stroke orders since a few times now she has been "wrong" when comparing to other sources!

Hmm, is this a native teacher or a non-native teacher? A native teacher might have been taught a different standard or non-standard stroke order, and a non-native teacher might be making it up as she goes. Generally, if you have an element semi-enclosed in one of those radicals like in 建 or 道, the enclosed element is written first. If there is more to the character, such as in 挺 or 随, then common stroke order rules apply for the rest of the character, so in the two previous examples the left-side radical would come first, then the top-right element, then the semi-enclosure.

In my experience, learning proper stroke order can really make a difference. I look at 武's that I wrote before I learned how to write it properly and after and it's a huge difference - the proper proportion often comes naturally with the proper stroke order.

I see Chinese teachers writing characters in a non-standard stroke order all the time, I remember even a Chinese teacher of around 50 years old writing the first stroke of 口 last. But maybe her thoughts were somewhere else at that time.

But really, it happens a lot, just usually not on characters like 口 and 二, that's rare.