A fascinating subject!
We never learned cursive script - or heard the term. We learned Sűtterlin script, named for the man who created it as a simplification/revision of Old German.
http://en.wikipedia.org/wiki/sutterlin Just took a quick look back and, lo and behold, the link works.
You can see what the letters looked like. The books were printed in the same Gothic style. I did not like the long straight lines of the 's' and the 't' and the flourishes of the capital letters.
When Latin and English were added to the curriculum, we switched (we were switched!) to what was called "the Latin alphabet" (das lateinische Alphabet). I found it a great deal easier, the product looked cleaner and more fluid.
Later, when I took Russian, I had to master the cyrillic alphabet, which has a few 'extra' letters - e.g. for the sound of 'shch'. I admit it was quite a challenge and decidedly an experience. The class, small to begin with, dwindled to half a dozen. Five completed the course. The professor, who had written the textbook we were using, was an inspiration.
We too were graded on penmanship in high school, but also in orthography, with an emphasis on correct spelling - not only in German but in French and in English - as well as grammar. In that regard. nothing is more valuable of course than Latin, the mother of all languages.