The research clearly supports invented spelling. However, the research doesn't support that teachers shouldn't teach how to spell correctly. In fact, the teacher's role is to move students from emerging literacy to conventional literacy. This should certainly be the case by second grade.

You'll have to take on this role since the teacher isn't. You don't want to correct your DD's work. Instead, ask her what words she's unsure of, help her to sound out and create approximate spellings, and teach her how to use a good children's dictionary to confirm her spelling or correct it.

These are two good articles. I teach writing at a university, so a pre-K specialist may be able to lead you to more current studies.

“Invention, Convention, and Intervention: Invented Spelling and the Teacher's Role” by Lawrence R. Sipe
Reading Teacher, 55:3, Nov. 2001: 264-73.

Abstract: Highlights the teacher's critical role in spelling instruction and provides examples of how to support spelling development in classrooms. Argues that educators need to look closely at children's emerging capacities as writers, focusing especially on the issue of invented spelling, and its use and misuse in classroom practices.


“Effects of Various Early Writing Practices on Reading and Spelling” by Laurence Rieben, Ladislas Ntamakiliro, Brana Gonthier, and Michel Fayol
Scientific Studies of Reading, 9:2, Apr 2005: 145-166

Abstract: The effects of different early word spelling practices on reading and spelling were studied in 145 five-year-old children. Three experimental treatments were designed to mimic different teaching activities by having children practice invented spelling (IS group), copied spelling (CS group), or invented spelling with feedback on correct orthography (ISFB group), whereas a control group only made drawings (D group). The main results indicate that (a) children in the ISFB group obtained significantly higher scores in the orthographic aspects of spelling and word reading than children in the IS and CS groups, (b) the superiority of the ISFB group did not extend to phonological aspects of reading and spelling, and (c) the performance of the IS and CS groups was not significantly better than that of the D group. These results suggest that neither invented spelling alone nor copied spelling alone is as effective as the practice of invented spelling combined with exposure to correct spelling.