I teach in a Catholic school where cursive is taught in Grade 2. I have taught Grades 1-6.
In Grade 3, start from the very beginning. Sometimes, you will get new students who did not have cursive in Grade 2. Students forget over the summer. Start from scratch. Students have difficult times with many of the connectives: br, os, mn, etc. 3rd graders are great in writing one syllable words. . .they need practice in writing longer words and sentences. Take your time with practice. Have them "picture frame" their best letters in each row of practice. Have them write in the air, on their "palm pilots" (on the palms of hands), on desktops to get the feel of the letters and their connectives. For practice papers, make models with orange markers to that the kids can trace them. At times, let them do their practice in marker. . .the markers pen glide easily over paper since cursive letters glide and flow together.
Zaner-Bloser handwriting research coupled with research by Richard Gentry (one of the top spelling researchers) states that students should not do spelling and dictation tests in cursive. . .work should be printed. If students write in cursive, their brains have to do two translations: one in how to spell the word and one in how to write the word in cursive. Many spelling mistakes are actually handwriting mistakes.
Please know that in Grade 3 many students have not truly mastered manuscript. Also do a lot of practice, modeling, guidance in mastering this.
Is it really necessary for students in Grade 3 to do a lot of work in cursive? When are times that they may choose? If you choose to have them do a lot of work in cursive, I would wait until at least 2nd semester with a gradual slide into it.
Something that I have found in my experience, too, is that many students have a very dificult time reading cursive. . .read any books written in cursive lately? When I write on the board, I write in manuscript no matter what the grade level. . .I do not want the information on the board to be misread or not read. When I write in cursive, I do so sparingly. Once in awhile, I will write a morning message in cursive.
Take your time with cursive. It will pay off.