A lack of accurate data about the subjects teachers are qualified for is contributing to a shortage of maths and science teachers in New South Wales, a new report has found.

On Tuesday the NSW auditor general published a review of the supply of secondary science, technology, engineering and maths – or Stem – teachers in the state.

It found the effectiveness of attempts to plug shortages in Stem teachers was being fundamentally limited by a lack of data about the demand for teachers, and also criticised “underperforming” scholarship programs.

About 40% of teachers in Stem-related disciplines are more than 50 years old, and both federal and state governments have sought to address what is seen as a looming shortage.

Last year former education minister Simon Birmingham suggested the government could possibly try to “influence” the number of teaching students considering specialising in maths and science subjects by tying it to enrolment funding.

But the auditor’s report found the effectiveness of measures in NSW was limited because the department was “not accurately tracking the supply and demand for secondary teachers by discipline due to incomplete data”.

According to the auditor’s report, the education department does not collate data about the extent of “out-of-field teaching”, where teachers run classes outside of their area of expertise, meaning it does not have a full understanding of teacher demand.

“Monitoring the level of out-of-field teaching by permanent or temporary teachers would provide the department with a more reliable understanding of the disciplines and locations of current demand,” the report stated.

It also found that one-fifth of early career teachers reported teaching out-of-field for at least five hours per fortnight.

“Half of these teachers indicated that they do not receive any additional support from their school to teach out of their approved area,” it stated. “Research suggests that students taught by out-of-field teachers have lower levels of engagement, and this can compromise student learning outcomes.

“Several principals we interviewed voiced their concerns over the quality of teachers’ content knowledge when conducting classes outside of their discipline.”

After an internal review in 2017, the department developed a new program that “aims to understand the current, and forecast the future, supply and demand for teachers, by subject and location”.

However, the auditor found the new system still had limitations: for example, it assumed teachers conduct a full-time load in each subject they are approved to teach, meaning it overestimates teacher availability.

The report also found high dropout rates in scholarship programs designed to attract Stem teachers.

An internal department review from 2017 found scholarship programs “were not targeting workforce need, and that there were no key performance indicators to determine the overall effectiveness of these strategies”.

“In addition, the review found that only 79% of available scholarship placements are allocated each year, and 31% of scholarship recipients withdraw prior to completing their required service period,” the report stated.

Similarly, the success of the programs “was not being effectively monitored so it was difficult to assess if the programs are helping to address areas of shortage”.