Investigators in Florida have found that online education company K12 Inc. has employed teachers to teach subjects for which they lacked the proper certification.

K12 Inc., the nation’s largest online education company, is seeking to operate a full-time virtual charter school in Maine but has been rebuffed by state authorities.

The draft report by the Florida Department of Education’s inspector general, made public Tuesday, found evidence that the company had assigned at least three teachers in Seminole County to teach classes for which they lacked state-mandated qualifications during the 2010-11 school year. It also found the company had given Seminole County school administrators inaccurate student/teacher rosters, listing many teachers who’d had “no student interaction or student recognition” with pupils they supposedly had taught.

The report found no evidence that the company had employed uncertified teachers in the Seminole County school district, which had lodged the complaint leading to the investigation. Data provided by the company, it said, showed that all teachers employed in K12’s virtual school for the Orlando-area district were certified to teach in the state.

K12 and the school district each criticized the draft report in letters sent to the inspector general, who may still make changes before releasing the final report.

Seminole County Public Schools expressed concern that investigators had limited the investigation to the 2010-11 school year and to Seminole County.

“If a statewide provider was utilizing a certain staffing practice, it is reasonable to expect that evidence of that practice may be found in other counties where that provider operates,” the school board’s response asserts.

The board also disagreed with the conclusion that there was no evidence of uncertified teachers being used, naming three teachers as alleged examples to the contrary.

In its response, K12 said it accepted that its course records had not been maintained properly, but said investigators had based their findings about the use of teachers with improper subject certifications on “a handful of cases” in which “K12 was not able to unearth records, two years after the fact, to affirmatively disprove” the allegations.

“K12 remains perplexed as to why Seminole did not first raise these issues with K12, its vendor, before requesting an investigation that has been costly for Florida and K12,” the company wrote.

The company also released a statement saying it already had implemented record-keeping changes and “believes its instructional model in Florida is fully compliant with all state requirements.”

The Florida investigation unfolded after Seminole County Public Schools obtained internal K12 Inc. emails that suggested the company was using improperly qualified teachers.

In one email from February 2011, a K12 manager, Samantha Gilormini, asked certified teachers to file paperwork claiming they taught students with whom they might never have had contact. “So if you see your name next to a student that might not be yours it’s because you were qualified to teach that subject and we needed to put your name there,” Gilormini wrote.

One teacher, Amy Capelle, balked at signing the form and noted that only seven of the 112 students listed on her form were actually hers. She alleged that a supervisor later signed the form on her behalf and without her knowledge.

According to the inspector general’s report, several former K12 teachers told investigators they also had refused to endorse student roster forms that contained many students they never had taught.

K12 officials told investigators that their virtual school model “could make it difficult for a virtual teacher to remember if he/she taught a student.” In addition to the lack of face-to-face contact, students in art, music, and physical education courses do not have “teacher interaction in real time. Consequently, teachers may have difficulty remembering who they taught.”

Another official, K12 Florida Academic Administrator Gila Tuchman, admitted to signing Capelle’s elementary class roll and told investigators that elementary level teachers might not  “recognize all of the students because they were assigned to her on an as needed basis with little or no direct contact.”

Tuchman told investigators that because each student had a “homeroom teacher” (who may or may not be certified in a particular subject) and subject area instructors (who are), a given teacher might not have contact with a student they were teaching. “She said a student could go through a whole course independently, master and complete that course, with just the homeroom teacher monitoring the student’s progress and without seeking the assistance of the assigned subject area specialist,” the report said.

The draft report recommended that in future, the company “should distinguish between the homeroom students and the specialized subject area students for each teacher,” and the company was reminded that teaching duties “are not delegatable to a “homeroom teacher” or to the parent or to the student.

Taxpayers pay K12 $4,800 per student per semester to attend the Seminole County virtual school at issue in the case, according to the company. K12 was founded by convicted junk bond trader Michael Milken and former federal education secretary William J. Bennett.

K12 — which is also under scrutiny in Colorado, Georgia and Tennessee — has sought to manage a taxpayer-financed full-time virtual charter school in Maine, the Maine Virtual Academy; but the charter school commission rejected the bid earlier this year because of concerns about the degree of control the company would maintain.

Under Maine law, virtual schools have to be governed by local boards; but the school’s proposal gives the Herndon, Va.-based company broad management powers, including the authority to hire and fire administrators and teachers. The proposal also called for K12 to provide the academic content and the student assessment data on which the schools might be judged.

The Maine Virtual Academy board has said it intends to reapply.

K12 and rival Connections Learning of Baltimore were the subjects of a MaineToday Media investigation, published Sept. 2, which showed how the companies were shaping Maine’s digital education policies and that their schools in other states have fared poorly in studies of student achievement.