Te Kura has about 475 full time-equivalent staff. About half its students use it for subjects or curriculum adaptation which their own school does not provide.
Under reforms passed by the National Government, any registered school, tertiary provider such as a polytechnic or an approved private company will be able to apply to be a COOL, teaching students online from 2019.
Te Kura was chosen to become the first online learning provider no later than December 31, 2019, although the detail of how the organisations will operate and selection criteria is yet to be worked through.
COOLs are strongly opposed by education unions, and PPTA members working at Te Kura contacted the union's president, Jack Boyle, with concerns about its "commercial turn" and the number of overseas trips taken by senior management.
Boyle said a senior teacher was told to pay to attend a subject conference because there was no money allocated in the budget.
Information provided under the Official Information Act and obtained by the PPTA shows spending on 14 overseas trips totalled $148,000 in 2014, with 21 trips costing $195,000 in 2015, and 18 trips totalling $261,000 last year.
The total spend of $604,000 over three years drops to about $567,000 after reimbursements from organisations including Education NZ.
The 2016 spend covered a total of 57 staff on 18 different trips.
Chief executive Mike Hollings last year travelled to Sydney, Port of Spain, Washington DC, Hobart and Johannesburg, at a cost of almost $30,000 in flights and accommodation.
Te Kura board chairwoman Karen Sewell said the increase in overseas travel was directly linked to the school's move to provide distance education online.
The school had contracted offshore IT suppliers and staff had to travel to attend user conferences. Staff were also sent for professional development in "future-oriented" teaching and learning, given it was not available in New Zealand.
Professional learning and development was a priority, with $1.4m budgeted this year, including $341,000 for curriculum-based development.
"Still, not all staff members can attend PLD events because we need to share the opportunities and be strategic in our spending."
Sewell said Te Kura's spending on overseas travel was less than half a per cent of its annual budget of $54m.
Education Minister Chris Hipkins, when in Opposition, cited Treasury warnings COOLs could be used as a "parking space" for children who are at-risk of failing, and the changes were opposed by NZ First and the Greens.
Asked if there were plans to scrap COOLs and what changes could be made to Te Kura, a spokesman for Hipkins would only say he had asked the Ministry of Education for advice.
National's education spokeswoman Nikki Kaye said the intention behind COOLs was to offer students more subjects and opportunities, mostly through organisations that would supplement existing school education.
"Particularly if they are in isolated communities or their school doesn't have access to that particular subject. We see huge benefit in this.
"If they are going to get rid of COOLs then I think people deserve to know."